Ricardo Daniel Costa Campos
Hexapod Locomotion:a Nonlinear Dynamical Systems Approach
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Universidade do MinhoEscola de Engenharia
Setembro de 2010
Tese de MestradoCiclo de Estudos Integrados Conducentes aoGrau de Mestre em Engenharia Electrónica Industrial e Computadores
Trabalho efectuado sob a orientação daProfessora Doutora Cristina Santos
Ricardo Daniel Costa Campos
Hexapod Locomotion:a Nonlinear Dynamical Systems Approach
Universidade do MinhoEscola de Engenharia
Abstract
Over recent years the technological progress has been growing interest in the study of
legged robots, taking a leading role in the development and improvement of these type of
machines. Walking machines have distinct advantages over wheeled robots, mainly, uneven
terrains navigation, capacity to overcome obstacles as well as better balance and stability
on unstructured or inclined terrains. However, the generation of robust locomotion on these
articulated robots, is still a difficult problem to solve, inparticular due to high number of
degrees of freedom that compose a legged robot and have to be controlled.
In this work we focus our research on hexapod machines using their inherent capacity of
walking in a wide variety of terrains which is one of their most important features. The aims
of this work are design and implement a bio-inspired controller architecture able to generate
a stable and robust locomotion in hexapod robots functionally divided in three layers.
The proposed architecture is able to generate different hexapodal gaits, switch between
the most common gaits and correct the posture of the robot in several different situations
where the robot balance is affected. Motor patterns are generated by coupled Central Pattern
Generators (CPGs), formulated as nonlinear oscillators. We proposed a CPG network that
enables the stable locomotion of the robot and switching between their different gaits. These
patterns are modulated by a drive signal, changing the oscillators frequency, amplitude and
the coupling parameters among the oscillators, proportionally to the drive signal strength.
Locomotion initiation, stopping and smooth gait switchingare achieved by changing the
drive signal. The velocity is changed accordingly and a natural hexapod locomotion is gen-
erated. In this contribution was also developed a posture controller for hexapod robots using
the dynamical systems approach.
Results were performed in simulation and a simulation modelof the Chiara hexapod
robot was developed. Results demonstrate the capability ofthe controller both to locomotion
generation and smooth gait transition. The postural controller is also tested in different
situations in which the hexapod robot is expected to maintain balance. The presented results
prove its reliability and robustness.
Keywords:Walking robot; locomotion; central pattern generator; dynamical systems; bio
control; mobile robots; nonlinear control systems; robot dynamics; robot programming.
i
Resumo
Nos ultimos anos o progresso tecnologico tem feito crescer o interesse no estudo de
robos com pernas, tendo um papel importante no desenvolvimento e na melhoria deste tipo
de maquinas. Maquinas com pernas tem vantagens distintas sobre os robos de rodas, prin-
cipalmente, navegacao em terrenos irregulares, capacidade de atravessar obstaculos, bem
como melhor equilıbrio e estabilidade em terrenos inclinados ou nao-estruturados. No en-
tanto, a geracao de locomocao robusta nestes robos articulados, e ainda um problema difıcil
de resolver, em particular devido ao elevado numero de graus de liberdade que compoem um
robo com pernas e que tem de ser controlados.
Neste trabalho focamos a nossa investigacao em maquinashexapodes usando a sua iner-
ente capacidade de andar numa ampla variedade de terrenos, aqual e uma das suas mais
importantes caracterısticas. Os objectivos deste trabalho sao projectar e implementar a ar-
quitectura para um controlador bio-inspirado capaz de gerar uma locomocao robusta e estavel
em robos hexapodes, funcionalmente dividida em tres camadas. A arquitectura proposta e
capaz de gerar diferentes tipos de movimentos dos hexapodes, transitar entre os seus tipos de
movimentos mais comuns e corrigir a postura do robo em varias situacoes diferentes onde
o equilıbrio do robo e afectado. Os padroes motores saogerados por Geradores de Padrao
Central (CPGs), formulados como osciladores nao-lineares. Propusemos uma rede CPG que
permite a locomocao estavel do robo e a transicao entre os seus diferentes movimentos. Estes
padroes sao modulados por um sinal modulatorio, alterando a frequencia, amplitude dos os-
ciladores e os parametros de acoplamento entre os osciladores, proporcionalmente ao valor
do sinal modulatorio. O iniciar, parar da locomocao e a transicao suave de movimento sao
alcancados mudando o sinal modulatorio. A velocidade e alterada em conformidade, e uma
locomocao natural do hexapode e gerada. Nesta contribuicao foi tambem desenvolvido um
controlador de postura para robos hexapodes usando uma abordagem de sistemas dinamicos.
Os resultados sao realizados em simulacao e foi desenvolvido um modelo de simulacao
do robo hexapode Chiara. Os resultados demonstram a capacidade do controlador tanto para
geracao de locomocao como para transicao suave de movimento. O controlador postural e
tambem testado em diferentes situacoes nas quais se espera que o robo hexapode mantenha
o equilıbrio. Os resultados apresentados provam a sua fiabilidade e robustez.
ii
Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Biological Hexapod Locomotion 6
2.1 Invertebrate Nervous Systems . . . . . . . . . . . . . . . . . . . . . .. . 7
2.1.1 The Central Nervous System . . . . . . . . . . . . . . . . . . . . . 9
2.2 Central Pattern Generators . . . . . . . . . . . . . . . . . . . . . . . .. . 13
2.2.1 Central Pattern Generators in Invertebrate Systems .. . . . . . . . 14
2.3 Proposed Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
2.3.1 Controller Requirements . . . . . . . . . . . . . . . . . . . . . . . 17
3 State of the Art 20
3.1 Legged Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Hexapod Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Control Models of Hexapod Locomotion . . . . . . . . . . . . . . . .. . . 40
3.3.1 Central Pattern Generation Approaches . . . . . . . . . . . .. . . 40
3.3.2 Finite State based Approaches . . . . . . . . . . . . . . . . . . . .43
3.3.3 Coordination based Approaches . . . . . . . . . . . . . . . . . . .43
3.4 Gait Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 Posture Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Development of Chiara Robot using Webots Simulator 49
4.1 Chiara Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
iii
iv CONTENTS
4.1.1 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.1.2 Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.1.3 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Shape Simplification using Solidworks . . . . . . . . . . . . . . .. . . . . 54
4.3 Webots Model of the Hexapod Robot . . . . . . . . . . . . . . . . . . . .. 55
4.3.1 Servo Node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.2 Physics Node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.3 TouchSensor Node . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5 Hexapod Locomotion Generation 63
5.1 Gait Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Locomotor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3 CPGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.4 Interlimb coordination . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75
5.5 Gait Generation Experiments . . . . . . . . . . . . . . . . . . . . . . .. . 76
5.5.1 Metachronal Gait . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.5.2 Ripple Gait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.5.3 Tripod Gait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6 Gait Transition 84
6.1 Gait Transition Mechanism . . . . . . . . . . . . . . . . . . . . . . . . .. 84
6.2 Initiating/stopping locomotion . . . . . . . . . . . . . . . . . . .. . . . . 84
6.3 Duty factor modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .85
6.4 Gait phases modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .85
6.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
7 Posture Control 94
7.1 Lateral Posture Control . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94
7.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
8 Conclusions 107
8.1 Results Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
List of Figures
2.1 Brain (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Ventral Nerve Cord (from [1]). . . . . . . . . . . . . . . . . . . . . . .. . 9
2.3 Commissure (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2.4 Intersegmental Connectives (from [1]). . . . . . . . . . . . . .. . . . . . . 10
2.5 Protocerebrum (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . .. 10
2.6 Deutocerebrum (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . .. 11
2.7 Tritocerebrum (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . .. . 11
2.8 Subesophageal Ganglion (from [1]). . . . . . . . . . . . . . . . . .. . . . 12
2.9 Circumesophageal Connectives (from [1]). . . . . . . . . . . .. . . . . . . 12
2.10 Thoracic Ganglia (from [1]). . . . . . . . . . . . . . . . . . . . . . .. . . 12
2.11 Abdominal Ganglia (from [1]). . . . . . . . . . . . . . . . . . . . . .. . . 13
2.12 Left: Functional division of the motor controller structures in the nervous
system of invertebrate. Right: Proposed locomotor controller architecture. . 16
3.1 Robot I (from [2]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Robot II (from [2]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Biobot (from [3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 Tarry I and Tarry II (from [4]). . . . . . . . . . . . . . . . . . . . . . .. . 24
3.5 Hamlet (from [5]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.6 RHex (from [6]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.7 Robot III (from [2]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.8 Lauron III (from [7]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.9 Genghis II (from [8]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.10 TUM Walking Machine (from [4]). . . . . . . . . . . . . . . . . . . . .. . 26
3.11 Gregor I (from [9]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
v
vi LIST OF FIGURES
3.12 Chiara (from [10]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
3.13 Lynxmotion (from [11]). . . . . . . . . . . . . . . . . . . . . . . . . . .. 28
3.14 Arthron (from [12]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28
3.15 HexCrawler (from [13]). . . . . . . . . . . . . . . . . . . . . . . . . . .. 28
3.16 a) BILL-Ant-p robot (from [14]). b) Acromyrmex versicolor (from [14]). . 29
3.17 a) Periplaneta americana (from [15]). b) Sprawlita (from [15]). . . . . . . . 30
3.18 Whegs. a) Whegs I (from [16]). b) Whegs II (from [16]). . .. . . . . . . . 30
3.19 LEMUR. a) LEMUR I (from [17]). b) LEMUR II (from [18]). . .. . . . . 31
3.20 ATHLETE ( 3.20(a) from [19], 3.20(b) from [20], 3.20(c)from [21]). . . . 31
3.21 AQUA Legged Underwater robot.a) AQUA with flexible fins underwater (from [22]).
b) AQUA with amphibious legs exiting the water (from [22]). .. . . . . . . 32
3.22 iRobots Ariel (from [22]). . . . . . . . . . . . . . . . . . . . . . . . .. . . 32
3.23 RiSE (from [23]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.24 COMET-IV (from [24]). . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.25 Walking Harvester (from [25]). . . . . . . . . . . . . . . . . . . . .. . . . 34
4.1 First Chiara prototype, built July 2008 (from [10]). . . .. . . . . . . . . . 50
4.2 Production Chiara Version (from [26]). . . . . . . . . . . . . . .. . . . . . 50
4.3 Chiara Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
4.4 Dynamixel AX-12 Servo ( 4.4(b) from [27]). . . . . . . . . . . . .. . . . 52
4.5 The two frames provided with Dynamixel AX-12 Servo. a) OF-12SH (from [27]).
b) OF-12S (from [27]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.6 Dynamixel AX-S1 Infrared Rangefinder ( 4.6(b) from [28]). . . . . . . . . 53
4.7 Chiara Solidworks Model. . . . . . . . . . . . . . . . . . . . . . . . . . .54
4.8 a) OF-12SH shape before simplification. b) OF-12SH shapeafter simplifi-
cation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.9 Webots diagram. a) Scene Tree. b) Webots operation. . . . .. . . . . . . . 56
4.10 Chiara Developed Model. a) Model of the Chiara robot rendered in Webots
platform. b) Chiara model rendered in Webots with his bounding objects
highlighted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.11 Developed model of the Chiara robot. a) Directions of rotation of each joint.
b) Chiara joints description. . . . . . . . . . . . . . . . . . . . . . . . . .. 58
4.12 Specification of the Servo node in Webots. . . . . . . . . . . . .. . . . . . 59
LIST OF FIGURES vii
4.13 Specification of the Physics node in Webots. . . . . . . . . . .. . . . . . . 61
4.14 Specification of the TouchSensor node in Webots. . . . . . .. . . . . . . . 62
5.1 Legs Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 Gait diagram depicting event sequences for three different hexapodal gaits.
White color indicates that the foot is in ground contact. a) Metachronal (low
- speed) Gait. b) Ripple (medium - speed) Gait. c) Tripod (fast - speed) Gait. 65
5.3 Relative phases for the most common hexapodal gaits. a) Metachronal gait.
b) Ripple gait. c) Tripod gait. . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.4 System’s overall architecture. The network of CPGs generate the motions of
locomotion for the coxa joints. The posture control mechanism generates the
necessary discrete movements on the femur and tibia, to correct the robot’s
body orientation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.5 a) Fixed point at (0, 0) withµ = −1, yi = 0, α = 0.5 andω = π . b) Oscil-
latory harmonic solution. The initial condition (xo,yo) = (0,−0.5), xi (solid
blue line) andzi (solid red line).The oscillator relaxes toxi = 0 andzi = 0. . 68
5.6 Solutions of the oscillator (4.2, 4.3). a) Limit-cycle with amplitude of 1,
µ = 1, yi = 0. The initial condition (xo,yo) = (0,−0.5), α = 0.5 andω = π .
b) Harmonic solution where thex variable is the solid blue line andz is the
solid red line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.7 Oscillatory solution with an amplitude of 2. . . . . . . . . . .. . . . . . . 70
5.8 Trajectory modulation through changes in theyi values (offset) when rhyth-
mic motion is turned off (µ < 0). The solid blue line is thexi solution and
the dashed red line isyi where the resultingxi trajectory converges asymp-
totically to the current value ofyi . . . . . . . . . . . . . . . . . . . . . . . 70
5.9 Trajectory modulation through changes in theyi values (offset) when rhyth-
mic motion is turned on (µ > 0). The solid blue line is thexi solution and
the dashed red line isyi where the resulting harmonicxi trajectory oscillates
around the offset (yi value). . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.10 Amplitude modulation of the generated trajectoriesxi andzi (top) by modi-
fying theµ parameter (bottom). Thexi variable is the solid blue line and the
zi is the solid red line (top figure). . . . . . . . . . . . . . . . . . . . . . . 71
viii LIST OF FIGURES
5.11 Frequency modulation of the generated trajectoriesxi andzi (top) by modi-
fying theω parameter (bottom). Thexi variable is the solid blue line andzi
is the solid red line (top figure). . . . . . . . . . . . . . . . . . . . . . . .. 72
5.12 Limit-cycle directions and resulting trajectories for ω > 0. a) Limit-cycle
with amplitude of 1 withω = 10. b) Generated trajectoriesxi andzi . Thexi
variable is the solid blue line and thezi is the solid red line. . . . . . . . . . 72
5.13 Limit-cycle directions and resulting trajectories for ω < 0. a) Limit-cycle
with amplitude of 1 withω = −10. b) Generated trajectoriesxi andzi . The
xi variable is the solid blue line and thezi is the solid red line. . . . . . . . . 73
5.14 Generated trajectoriesxi (solid blue line) andzi (solid red line). ForTsw= 0.3
and initialβ = 0.5, att = 4 s theβ value is changed to 0.9. . . . . . . . . . 74
5.15 Generated trajectoriesxi (solid blue line) andzi (solid red line) for different
signs ofω andβ = 0.8. a)xi andzi solutions forω < 0. b)xi andzi solutions
for ω > 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.16 Coupling Network to achieve interlimb coordination. .. . . . . . . . . . . 75
5.17 Top: Generated coxa jointsxi trajectories. Bottom: Recordedxi trajectories
from the servos. Solid blue line represents L1 trajectory, solid dark green is
R1 trajectory, solid red line is L2 trajectory, light blue represents R2 trajec-
tory, dashed purple is L3 trajectory and dashed light green is R3 trajectory.
The recordedxi trajectories are very closely to the generated onesxi . . . . . 77
5.18 Recordedxi trajectories from the servos (dashed line) and generated coxa
jointsxi trajectories (solid line) for metachronal gait. . . . . . . . . .. . . 78
5.19 Achieved footfall sequence for Metachronal gait. Below each feet sequence
are depicted the corresponding recordedxi trajectories from the coxa servos. 78
5.20 Top: Generated coxa jointsxi trajectories. Bottom: Recordedxi trajectories
from the servos. Solid blue line represents L1 trajectory, solid dark green is
R1 trajectory, solid red line is L2 trajectory, light blue represents R2 trajec-
tory, dashed purple is L3 trajectory and dashed light green is R3 trajectory.
The recordedxi trajectories are very closely to the generated onesxi . . . . . 79
5.21 Recordedxi trajectories from the servos (dashed line) and generated coxa
jointsxi trajectories (solid line) for ripple gait. . . . . . . . . . . . . . .. 80
LIST OF FIGURES ix
5.22 Achieved footfall sequence for Ripple gait. Below eachfeet sequence are
depicted the corresponding recordedxi trajectories from the coxa servos. . . 80
5.23 Top: Generated coxa jointsxi trajectories. Bottom: Recordedxi trajectories
from the servos. Solid blue line represents L1 trajectory, solid dark green is
R1 trajectory, solid red line is L2 trajectory, light blue represents R2 trajec-
tory, dashed purple is L3 trajectory and dashed light green is R3 trajectory.
The recordedxi trajectories are very closely to the generated onesxi . . . . . 81
5.24 Recordedxi trajectories from the servos (dashed line) and generated coxa
jointsxi trajectories (solid line) for tripod gait. . . . . . . . . . . . . . .. 82
5.25 Achieved footfall sequence for Tripod gait. Below eachfeet sequence are
depicted the corresponding recordedxi trajectories from the coxa servos. . . 83
6.1 Abrupt Transition. a) Top: Modulatory drive,m, is abruptly changed be-
tween the gaits transition. a) Bottom: Duty factor modulation. b) Recorded
xi trajectories from the servos betweent = 15sandt = 20swhere the robot
performs the metachronal gait. c) Recordedxi trajectories from the servos
betweent = 35 s andt = 40 s when the robot finishes the transition to rip-
ple gait. d) Recordedxi trajectories from the servos betweent = 55 s and
t = 60s when the robot finishes the transition to tripod gait. . . . . . .. . . 87
6.2 Gradual Transition. a) Top: Modulatory drive,m, is gradually changed be-
tween the gaits transition. a) Bottom: Duty factor modulation. b) Recorded
xi trajectories from the servos betweent = 15sandt = 20swhere the robot
performs the metachronal gait. c) Recordedxi trajectories from the servos
betweent = 40 s andt = 45 s when the robot finishes the transition to rip-
ple gait. d) Recordedxi trajectories from the servos betweent = 85 s and
t = 90swhen the robot finishes the transition to tripod gait. In thissituation
the robot takes more time to achieve the desired behaviors. .. . . . . . . . 88
x LIST OF FIGURES
6.3 a) Top: Modulatory drive,m, is abruptly changed to 2 att = 10 s when the
robot is performing the transition between tripod gait and ripple gait. From
t =30s, m, is gradually decreased in order to achieve the metachronalgait. a)
Bottom: Duty factor modulation. b) Recordedxi trajectories from the servos
betweent = 0 s andt = 5 s when the robot is in tripod gait. c) Recordedxi
trajectories from the servos betweent = 10 s andt = 15 s where the robot
is starting the transition to ripple gait. d) Recordedxi trajectories from the
servos betweent = 25 s andt = 30 s when the robot is in full ripple gait.
e) Recordedxi trajectories from the servos between 55s and 60s when the
robot is already performing the metachronal gait. . . . . . . . .. . . . . . 90
6.4 Feet Sequence betweent = 0 s and t = 5 s. L1, L2, L3, R1, R2 andR3
demonstrate the readings from the touch sensors from these legs. x1, x2,
x3, x4, x5 and x6 present the recorded trajectories from coxa servos for the
respective legs(L1,L2,L3,R1,R2 and R3). . . . . . . . . . . . . . . . . . 91
6.5 Feet Sequence betweent = 10 s andt = 15 s. L1, L2, L3, R1, R2 andR3
demonstrate the readings from the touch sensors from these legs. x1, x2,
x3, x4, x5 and x6 present the recorded trajectories from coxa servos for the
respective legs(L1,L2,L3,R1,R2 and R3). . . . . . . . . . . . . . . . . . 91
6.6 Feet Sequence betweent = 25 s andt = 30 s. L1, L2, L3, R1, R2 andR3
demonstrate the readings from the touch sensors from these legs. x1, x2,
x3, x4, x5 and x6 present the recorded trajectories from coxa servos for the
respective legs(L1,L2,L3,R1,R2 and R3). . . . . . . . . . . . . . . . . . 92
6.7 Feet Sequence betweent = 55 s andt = 60 s. L1, L2, L3, R1, R2 andR3
demonstrate the readings from the touch sensors from these legs. x1, x2,
x3, x4, x5 and x6 present the recorded trajectories from coxa servos for the
respective legs(L1,L2,L3,R1,R2 and R3). . . . . . . . . . . . . . . . . . 92
7.1 Lateral posture control. Process of stretch and fold thelegs. a) Robot stretch-
ing the right legs and folding the left legs. b) Normal position of the robot.
c) Robot stretching the left legs and folding the right legs.. . . . . . . . . 95
7.2 Functionf (φ). When−0.2 < φ > 0.2, f (φ) has the value zero and else-
where f (φ) has the value 0.8φ . . . . . . . . . . . . . . . . . . . . . . . . . 96
LIST OF FIGURES xi
7.3 Posture control scheme where only the used structure to one leg of the hexa-
pod is demonstrated since the procedure for the other legs isthe same. . . . 96
7.4 Posture control experiments: a) Lateral tiltφ of the robot (solid blue line) and
platform inclination (dashed red line). b)yFemur trajectories for the left front
leg (solid blue line) and right front leg (dashed red line). c) yTibia trajectories
for the left front leg (solid blue line) and right front leg (dashed red line). d)
yFemur trajectories for the left front leg (solid blue line) and right front leg
(dashed red line). e) ˙yTibia trajectories for the left front leg (solid blue line)
and right front leg (dashed red line). . . . . . . . . . . . . . . . . . . .. . 98
7.5 Robot behavior during the posture control in first experiment. a)t = 2 s.
b) t = 10 s. c)t = 12 s. d)t = 16 s. e)t = 20 s. f) t = 26 s. g)t = 28 s.
h) t = 30 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.6 Posture control experiments: Top figure: Lateral tiltφ of the robot (solid
blue line) and platform inclination (dashed red line); Middle figure: yFemur
trajectories for the left front leg (solid blue line) and right front leg (dashed
red line); Bottom figure: ˙yTibia trajectories for the left front leg (solid blue
line) and right front leg (dashed red line). . . . . . . . . . . . . . .. . . . 100
7.7 Posture control experiments: a) Lateral tiltφ of the robot (solid blue line) and
platform inclination (dashed red line). b)yFemur trajectories for the left front
leg (solid blue line) and right front leg (dashed red line). c) yTibia trajectories
for the left front leg (solid blue line) and right front leg (dashed red line). d)
yFemur trajectories for the left front leg (solid blue line) and right front leg
(dashed red line). e) ˙yTibia trajectories for the left front leg (solid blue line)
and right front leg (dashed red line). . . . . . . . . . . . . . . . . . . .. . 101
7.8 Robot behavior during the posture control in second experiment. a)t = 10 s.
b) t = 15 s. c)t = 20 s. d)t = 21 s. e)t = 21.5 s. f) t = 22 s. g)t = 24 s.
h) t = 27 s. i)t = 30 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
xii LIST OF FIGURES
7.9 Posture control experiments: a) Lateral tiltφ of the robot (solid blue line) and
platform inclination (dashed red line). b)yFemur trajectories for the left front
leg (solid blue line) and right front leg (dashed red line). c) yTibia trajectories
for the left front leg (solid blue line) and right front leg (dashed red line). d)
yFemur trajectories for the left front leg (solid blue line) and right front leg
(dashed red line). e) ˙yTibia trajectories for the left front leg (solid blue line)
and right front leg (dashed red line). . . . . . . . . . . . . . . . . . . .. . 104
7.10 Robot behavior during the posture control in third experiment. a)t = 10 s.
b) t = 15 s. c)t = 19 s. d)t = 20 s. e)t = 23 s. f) t = 26 s. g)t = 28 s.
h) t = 30 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.11 Posture control experiments: Top figure: Lateral tiltφ of the robot (solid
blue line) and platform inclination (dashed red line); Middle figure: yFemur
trajectories for the left front leg (solid blue line) and right front leg (dashed
red line); Bottom figure: ˙yTibia trajectories for the left front leg (solid blue
line) and right front leg (dashed red line). . . . . . . . . . . . . . .. . . . 106
List of Tables
3.1 Robots Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
3.2 Robots Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
4.1 Specification of Servos nodes parameters for Chiara simulation model. . . . 58
4.2 Specification of Servos nodes parameters for Chiara simulation model (Con-
tinuation). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 Specification of Physics nodes parameters for Chiara simulation model. . . 61
4.4 Specification of Physics nodes parameters for Chiara simulation model (Con-
tinuation). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.1 Relative Phases between oscillators. . . . . . . . . . . . . . . .. . . . . . 75
5.2 Parameter values used in the gait generation experiments. . . . . . . . . . . 76
5.3 Parameter values used in metachronal gait generation experiments. . . . . . 76
5.4 Parameter values used in ripple gait generation experiments. . . . . . . . . 79
5.5 Parameter values used in tripod gait generation experiments. . . . . . . . . 81
7.1 Parameter values used in the posture control experiments. . . . . . . . . . . 97
xiii
Chapter 1
Introduction
This report presents and describes in detail all the realized work in the study of hexapod
locomotion during about an year in the Adaptive System Behaviour Group of Industrial
Electronics Department at University of Minho in Portugal.The main goal of this work is
the development of a robust controller to the hexapod robot in order to reproduce the most
common hexapodal gaits based on biologically inspired robotic locomotion and dynamical
systems as a tool. In this work we propose a bio-inspired controller architecture to the hexa-
pod locomotion based on the concept of Central Pattern Generators that are rhythmogenic
regions located in the spinal cord of animals and on the functional architecture of the animal
motor control system. With this work is demonstrated that using the biological concepts and
the dynamical systems it is possible to implement the behaviors of the animals into robots.
1.1 Motivation
Many research groups have been studying approaches for the control of locomotion in hexapo-
dal walking robots. The motivation of this interest by the hexapodal platform is mainly due
to its physical nature extremely stable and also because thecapacity of walking in rough
terrains that is one of the most important features of hexapod insects. Additionally, since the
hexapod has redundant legs compared to other legged robots,it is possible for this sort of
walking machine to be able to continue operation in the eventof disabled limbs.
On uneven and rough terrains the walking robots have clear advantages over conventional
robots, using wheels or tracks, because these kinds of surfaces may be comprised by several
kinds of obstacles, holes, steps and ditches.
By the fact of the legged robots can select the points of the ground they tread, becomes
easier with this type of machine to avoid obstacles, holes and remains with a stable locomo-
1
2 CHAPTER 1. INTRODUCTION
tion on different kinds of surfaces. The articulation of their limbs also provides to the legged
robots a stable and smoother locomotion in uneven terrains as well as a faster adaptation to
irregularities.
However, the control of a walking machine locomotion is a difficult and complex task
mainly due to the high number of degrees of freedom (DOFs) that composes the robot. More-
over the controller of a legged robot must have the capacity to deal with constant changes
on body dynamics by lifting and placing the feet, and unpredictable dynamics during the
contact of a foot with the ground. This controller also must have the ability of adapt the leg
movements in order to support the robot body and not letting the robot fall.
1.2 Objectives
This work is a combination of different important concepts.The purpose of this work re-
quires an high use of dynamical systems theory, bio-inspired controllers and robotics. The
main goal of this work is, in a first step, start a detailed study of the type of existing hexapod
robots and the several models of bio-inspired controllers to reproduce their locomotion.
On this work we want to generate the most common hexapodal gaits and also smoothly
switch among these according to changes in the walking velocity to achieve stable locomo-
tion. The generated gaits are metachronal gait (”wave gait”) that specifies slow walking,
ripple gait corresponding to a medium speed gait and the fastspeed tripod gait.
In order to achieve smooth walking from low speed to high speed, robotic gait switching,
similarly to their biological counterparts [29], should take place continuously with both the
duty factor and the interlimb phase relationships properlyadjusted.
In this work we propose a bio-inspired closed-loop controller architecture, based on bi-
ological principles of the animals, with a particular focuson reproduce a stable locomotion,
that allow a gait changing through the control of a small set of parameters and allow a correct
posture control of the robot in several different situations as inclined surfaces in which the
hexapod robot is expected to maintain balance.
In this work we make use of the dynamical systems framework topropose a two-layer
architecture based in the invertebrate biological motor systems [29, 30].
The lower level generates movement patterns using networksof Central Pattern Genera-
tors (CPGs) modelled by nonlinear oscillators.
Interlimb coordination is achieved by coupling six CPGs in anetwork. This network
1.2. OBJECTIVES 3
must produce coordinated rhythms of motor activity, i.e. the correct pattern for locomotion.
These systems are solved using numerical integration and sent to the lower level PIDs of the
joints.
The second layer should model very basically the brainstem command centers for ini-
tiating, regulating and stopping CPGs activity and therefore initiate a walking gait, switch
among gaits and stop the locomotion. This layer should receive a modulatory signal that
regulates the CPGs activity. This signal strength is mappedonto different sets of the CPG
parameters, and hence result in the different motor behaviours.
A unique signal should be able to achieve interlimb coordination and control both the
velocity and the gait transition.
Furthermore, we also should include sensory feedback to correct the robot body orienta-
tion with respect to lateral inclination. The goal is to propose a lateral posture mechanism in
which the measured roll corrects the robot posture and adapts the generated locomotion on
inclined terrains by generating discrete trajectories forthe femur and tibia.
In order to fulfill the objectives mentioned above we need a robot. After making a com-
plete state of the art of the existing hexapod robots we should choose one of them and de-
velop a simulation prototype on Webots robotics platform. In this work all tests should be
performed in simulation environment using this robotics simulator.
So, to accomplish the purposes of this thesis the following main objectives should be
achieved:
• Prepare a proper state of the art of existing hexapod robots.
Choose a real robot to develop its prototype in the Webots simulator using the VRML
language.
• Design a six coupled CPGs network, formulated as nonlinear oscillators as a modular
generator for discrete and rhythmic primitives, that when superimposed result in complex
movements. These nonlinear oscillators generate smooth trajectories modulated by simple
parameters change. This CPG network should also coordinateall the movements of the joints
in a limb in order to generate the required limb movements. The use of the nonlinear oscilla-
tors allows a proper coordination between all members of therobot to reproduce the desired
patterns of movement.
4 CHAPTER 1. INTRODUCTION
•Develop a mechanism in order to achieve a smooth gait transition through a simple drive
signal. Locomotion initiation, stopping and smooth gait switching is achieved by changing
the drive signal. The velocity is changed accordingly and a natural hexapod locomotion is
generated.
• Propose a lateral posture mechanism in which the measured roll corrects the robot
posture and adapts the generated locomotion on inclined surfaces by generating discrete tra-
jectories for the femur and tibia. This method should include sensory feedback to correct the
robot body orientation with respect to lateral inclination.
1.3 Structure of the Thesis
This thesis is organized as follows:
In chapter 2 is presented a study of biologically inspired robots based mainly in the
nervous systems of invertebrate animals.
Chapter 3 provides a state of the art of existing hexapod robots describing their main
features and the different hexapod control models approaches.
The development of chosen hexapod robot using Webots Simulator is described in chap-
ter 4.
In chapter 5 is introduced the locomotion of the robot, describing the CPG coupling
network, CPG design and hexapodal gaits generation.
Chapter 6 explains the implemented mechanism of switch between the most common
hexapodal gaits using a simple modulatory drive to regulatethe activity of the CPGs signal.
In chapter 7 is demonstrated the lateral posture mechanism to compensate the robot lat-
eral tilt using a dynamical systems approach.
Finally, in chapter 8 are presented the most important conclusions, discussing the ob-
tained results and are suggested proposals for future work.
1.4. PUBLICATIONS 5
1.4 Publications
During the last year of work in CAR-ASBG group, was possible to publish two articles in
national and international conferences:
• ”Hexapod Locomotion: a Nonlinear Dynamical Systems Approach” , Ricardo Cam-
pos, Vitor Matos and Cristina Santos. Accepted in 36th Annual Conference of the IEEE
Industrial Electronics Society (IECON2010), Phoenix, USA.
• ”Gait Generation For a Simulated Hexapod Robot: a NonlinearDynamical Systems
Approach” , Ricardo Campos, Vitor Matos, Miguel Oliveira and Cristina Santos. Accepted
in 9th Portuguese Conference On Automatic Control (Controlo 2010), Coimbra, Portugal.
Chapter 2
Biological Hexapod Locomotion
Since few years, great interest has been directed to the study of biologically inspired robots [31].
This kind of robots include different degrees of biologicalinspiration and involves theories
like robotics, neuroscience or biology. Talk about biologically inspired robots, normally
refers to robotic animal models that are useful to a better exploration of biological behav-
iors [32].
Biologically inspired robots can be defined as the intersection of biology and robotics.
If we understand how a biological system works we may be able to develop something that
works the same way. Due the advances in neurobiology and technology has been a large
growth in the interest on the possibility of developing robots with the capabilities of ani-
mals [33].
The most common knowledge is that robots and animals are bothmoving, behaving
systems and both incorporate sensors, actuators as well as require an autonomous control
system that provides them the capacity of successfully carry out various tasks in a dynamic
world [34].
The intensive researches in ’biorobotics’ indicate that the study of autonomous robots
is analogous to the study of animal behavior and robots couldbe used as models of ani-
mals [35].
It is easy to verify that animals have the capacity of locomoting in several different kinds
of terrain and navigating in complex environments where thecurrent robots have many dif-
ficulties. Also, they have the ability of adapt the walking performance to environment con-
ditions, adjust the performed movements and correct the balance of their body.
The locomotor circuits in the nervous system of animals havebeen intensively studied in
order to verify their functional organization and crucial features.
6
2.1. INVERTEBRATE NERVOUS SYSTEMS 7
Abilities as stepping and adapting the movements of animalsmake the locomotor circuits
in the nervous system a fundamental subject of study of researchers on the field of legged
robotics.
For the aim of this work we take inspiration from nervous systems of animals hoping that
their motor control capacities improve the development of our controller. We do not want to
model the nervous systems of animals but understand how the nervous system works when
generating the locomotor movements, while interacting with sensory information.
Invertebrate neuroscience, in particular, is providing many neural ’circuit diagrams’ that
can be applied as sensorimotor controllers for robotics.
The main goal is to design a hexapod controller able to generate the locomotor move-
ments, integrating concepts of the structure organizationof invertebrate nervous system and
functions in order to increase flexibility, adaptability and performance of the walking robot.
Hexapod robot is one of the most typical robots, that is seen like a walking robot that
imitates limb structure and motion control of insects or arthropod animals and can walk in
unstructured terrain with a high probability of success [36].
Due to the existing redundant limb, hexapod robot could continue its movement even if
limb is lost.
These important advantages and others that will be evidenced in this work, make it reli-
able for some autonomous and high-reliability works, like field scouting, underwater search-
ing, space exploring, disaster areas, rigs, excavations, and much others important applica-
tions [37].
2.1 Invertebrate Nervous Systems
All animals without a backbone (spinal column) are considered invertebrates such as insects,
worms, jellyfish, spiders. Invertebrates are useful animals to several researches because their
nervous system has a similar operation process as that of vertebrates [38].
The nervous system is a network of specialized cells that control all body functions,
controlling all the organs and muscles, sending, receivingand processing nerve impulses
throughout the body.
An invertebrate nervous system is a network of cells, calledneurons, that function as an
”information highway” inside the body.
The nervous system has two main functions which are indispensable to maintain the life
8 CHAPTER 2. BIOLOGICAL HEXAPOD LOCOMOTION
of the organism. First, sensory receptors allow the organism to control its external environ-
ment and detect possible changes as an increase in temperature.
Then, the nervous system activates structures such as muscles and glands, allowing the
organism to respond properly to the environmental changes.Second, the nervous system
also provides the capacity to control the organism’s internal environment, monitoring heart
rate so that enough blood is delivered to organs, or measuring nutrient levels to alert if an
organism needs food.
All nervous systems have these basic abilities but their structure and complexity varies
greatly depending on the types of organisms.
In vertebrate systems, it is divided into the central nervous system (CNS), that is com-
posed by the brain and spinal cord, and the peripheral nervous system (PNS), which have the
nerves responsible for transporting information to and from the CNS.
On the other hand, invertebrate nervous systems may or may not have distinct periph-
eral and central regions. However, communication with and response to the environment
still occurs [39]. Usually invertebrate systems are much less complex than vertebrate ner-
vous systems which may contain a trillion neurons, that are primary cells types found in the
nervous system, and an invertebrate may have as few as 305 [39].
Overall, invertebrate nervous systems are less complex than the nervous systems found in
vertebrates, but there is still a certain complexity depending on the type of invertebrate. There
is a particular separation of peripheral and central nervous systems in invertebrate animals
such as insects and mollusks, like the squid. Usually, in theanimal’s midline there are neuron
cell bodies grouped into clusters called ganglia. A ganglion is a group of interconnected
neurons with the function of process sensory information orcontrol motor outputs.
The peripheral part of the nervous system is composed by the extensions of the cells
in these ganglia where some have function of transporting sensory information from the
environment to the ganglia, and others transport signals from the ganglia to obtain a response
such as movement.
This type of functional organization allows a segmentation, where each ganglion has the
capacity to respond to and control an individual segment of the body. In order to coordinate
the segments, these ganglia are linked to each other in a chainlike fashion by a nerve cord,
that is a bundle of neurons that runs the length of the animal [39]. Next is detailed explained
the Central Nervous System (CNS) of an invertebrate.
2.1. INVERTEBRATE NERVOUS SYSTEMS 9
2.1.1 The Central Nervous System
Invertebrate animals, specifically the insects which are addressed during this work, have a
relatively simple central nervous system consisting in a dorsal brain (Fig. 2.1) linked to a
ventral nerve cord (Fig. 2.2) that can be defined as paired segmental ganglia running along
the ventral midline of the thorax and abdomen [1].
Figure 2.1: Brain (from [1]).
Figure 2.2: Ventral Nerve Cord (from [1]).
Ganglia of each segment are connected to one another by a short medial nerve called
commissure (Fig. 2.3) and also linked by intersegmental connectives (Fig. 2.4) to ganglia in
adjacent body segments [1].
Normally, the central nervous system is rather ladder-likein appearance, where a ladder
is a vertical or inclined set of rungs or steps. In central nervous system the commissures can
be considered the rungs of the ladder and intersegmental connectives are the rails.
An invertebrate brain is a complex of six fused ganglia (three pairs) placed dorsally in-
side the head capsule. The invertebrate brain is divided into different parts (Protocerebrum,
Deutocerebrum and Tritocerebrum) where each controls a limited set of activities in the in-
10 CHAPTER 2. BIOLOGICAL HEXAPOD LOCOMOTION
Figure 2.3: Commissure (from [1]).
Figure 2.4: Intersegmental Connectives (from [1]).
vertebrate body [1].
In Protocerebrum (Fig. 2.5), the first pair of ganglia are largely related with vision, inner-
vating the compound eyes and ocelli.
Figure 2.5: Protocerebrum (from [1]).
The second pair of ganglia, Deutocerebrum (Fig. 2.6), are responsible for the monitor-
ing of sensory information collected by the antennae. The third pair of ganglia, Tritocere-
brum (Fig. 2.7), innervates the labrum (the labrum is a smallsclerite, that is a hardened
body part, articulated the lower margin of the insect’s ”face” , concealing some or most of
the mandibles) and integrate sensory information acquiredfrom proto- and deutocerebrums.
2.1. INVERTEBRATE NERVOUS SYSTEMS 11
They also connect the brain with the rest of the ventral nervecord and the stomodaeal ner-
vous system which has the function of control the internal organs. The commissure for the
Tritocerebrum is around the digestive system, allowing us to understand that these ganglia
were initially placed behind the mouth and migrated forward(around the esophagus) during
evolution [1].
Figure 2.6: Deutocerebrum (from [1]).
Figure 2.7: Tritocerebrum (from [1]).
Below the brain and esophagus is ventrally placed (in the head capsule) another set of
fused ganglia, jointly called the subesophageal ganglion (Fig. 2.8). This structure is com-
posed by neural elements from the three primitive body segments which merged with the
head to form mouthparts. In the most recent insects, the subesophageal ganglion has the
function of innervate not only mandibles, maxillae, and labium, but also the hypopharynx,
salivary glands, and neck muscles.
A pair of circumesophageal connectives (Fig. 2.9) is aroundthe the digestive system in
order to connect the brain and subesophageal complex together.
Three pairs of thoracic ganglia (Fig. 2.10), sometimes fused, are located in the thorax to
control locomotion by innervating the legs and wings, and associated with these ganglia are
12 CHAPTER 2. BIOLOGICAL HEXAPOD LOCOMOTION
Figure 2.8: Subesophageal Ganglion (from [1]).
Figure 2.9: Circumesophageal Connectives (from [1]).
also the thoracic muscles and sensory receptors.
Figure 2.10: Thoracic Ganglia (from [1]).
Similarly, abdominal ganglia (Fig. 2.11) has the function of control the movements of
abdominal muscles. In thorax and abdomen the spiracles are examined by a pair of lateral
nerves that arise from each segmental ganglion. A pair of terminal abdominal ganglia, nor-
mally fused in order to form an extensive caudal ganglion, innervates the anus, internal and
external genitalia as well as sensory receptors placed on the insect’s back end [1].
2.2. CENTRAL PATTERN GENERATORS 13
Figure 2.11: Abdominal Ganglia (from [1]).
2.2 Central Pattern Generators
The subject of controlling locomotion in robots has been largely studied where neuroscience
and robotics can successfully interact. The interaction between biology and robotics is very
important.
Central pattern generators (CPGs) are considered neural circuits able to produce coordi-
nated patterns of rhythmic output signals while receiving only simple input signals. Usually,
CPG models can be implemented using the paradigm of neural networks or systems of cou-
pled oscillators. In robotics, CPG models can be applied forcontrolling the locomotion of
articulated robots [40].
Robots are effective platforms that can be used as scientifictools to have a better under-
standing of the functioning of biological CPGs. There are several methods for designing and
developing CPGs able to control distinct modes of locomotion. The capacity to successfully
move in complex environments as irregular terrain is a distinct property of animals. It is a
crucial factor to their survival, i.e. to avoid predators, to found food, and to find mates for
reproduction.
This singular property of animals means that several aspects of animals morphologies
and central nervous systems have been defined by certain constraints related to locomotor
skills.
In the same way, providing adequate locomotor skills to robots have a lot of importance
in order to design and develop robots that can have the capacity to perform diverse tasks in
different types of environments.
This set of facts for biology and robotics has led to multipleinteresting interactions
14 CHAPTER 2. BIOLOGICAL HEXAPOD LOCOMOTION
between the two fields in one main goal, with robotics taking inspiration from biology in
morphology, modes of locomotion, and control mechanisms. Several robots functional or-
ganizations are widely inspired by animal morphologies andbehaviors, from snake robots,
quadruped robots, hexapod robots to humanoid robots.
Central pattern generators (CPGs) can be found in both invertebrate and vertebrate an-
imals. In the development of locomotor neural circuits found both in invertebrate and ver-
tebrate animals, CPGs are also fundamental building blocksdue their different important
properties such as distributed control, capacity to deal with redundancies, fast control loops,
and enabling modulation of locomotion using simple controlsignals. These distinct abilities,
when defined as mathematical models, make CPGs interesting building blocks for locomo-
tion controllers in robots. CPGs define many rhythmic behaviors both in invertebrate and
vertebrate animals [40].
CPGs can generate complex locomotor behaviors but also switch between very different
gaits while receiving only simple input signals [41].
Therefore, from a control point of view, CPGs have the capacity to implement some
type of internal models who have the knowledge of which command signals need to be
rhythmically produced to have a desired speed of locomotion.
In the different types of CPG models implemented in roboticsit is normally cited the
connectionist models ( [42]; [43]), vector maps ( [44]), andsystems of coupled oscillators
( [45]; [46]; [47]; [48]). Only, in exceptional circumstances spiking neural network models
have been applied ( [49]).
Concluding, CPG models have been used to control the locomotion of robots and are
increasingly applied in the robotics community. This issuewill be addressed in more detail
more later in this thesis.
2.2.1 Central Pattern Generators in Invertebrate Systems
As previously reviewed, Central Pattern Generators (CPGs)are neural circuits able to gener-
ate organized and repetitive motor patterns, such as feeding, locomotion and respiration.
Recent work on invertebrate CPGs ( [50]) has provided relevant data about how rhythmic
motor patterns are produced as well as the mechanism that is used to be controlled by higher-
order command and modulatory interneurons.
There has been a larger interest in CPGs, due the fact that outputs of these circuits are
2.2. CENTRAL PATTERN GENERATORS 15
easy to measure, and their functional structure important to animal functional organization
both in vertebrates and in invertebrates [51], [52].
Research on invertebrate CPGs with small numbers of easily identified neurons has used
several principles with relevant importance to the organization of CPGs and other circuits in
the brain.
Important rhythmic movements such as breathing, walking, swimming and feeding are
produced by CPGs. The most simple demonstration that motor patterns can be centrally
generated, using CPGs, without sensory input is the result of a great number of preparations
that generate fictive motor patterns when are extracted fromthe animal and studied invitro.
Fictive motor patterns are defined as the signals recorded from the ventral nerve cord during
certain preparations, which do not result in locomotor movements.
In the case of several invertebrate preparations, the relationship among these fictive motor
patterns and those generated by the animal’s behavior, leading to evidence that solutions
investigated invitro have a lot of relevance to the generation of behavior.
In the last years have seen an enormous set of new research on the development of CPGs
in vertebrates [53], [54] such as molecular methods, genetic manipulations, and the develop-
ment of more new invitro preparations leading researchers to conclude that identification of
CPG neurons in the vertebrate spinal cord and brainstem willbe a possible situation.
At the same time, has been a slow evolution on the developmentof CPGs in inverte-
brates and there is still relatively little knowledge aboutthe adult CPGs of the invertebrate
preparations.
It has been proposed that the CPG for each limb is composed by neural circuits, the
unit-CPG, where each unit controls one joint in a limb [55].
The organization and structure of the CPG is very important considering the required
flexibility when generating the different types of limb movements during locomotion. This
interlimb coordination of the generated motor patterns depends of the limb movements to
perform, because when walking forward the unit-CPGs can be coordinated in a way and for
walking backwards it may required different coordination in order to generate a different
activation pattern.
It is believed that the network of CPGs in invertebrate systems is along the ventral nerve
cord.
16 CHAPTER 2. BIOLOGICAL HEXAPOD LOCOMOTION
2.3 Proposed Architecture
The main aim of this project is develop a bio-inspired controller architecture for the au-
tonomous generation, modulation and planning of robust andcomplex motor behaviors for
legged robots in specific for hexapods. We explore an approach that uses dynamical systems
to implement the locomotor controller. Due to their intrinsic stability property, the dynami-
cal systems have often proven to ensure a robust control of the movements in time-varying
environments.
The architecture for this locomotor controller (fig. 2.12) is divided in three layers, func-
tionally similar to the motor control systems involved in goal-directed locomotion in inver-
tebrates.
Figure 2.12: Left: Functional division of the motor controller structures in the nervous system ofinvertebrate. Right: Proposed locomotor controller architecture.
In layer one of proposed architecture are generated the motor patterns of limbs by a
CPG network of six coupled nonlinear oscillators. It is demonstrated the role of ventral
nerve cord where are located the segmental ganglia (thoracic ganglia and abdominal ganglia)
responsible of limb movements. This layer provides the capacity of generate and coordinate
2.3. PROPOSED ARCHITECTURE 17
the movements on the limbs in order to achieve the locomotor movements, as well generating
movements for performing other tasks.
Assuming that any movement can be decomposed in simple discrete, goal-directed tra-
jectories, and rhythmic motor primitives, as oscillatory trajectories based on amplitude and
frequency, the movements can be generated in a modular fashion.
These assumptions allow us simplify the complexity associated to the design of dynam-
ical systems, respond quickly to stimuli, and an easy switching between behaviors, because
it turns a high dimensional trajectory generation problem into a simple selection between
pre-defined behaviors.
The second layer has as abilities mimics the functionalities of segmental ganglia (thoracic
ganglia and abdominal ganglia) in invertebrates and it is responsible for selecting a motor
program as well as sending the commands to the CPG network at the right time in order
to reproduce the limb movements. A set of parameters composea motor program and are
needed by the network to generate the trajectories in order to complete a task.
The third layer is responsible for planning normally by the specification and selection
between independent voluntary movements and behaviours. This layer addresses higher
regions of dorsal brain generating the needed commands for tasks such as locomotion initi-
ation, gait switch, speed change, steering and obstacle avoidance, reaching and environment
exploration.
The proposed CPG generates on-line trajectories in a modular way, coordinating all the
joints in a limb, allowing stepping in any direction.
A CPG network was designed in order to control the limbs of a legged robot, in our case
an hexapod, with the aim of achieve locomotion. The second layer has also a role of control
the CPG network for the motor programs of locomotion initiation and gait switching.
2.3.1 Controller Requirements
The design and development of locomotor controller should take into account certain re-
quirements in order to control a robotic platform. The controller should generate smooth
trajectories, in order to result in smooth movements. The controller also should be stable and
reliable to small perturbations, integrating the possibility of deal with deviations in results
and enabling feedback integration, making the locomotion more robust.
The aim is to develop a locomotor controller for an hexapod robot, inspired in the neural
18 CHAPTER 2. BIOLOGICAL HEXAPOD LOCOMOTION
systems of invertebrate animals, applying concepts of their functional organization. From an
extensive research in the understanding locomotor systemsof animals, we are prepared to
define several required features that must be included in thelocomotor controller in order to
achieve locomotion and obtain flexibility and adaptabilitywhich are intrinsic characteristics
of animals.
Summarizing, the desired locomotor controller should contain the following require-
ments:
• Hierarchically organization of neural circuits, one unit-CPG per joint;
• Self-contained rhythmic generation for each limb, the CPG;
• Independent control of swing and stance phase durations in order to achieve different
velocities;
• Coordination between the different joints of a limb in orderto correctly generate the
locomotor movements;
• Coordination between the limbs in order to achieve the desired hexapodal gaits;
• Motor patterns generated by CPGs should be modulated by a drive signal, changing the
oscillators frequency, amplitude and the coupling parameters among the oscillators, propor-
tionally to the drive signal strength;
• Locomotion initiation, stopping and smooth gait switchingshould be achieved by
changing the drive signal;
• Include a lateral posture mechanism in which the measured roll corrects the robot pos-
ture adapting the generated locomotion on inclined surfaces by generating discrete trajec-
tories for the femur and tibia. This method should include sensory feedback to correct the
robot body orientation to keep its balance in disturbance situations.
In the next chapter will be presented a complete state of the art about legged robots,
2.3. PROPOSED ARCHITECTURE 19
especially hexapod robots and their different control models. Also will be described some
important research in hexapodal gait transitions and hexapod posture controllers that are
themes with very importance in this work.
Chapter 3
State of the Art
In this chapter will be described de main features of legged robots enunciating the most
important advantages and disadvantages of this type of machines. Also, will be provided
a state of the art of existing hexapod robots describing their main characteristics and the
different hexapod control models approaches. In this part of the thesis will be also addressed
a state of the art of subjects as hexapodal gait transitions and hexapod posture controllers
that were used in this work.
3.1 Legged Robots
In this section will be presented and described the diversity of legged robots. In this per-
spective are enhanced the main features of locomotion systems for legged robots namely the
advantages and disadvantages.
Advantages of legged robots
As advantage the legged robots have greater mobility in natural surroundings, because these
vehicles can use insulated support for each foot, unlike traditional machines with wheels,
that need a continuous support surface. These vehicles havea distinct capacity to walk on
uneven terrain, using a mechanism of change the configuration of the legs in order to adapt
to surface irregularities, and therefore are inherently suited to locomotion on this kind of
terrain. The use of multiple DOFs in the joints of the legs provides machines with legs the
capacity of change their direction of motion without slipping. There is still the possibility of
vary the height to the ground by introducing a damping effectand decoupling between the
irregularities of the terrain and the body of the walking machine. These machines can move
”embraced” to the land that travel in situations of movement, for example, on the outside
20
3.1. LEGGED ROBOTS 21
of tubes, to increase their ability to balance ( [56]). Another recent important advantage is
the fault tolerance during locomotion where a failure in oneof the wheels, that compose
these type of machines, results in great loss of mobility, due the fact that all the wheels
should always be in contact with the ground during locomotion. However, walking ma-
chines can maintain the stability and keeping the movement with one or more legs damaged
( [57]; [58]; [59]; [60]; [61]; [62]).
It is important to note that the legs can be used not only for locomotion, but also with
the vehicle stationary, where the upper body can work while feet are fixed to the ground,
acting as a support base to help the movement of a manipulator( [63]; [64]) or a tool ( [65])
mounted on the body.
Alternatively, the legged robots, rather than having a handle on your body can use one or
more of their legs to manipulate objects such as various animals use them for tasks such as
hold, manipulate and transport objects.
Limitations of legged robots
Despite the above referenced aspects suggest that legged locomotion is advantageous com-
pared to wheeled vehicles it is important to note that these vehicles still suffer from severe
limitations such as: require a large number of actuators to move the legs with multiple DOFs,
low speeds, are difficult to build, require complex control algorithms, and have a high energy
consumption.
Application fields
Mobile robots are vehicles that can replace humans in order to avoid endangering the life of
any hazardous task or in areas in which humans can not easily access.
The legged robots can be used in exploration of remote locations and hostile environ-
ments such as volcanoes ( [66]), seabed ( [67]; [68]), in space or on planets ( [69]; [70];
[71]; [72]; [73]), in nuclear power stations or locations with high levels of radiation, in min-
eral exploration, in disaster areas, in search and rescue operations, in military operations.
Beyond this type of applications the vehicles with legs can also be used in a wide variety
of tasks such as: cutting and transporting trees in forests,in aid to humans in the transport of
cargo ( [74]; [75]), excavation and construction ( [76]), medical applications ( [77]) and as
an alternative to wheelchairs ( [78]; [79]), in services, especially in applications to support
22 CHAPTER 3. STATE OF THE ART
people in buildings ( [80]; [81]).
Today, such robots can be placed in homes to be used in severalsituations as service
robots ( [82]), entertainment ( [83]; [84]), accompanying,educational ( [85]) and other im-
portant tasks.
However it is not yet possible to say with certainty that these robots are an effective
alternative for locomotion to vehicles with wheels or caterpillar because of the many working
situations that must be solved.
3.2 Hexapod Robots
There are several kinds of hexapod robots with different number of degrees of freedom, joints
and articulations. The main aim and advantage of these machines has been locomotion over
rough, irregular terrain.
The hexapods have complex dynamic approaches due to their high number of legs and
articulations and due to the difficulty to coordinate the several degrees of freedom of the
robot.
Walking machines, especially hexapods, are a sort of robotswhich their motion can be
similar to insect movements. These robots successfully walk in unstructured terrain and may
serve as vehicles of scientific study to postulate or test hypotheses about animal locomo-
tion [86].
Several research groups have developed studies for the control of locomotion in hexapo-
dal walking robots. The main motivation to their interest isthat the hexapodal machine
has a physical nature extremely stable. Since the hexapod has redundant legs compared to
quadruped robots, it is theoretically possible to be able tocontinue operation in the event of
disabled limbs [35].
In natural terrains, legs performance is often superior to wheels mainly because they
avoid undesirable footholds and make discrete contacts where wheels must propel with con-
tinuous rolling contact [87].
The development of six-legged robots enables the generation of static stable gaits and
these kind of machines have the capacity to walk even if one ortwo limbs are lost. More-
over, hexapod legs are usually developed with 3 DOFs which allow them Omni-directional
walking [12].
An important feature of these robots is their capacity to perform tasks that could endanger
3.2. HEXAPOD ROBOTS 23
the life of a human. Actually most of them are only prototypes, but in the future these
machines will be used to explore a space, geological and archeological places on the earth,
or to help people in rescue actions [36].
Their application include distinct areas as mining, exploration, military, rescue, industrial
environments and recreation [5].
On one hand, legged robots, mainly hexapods, possess clear advantages over wheeled
robots like obstacle climbing capability and mechanical graceful degradation. Hexapod
robots are widely used in abrupt outdoor areas (forests, volcanoes, mountains, etc.) that are
the kind of environments where legged robots result advantageous with respect to wheeled
ones [8].
Summarizing, the biggest advantage of hexapod robots is their capacity of walking over
rough terrain where the wheeled locomotion is very complicated. Their main disadvantage
is the difficult control due the multiple DOFs.
Then are presented some models of hexapod robots and will be described their most
important features. Also will be described their mechanical characteristics and the research
groups that have used them. In order to facilitate understanding the description of each robot,
there are tables (Tables 3.1, 3.2 ,3.3 , 3.4 and 3.5) with the submission of its most important
features.
Figure 3.1 presents Robot I. This hexapod robot is used on thework of K.S.Espenschied
in [88] and was developed in Case Western Reserve Universityas Robot II and Robot III.
Figure 3.1: Robot I (from [2]).
Robot II (Fig. 3.2) is used by K.S.Espenschied et al. in [89],where they study the diffi-
culty of legged robots to walk on rough terrain.
24 CHAPTER 3. STATE OF THE ART
Figure 3.2: Robot II (from [2]).
Biobot (Fig. 3.3) is an hexapod robot based on the features ofan agile insect, used in [3].
This hexapod has a great speed and agility. Each leg of the robot has three segments, corre-
sponding to the three main segments of insect legs: coxa, femur, and tibia.
Figure 3.3: Biobot (from [3]).
Figure 3.4 presents Tarry I and Tarry II built by the Department of Engineering Mechanics
at the University of Duisberg [90]. Tarry II is similar to Tarry I, but more loosely based on
the stick insect.
Figure 3.4: Tarry I and Tarry II (from [4]).
Hamlet (Fig. 3.5) is an hexapod walker used by M.Fielding et al. in [5] and was con-
structed at the University of Canterbury, New Zealand. Its legs are all identical and each
have three revolute joints.
U.Saranli et al. use the RHex (Fig. 3.6) in [6]. RHex design consists of a rigid body
3.2. HEXAPOD ROBOTS 25
with six compliant legs, each one with a only degree of freedom. Thus, RHex has only six
actuators which each hip has one motor gives a mechanical simplicity to achieve reliable and
robust operation in real tasks.
Figure 3.5: Hamlet (from [5]).
Figure 3.6: RHex (from [6]).
In figure 3.7 we have the Robot III used in [91]. This robot has atotal of 24 degrees of
freedom, where each rear leg has three DOF, each middle leg four DOF and each front leg
five DOF. Its functional organization is based on the structure of cockroach and try to imitate
their behavior.
Figure 3.7: Robot III (from [2]).
Figure 3.8 shows the Lauron III hexapod robot. This robot is used in [7]. Lauron III is the
26 CHAPTER 3. STATE OF THE ART
result of about ten years of progressive improvement on the previous configurations, Lauron
I and II. Each leg of this hexapod model has three degrees of freedom where each foot has
three-axis force sensor, and each motor has a current sensorthat detect forces opposing to its
movement.
J.M.Porta and E.Celaya use the Genghis II (Fig. 3.9) hexapodrobot in [8]. The aim of
this project is possible without a map of the terrain and the controller can be used by robots
with low computational and sensing requirements. Genghis II has force sensors at each joint.
Figure 3.8: Lauron III (from [7]).
Figure 3.9: Genghis II (from [8]).
TUM Walking Machine (Fig. 3.10) began created by Dr. Friedrich Pfeiffer in 1991 [92].
This robot, like the others listed above, is based on the stick insect.
Figure 3.10: TUM Walking Machine (from [4]).
3.2. HEXAPOD ROBOTS 27
Gregor I (Fig. 3.11) is an hexapod robot used on the work of P.Arena and his group [9].
The main goal of this work is reproduce the cockroach’s extraordinary agility where the
locomotion control is based on the theory of the Central Pattern Generator.
Figure 3.11: Gregor I (from [9]).
Gregor I has a biological inspiration where each leg pair hasa unique design. Front
legs are used to provide enough flexibility to allow efficientobstacle approach and effective
postural control. Middle leg design is like front leg designand have to provide part of the
forward thrust. Rear legs are divided into two segments and the most important function of
rear legs is powerful thrust. The front leg pair and the middle leg pair have three Degrees of
Freedom (DOF) on each leg, and the rear leg pair has two Degrees of Freedom.
Chiara (Fig. 3.12) is one of the most recent hexapod robots. The first prototype was
developed at Carnegie Mellon University’s Tekkotsu lab in 2008 [93]. This robot has 3
DOFs in each leg except in the right front leg that is a specialleg and has 4 DOFs. Each leg
is about 30 cm long and the arm is about 35 cm long.
Figure 3.12: Chiara (from [10]).
Figure 3.13 presents Lynxmotion Hexapod Robot BH3-R that isan hexapod robot used
by J.Currie and his team in [11]. Their work describe the process to evolve an hexapod robot
walking gait within a simulated software environment. Eachof the six legs of Lynxmotion
has three Degrees of Freedom (DOF), represented as a pelvic joint, a hip joint, and a knee
28 CHAPTER 3. STATE OF THE ART
joint. This robot has a round body symmetry.
Figure 3.13: Lynxmotion (from [11]).
Figure 3.14 shows ARTHRON. This is an hexapod robot used in [12].
Figure 3.14: Arthron (from [12]).
In [13] they use an hexapod robot called HexCrawler (Fig. 3.15).
Figure 3.15: HexCrawler (from [13]).
Lewinger and his group [14] propose the new robot BILL-Ant-p(Fig. 3.16) that is power
3.2. HEXAPOD ROBOTS 29
and control autonomous, capable of navigating uneven terrain, manipulating objects within
the environment, very strong for its size and relatively inexpensive compared to other similar
robots. This robot is based on insects behavior and is composed by 3 DOFs on each leg with
six force-sensing feet, a 3-DOF neck and head, and actuated mandibles with force-sensing
pincers for a total of 28 degrees of freedom.
(a) (b)
Figure 3.16: a) BILL-Ant-p robot (from [14]). b) Acromyrmexversicolor (from [14]).
Based on the principles of animal locomotion Cham et al. [94]developed an hexapod
robot called Sprawlita (Fig. 3.17) following the basic principles of locomotion of cock-
roaches: self-stabilizing posture, different functions for the legs, passive visco-elastic struc-
ture, control by advance open-loop and integrated construction. This walking machine is
considered a biomimetic robot because is based on the biologically-inspired robotics princi-
ples.
The robot has six rotational liabilities DOFs corresponding to the link compliant hip of
the leg with the body of the robot. Moreover, each leg has another DOF, prismatic, driven by
a pneumatic cylinder.
Each of these legs can be rotated using a servomotor, which allows you to change your
direction and take actions such as braking and accelerating. Due to the use of these principles
in its construction, the robot has a strength unusual for robots of this size and are capable of
traveling on land regularly with a speed of six body lengths per second.
30 CHAPTER 3. STATE OF THE ART
(a) (b)
Figure 3.17: a) Periplaneta americana (from [15]). b) Sprawlita (from [15]).
A slightly different approach of the existing robots consists on the use of the concept
designed by ”Wheel−With−Legs”. Normally these robots have only an independent ro-
tational DOF and use principles of locomotion similar to thehexapod robot called RHex.
Despite their simplicity, these robots can walk, run, bend and so dynamically stable. One of
these kind of robots, called Whegs I (Fig. 3.18(a)) was presented by Quinn et al. in [95]. Its
six appendices, designed by Whegs, consist of three equallyspaced rays. The mechanisms
that make this robot allows you to move on different terrain types in a similar way to cock-
roach and according to the authors is faster than any other robot with legs of similar size and
can climb over larger obstacles.
In [16], is presented a posterior version of this robot, called Whegs II (Fig. 3.18(b)).
(a) (b)
Figure 3.18: Whegs. a) Whegs I (from [16]). b) Whegs II (from [16]).
Another important kind of hexapod robots are the machines used in spacial missions
because the assembly, inspection, and maintenance requirements of permanent installations
in space require robotic platforms that provide a high levelof operational flexibility relative
to the mass and volume of the robotic system. In figure 3.19 we have the two versions of the
LEMUR robot.
In [96] they use the LEMUR II robot.
3.2. HEXAPOD ROBOTS 31
(a) (b)
Figure 3.19: LEMUR. a) LEMUR I (from [17]). b) LEMUR II (from [18]).
In [20] the group study the motion of a large and highly mobilesix-legged lunar robot
called ATHLETE (Fig. 3.20), developed by the Jet PropulsionLaboratory. This robot has
the ability to roll rapidly on rotating wheels over flat smooth terrain and walk carefully on
fixed wheels over irregular and steep terrain.
This vehicle rolls on wheels in the majority of the situations, but can use the wheels as
feet to walk when necessary like in rough terrain.
Each ATHLETE has a payload capacity of 450 kilograms , with the capability of docking
multiple ATHLETE vehicles together to support larger loads.
ATHLETE is much larger than the most common robotic systems previously used and
has a diameter of around 4 m and a reach of around 6 m.
(a) (b) (c)
Figure 3.20: ATHLETE ( 3.20(a) from [19], 3.20(b) from [20],3.20(c) from [21]).
An interesting feature of the legged robots is the fact that they can move in several dis-
tinct kinds of terrains but already exist legged robots thatmove underwater that resemble
lobsters or crabs. Figure 3.21 presents AQUA that is one of the most famous legged under-
water vehicles. This robot was developed in [97] with funding from the Canadian Institute
for Robotics and Intelligent Systems (IRIS). AQUA is an amphibious hexapod robot with
six independently-controlled leg actuators and was specifically designed for amphibious lo-
32 CHAPTER 3. STATE OF THE ART
comotion.
(a) (b)
Figure 3.21: AQUA Legged Underwater robot.a) AQUA with flexible fins underwater (from [22]). b)AQUA with amphibious legs exiting the water (from [22]).
One of the most important features of this robot is the ability to switch from walking
to swimming gaits as it moves from a sand beach or surf-zone todeep water. The physical
structure of this hexapod is based on the popular hexapod robot called RHex.
The robot has the capacity of walk in rugged terrains, and with the use of amphibious
legs, it can also swim in water. In order to obtain these desired behaviors, several legs
have been designed for the appropriate terrain: semi-circle compliant legs for rugged terrain,
amphibious straight legs for beach and water, flippers for underwater swimming.
In figure 3.22 we have another hexapod underwater robot called iRobots Ariel.
Figure 3.22: iRobots Ariel (from [22]).
In figure 3.23 is presented a new concept of hexapod robot. This is an hexapod robot
called RiSE used in [23] that is able to climb on a variety of vertical surfaces as well as
demonstrates horizontal mobility.
3.2. HEXAPOD ROBOTS 33
Figure 3.23: RiSE (from [23]).
A new mechanism is applied in RiSE that uses compliant microspines on its feet to reli-
able attach to textured vertical surfaces, such as stucco, in order to carry the load of the robot
while it climbs.
In [24] the research group designed the COMET-IV robot (Fig.3.24). To realize a syn-
chronous control between virtual 3D animation and COMET-IVphysical on the real environ-
ment they propose the online 3D virtual reality technique. This research group has developed
a series of mine detection and clearance robots, like COMET-I, COMET-II, COMET-III [98].
In figure 3.25 is demonstrated the Walking Harvester hexapodrobot that has been devel-
oped by Plustech Oy Ltd. This vehicle has 3 DOFs on each leg with hydraulic drive, using
a diesel engine to power, and can reach a maximum speed of 1ms−1. This robot requires an
human operator to control the machine via a joystick and due to its enormous applicability
this robot has been honored with several awards.
Figure 3.24: COMET-IV (from [24]).
34 CHAPTER 3. STATE OF THE ART
(a)
Figure 3.25: Walking Harvester (from [25]).
Robot Name Physical StructureWeight (Kg) Length (cm) Width (cm) Height (cm) Number of Legs
Robot I 1 50 30 − 6Robot II 1 50 25 50 6Biobot 11 58 14 23 6Tarry I 2.2 40 15 30 6Tarry II 2.9 50 20 40 6Hamlet 13 − − 40 6RHex 7 53 20 15 6
Robot III 13.61 76.2 − − 6Lauron I 12 80 30 70 6Lauron II 16 70 30 70 6Lauron III 18 50 30 80 6Genghis II 1 40 15 − 6
TUM 23 80 40 100 6Gregor I 1.2 30 9 4 6Chiara − 30 10 40 6
Lynxmotion BH3-R 4.6 − − − 6Arthron 2.3 − 54.8 9.8 6
HexCrawler 1.8 50.8 40.64 12.45 6BILL-Ant-p 2.85 47 33 16 6Sprawlita − 16 − − 6Whegs I − − − − 6Whegs II − − − − 6LEMUR I − − − − 6LEMUR II 9 − − − 6ATHLETE − − − − 6
AQUA 18 66 21 13 6iRobots Ariel − − − − 6
RiSE 2.8 41 − − 6COMET-IV 2000 250 330 280 6
Walking Harvester − − − − 6
Table 3.1: Robots Description.
3.2. HEXAPOD ROBOTS 35
Robot Name Mechanical Features (DOFs)Total Per Leg Achieved Velocity (m/s)
Robot I 12 2 0.14Robot II 18 3 0.14Biobot 18 3 −Tarry I 18 3 0.15Tarry II 18 3 0.20Hamlet 18 3 0.1RHex 6 1 0.55
Robot III 24 − −Lauron I 18 3 1.0Lauron II 18 3 0.5Lauron III 18 3 0.4Genghis II 6 2 −
TUM 18 3 0.3Gregor I 16 − −Chiara 22 − −
Lynxmotion BH3-R 18 3 −Arthron 18 3 −
HexCrawler 12 2 −BILL-Ant-p 18 3 0.004Sprawlita 12 2 0.55Whegs I 6 1 1.527Whegs II 6 1 −LEMUR I − − −LEMUR II 24 4 −ATHLETE 36 6 −
AQUA − − −iRobots Ariel − − −
RiSE 12 2 −COMET-IV 24 4 −
Walking Harvester 18 3 1
Table 3.2: Robots Description.
Table 3.3: Robots Description.
Robot Name Purposes-Project Aims
Robot I Test the control of locomotion in the hexapod
robot using three mechanisms believed to be
responsible for leg coordination in the stick insect.
continued on the next page
36 CHAPTER 3. STATE OF THE ART
Table 3.3: Robots Description.(continued)
Robot Name Purposes-Project Aims
Robot II Propose a strategy to more stable rough terrain
locomotion in the hexapod robot using biologically
based distributed control and local reflexes.
Biobot Prove how sensory feedback can serve as the basis
of the control system for the robot to achieve the necessary
adaptability of locomotion over rough terrain exhibited byinsects.
Tarry I Develop an autonomous hexapod vehicle to successfully
navigate on uneven terrains while under operator control,
to autonomously explore and define what path to take when
moving to a pre-defined goal.
Tarry II Develop an autonomous hexapod vehicle to successfully
navigate on uneven terrains while under operator control,
to autonomously explore and define what path to take when
moving to a pre-defined goal.
Hamlet Verify the effectiveness of combined force and position
control to keep robust walking on unknown environments.
RHex Describe the design an control of this hexapod robot
and compare with others legged robots.
Robot III Try to get the biologically inspired legged
robot to walk.
Lauron I −Lauron II −Lauron III Propose a control structure for the walking
robot and prove their hierarchical walk controller.
Genghis II Develop of a reactive controller that allow
the movement of a legged robot during an arbitrary
trajectory with a high accuracy and performance.
TUM Introduce a model of hexapod walking machine
following biological principles.
Gregor I Implementation both structure and locomotion
control of the robot inspired in biological
observations in cockroaches.
Chiara Open source educational robot.
Lynxmotion BH3-R Use a Genetic Algorithm (GA) to evolve
walking gaits for the robot.
Arthron Describe its mechanical construction demonstrating
continued on the next page
3.2. HEXAPOD ROBOTS 37
Table 3.3: Robots Description.(continued)
Robot Name Purposes-Project Aims
the Kinematic calculation and a control system.
HexCrawler Propose a study of the use of the Soar cognitive
architecture in order to control gait selection
of the six-legged robot.
BILL-Ant-p Development of a new biologically inspired
legged robot.
Sprawlita Development of an hexapod robot following the
basic principles of locomotion of cockroaches.
Whegs I Use a concept of movement based on the behavior
of cockroaches.
Whegs II Use a concept of movement based on the behavior
of cockroaches.
LEMUR I Design an Hexapod robot for assembly, inspection,
and maintenance tasks at space installations.
LEMUR II Design an Hexapod robot for assembly, inspection,
and maintenance tasks at space installations.
ATHLETE Designed to scramble across terrain so rough and
such terrain is abundant on the Moon, most of
which is rough, mountainous, and heavily cratered.
AQUA Develop a platform able to walking on land, crawling
at the bottom of the sea, swimming on the surface
and underwater, and diving to a depth of 10 m.
iRobots Ariel Development of an hexapod robot able to walk
either on land or underwater in the turbulent surf zone.
RiSE Propose a revolutionary method of applying feedback
control for legged robots, by directly modifying
parameters of a robots gait pattern.
COMET-IV Design of an hydraulically actuated hexapod robot for
multitasks on outdoor situations with the unknown environment
applying a teleoperation-based system in order to deal with
extreme environment.
Walking Harvester Development of an hexapod robot to work in forests.
38 CHAPTER 3. STATE OF THE ART
Table 3.4: Robots Description.
Robot Name Bio Inspired Research Group
Robot I Yes Case Western Reserve University Biorobotics Lab
Robot II Yes Case Western Reserve University Biorobotics Lab
Biobot Yes Department of Entomology, University of Illinois
Tarry I Yes Department of Engineering Mechanics at the
University of Duisberg
Tarry II Yes Department of Engineering Mechanics at the
University of Duisberg
Hamlet Yes University of Canterbury, New Zealand
RHex Yes University of Michigan
Robot III Yes Case Western Reserve University
Lauron I − −Lauron II − −Lauron III − Institut de Robotica i Informatica Industrial
Barcelona, Spain
Genghis II Yes Institut de Robotica i Informatica Industrial
Barcelona, Spain
TUM Yes Technische Universitt Mnchen
Gregor I Yes Dipartimento di Ingegneria Elettrica Elettronica
e dei Sistemi Universita degli Studi di Catania,Italy
Chiara No Carnegie Mellon University’s Tekkotsu lab
Lynxmotion BH3-R − Engineering Research Institute, AUT
University
Arthron − P. Graca, Student Member, IEEE, J. Zimon, IEEE
Member
HexCrawler − Department of Aerospace Engineering, The
Pennsylvania State University
BILL-Ant-p Yes Department of Electrical Engineering and
Computer Science, Case Western Reserve
University, Cleveland
Sprawlita Yes Cham, Jorge G.; Bailey, Sean A.; Clark,
Jonathan E.; Full, Robert J.; CutKosky Mark R.
Whegs I Yes Case Western Reserve University, Cleveland,
Ohio, U.S.A
Whegs II Yes Case Western Reserve University, Cleveland,
Ohio, U.S.A
LEMUR I Yes −continued on the next page
3.2. HEXAPOD ROBOTS 39
Table 3.4: Robots Description.(continued)
Robot Name Bio Inspired Research Group
LEMUR II Yes Jet Propulsion Laboratory, California
Institute of Technology
ATHLETE − Kris Hauser, Timothy Bretl, Jean-Claude
Latombe, and Brian Wilcox
AQUA − C. Georgiadis et al.
iRobots Ariel − −RiSE Yes The Robotics Institute, Carnegie Mellon
University
COMET-IV − Graduate School of Science and Technology
, Chiba University, Japan
Walking Harvester − Plustech Oy Ltd
Table 3.5: Robots Description.
Robot Name Cost (dolares) Year
Robot I − 1993
Robot II − 1996
Biobot − 2000
Tarry I − 1992
Tarry II − 1998
Hamlet − 2001
RHex − 2001
Robot III − 2002
Lauron I − −Lauron II − −Lauron III − 2003
Genghis II − 2004
TUM − 1991
Gregor I − 2006
Chiara 3000 2008
Lynxmotion BH3-R 712.47 2008
Arthron − 2009
HexCrawler 549.95 2008
BILL-Ant-p − 2005
Sprawlita − 2002
continued on the next page
40 CHAPTER 3. STATE OF THE ART
Table 3.5: Robots Description.(continued)
Robot Name Cost (dolares) Year
Whegs I − 2003
Whegs II − 2003
LEMUR I − −LEMUR II − 2002
ATHLETE − 2006
AQUA − 2004
iRobots Ariel − −RiSE − 2006
COMET-IV − 2009
Walking Harvester − −
3.3 Control Models of Hexapod Locomotion
Several research groups have suggested different approaches for control and generation of
locomotion in hexapod robots. Their physical nature extremely stable and the capacity to
walk on rough terrain are the most important motivations to continue the study of this kind
of locomotion.
The several approaches for the control of locomotion in hexapods can be divided into
three main categories, central pattern generation approaches, finite state approaches and co-
ordination based approaches [99].
3.3.1 Central Pattern Generation Approaches
Central Pattern Generators (CPGs) are defined as spine-neural networks able to autonomously
produce coordinated rhythmic output signals in vertebrateanimals [100]. They are able to
generate these complex patterns without sensory feedback and without any rhythmic inputs,
when activated by simple commands that encode their rhythmic activation, frequency and
amplitude.
In robotics, the most common way to design CPGs is using artificial neural networks or
systems of coupled oscillators with sensory feedback [101].
After the revive of interest for artificial Neural Networks,a lot of different implemen-
tations for this concept have been studied and developed. The main disadvantage of the
3.3. CONTROL MODELS OF HEXAPOD LOCOMOTION 41
majority of neural network implementations is the number ofinterconnections between neu-
rons [102]. So, to reduce the number of interconnections buthold the advantages of parallel
processing, in 1988 [103], Chua and Yang proposed the Cellular Neural Networks (CNN’s)
where neurons were only connected to other neurons inside a certain neighborhood.
CNNs are a new class of information-processing systems. They are compared with neural
networks because they are a large-scale nonlinear analog circuits able to process signals in
real time. They have some of the main features of neural networks and have important
applications as image processing and pattern recognition.The basic unit of CNNs is called a
cell [103]. CNNs can be used to modulate CPGs. Normally, CPGs are designed as networks
of nonlinear oscillators coupled together and CNN paradigmprovides a framework for the
implementation of these nonlinear oscillators where each oscillator is defined as a cell of a
CNN [9].
CPGs are often modeled and built by means of coupled nonlinear oscillators [104]. Sev-
eral works on hexapod robots have used coupled oscillators like Hopf, Van der Pol [105],
Rayleigh [106], Matsuoka [107], [108], or Fitzhugh-Nagumo.
In [109], J. J. Collins and Ian Stewart realize a mathematical study of Hopf oscillator
to investigate the modeling of Central Pattern Generators (CPGs) in hexapods by different
networks of six coupled nonlinear oscillators. Hopf is a nonlinear dynamical oscillator that
presents an Hopf bifurcation wherex andz are the state variables that present oscillatory
harmonic solutions or a stable fixed point.
They concluded that some generic patterns of motion in several networks of six coupled
nonlinear oscillators correspond to the common walking gaits adopted by hexapods.
In [32], the control of biologically inspired robot is realized using an analog distributed
system working as Central Pattern Generator that performs the locomotion control and the
leg controller is constitute by CNNs. The main aim of this work was to investigate the best
way to include in the biologically inspired CPG an attitude control.
The WalkNet structure proposed by Cruse [35] is based on the neural control structure of
the insect Carausius morosus. It is a system of interconnected neural networks that emulates
the circuitry that coordinates locomotion in the insect.
L.Fortuna and his group, in [110], use Cellular Neural Networks (CNNs) to provide a de-
centralized locomotion control of an hexapod robot using anapproach based on locomotion
control in the stick insect. They apply the Walknet model to implement the decentralized
42 CHAPTER 3. STATE OF THE ART
locomotion control. In this work they investigate the structure of a network of coupled
nonlinear dynamical systems that provides the same complexbehavior of the stick insect
locomotion generator.
This group concluded that using CNNs to realize the leg controllers on the Walknet model
of decentralized locomotion, the local influences can be a suitable way to model the stick
insect gait even when exists a change in the dynamics of each cell.
In [111] they propose a CPG implemented through CNNs for an hexapod in order to
control the direction of the robot and also include feedbackfrom sensors.
In [112] it is proposed a new design of a CNN to control hexapodrobot movement. They
propose new state equations that reduce the number of CNN pattern generation cells from
12 to 6, which reduce the system architecture. With only 6 cells they obtain the same results
like when use 12 cells. This fact can reduce the complexity ofCNN circuit.
In [15] it is used a coupled nonlinear oscillator to control the locomotion of an hexapod
robot. The nonlinear oscillator is a two neuron Matsuoka oscillator with mutual inhibition.
In this work it is possible conclude that beyond being an adaptive controller, the coupled
nonlinear oscillator is also robust to sensor failure.
In the Matsuoka oscillator model, the two first order differential equations demonstrate
the behavior of each neuron, where the input variables definethe firing rate and fatigue of
each neuron, respectively. The output of each neuron represents the positive part of the firing
rate. The network output is represented by the difference between these referenced outputs.
There are two parameters that define the first order time constants for the firing rate and the
fatigue.
In [9], Cellular Nonlinear Networks play the role of an artificial CPG to the locomotion
control. The structure of the adopted CPG is based on nonlinear oscillators coupled together
forming a network that generates a pattern of synchronization to control robot actuators.
This work have a good results where the adopted structure is suitable for the locomotion
control of the legged robot with complex design legs. Also, the hexapod walks at the travel
speed of 0.1 body length per second and has the capacity to negotiate obstacles with success,
more than 170% of the height of its mass center.
In our approach we apply coupled CPGs, formulated as Hopf nonlinear oscillators in
order to generate motor patterns. The required motions of the limbs for locomotion are
produced using a network of CPGs, on-line generating coordinated trajectories for the coxa
3.3. CONTROL MODELS OF HEXAPOD LOCOMOTION 43
joints, which we can modulate through simple and predictable parameter changes.
3.3.2 Finite State based Approaches
In the CPG approaches, a gait is pre-selected and a CPG provides each leg with a trajectory
signal.
Unlike the CPG approaches, the finite state approaches incorporate a set of conditions
that place the robot into one of several states, previously determined by a set of rules for
several types of environmental interactions (i.e., walking over flat terrain). This method
basically uses finite state machines to control hexapod locomotion.
The point of view behind this approach considers the locomotion as a sequence of events,
rather than a continuous dynamical process. The advantage of this method is that it makes
possible the constitution of any gait pattern as a sequence of states, and the control of the
gait then requires only a finite algorithm for description.
In [113], Y.Tanaka and Y.Matoba develop an hexapod walking robot to be used in the
houses and work shops where there are several obstacles and stairs to overcome. The hexa-
pod used in this work has eight CPUs for controlling the movement of twenty driving motors
and to detect the environments around it. They use the finite state based approaches to con-
trol the robot. The software that controls each CPU has a set of functions like check the state
of emergency-stop key and necessary treatment, driving motors and reading the states of mo-
tors, calculating the pulse numbers and speed for elevatingand lowering the legs, detecting
the distance to the wall and obstacle.
Basically they follow a set of conditions that place the robot into a determined state.
In [114], they also make use of finite state approaches to control the hexapod robot RHex.
In this work they present the design, modeling and control ofRHex. With a set of simulations
and experiments they prove that, by using finite state approaches, the Rhex can achieve
dynamically stable walking, running and turning.
These above works use finite state approaches to control the hexapod robot and there are
other groups working in the same method.
3.3.3 Coordination based Approaches
In the coordination based approaches the gait is not statically defined and the behavior result
from some sort of coordination system. This kind of system normally is able to more easily
44 CHAPTER 3. STATE OF THE ART
traverse hostile terrain. Some groups have used this approach to control hexapod robots.
In [115] it is developed a biologically inspired distributed neural-network controller to
control an hexapod robot. In this work they conclude and clarify that the biologically inspired
controller for hexapod locomotion is quite robust.
The WalkNet structure is another important approach for thecontrol of locomotion in
hexapodal walking robots. This approach, as previously referred, was proposed by Cruse et
al. [35] and basically consists on a system of interconnected neural networks. Cruse’s neural
network consists of three main subsystems, designed of swing net (that generates a leg’s
trajectory during swing phase), stance net (that does the same for the stance phase), and the
selector net (that decides the trajectories to use for each leg).
A. Calvitti and R. D. Beer make use of this approach in [116]. In this work they clarify
the role of individual coordination mechanisms using a system of two coupled oscillators on
the leg. They focus their work on the Cruse [35] model where the position at which a leg
switches state depends of the state of adjacent legs using a specific network of coordination
mechanisms.
In [117], the researchers study the emergence of stable gaits in robots locomotion using
the coordination based approach.
In [118], Eric klavins et al. use this approach on their work.They employ this method to
generate locomotion on an hexapod robot.
It is possible conclude that several groups have used the coordination based approaches
to generate the hexapod locomotion.
3.4 Gait Transition
In this work the generated gaits are metachronal gait (”wavegait”) that specifies slow walk-
ing, ripple gait corresponding to a medium speed gait and thefast speed tripod gait. One of
the aims is also propose a mechanism in order to switch between these different gaits of an
hexapod robot.
In order to achieve smooth walking from low speed to high speed, robotic gait switching,
similarly to their biological counterparts [29], should take place continuously with both the
duty factor and the interlimb phase relationships properlyadjusted.
This gait switching issue in hexapod robots has already beenaddressed.
[62] proposes a new gait rule named ”adaptive wave gait”. It is combined the adap-
3.4. GAIT TRANSITION 45
tive wave gait and a synchronized motion control, to reproduce the gait generation and gait
transition in a smooth way. Our work is based on this approachmainly because of its sim-
plicity and with the proposed method it is possible to realize a smooth and effective transition
between the desired gaits.
Another contribution to this issue is proposed in [119]. Three insect inspired controllers
implemented on an autonomous hexapod robot are compared to verify the locomotion per-
formance and the efficiency on gait transitions. In order to develop the controllers they used
reflex-based mechanisms and pattern-based mechanisms (CPGs). The reflexive controllers
exploit sensory stimulus and response reactions to reproduce the hexapod locomotion and
gait transition but unlike these, pattern-based controllers depend more upon pre-programmed
patterns of behavior that can be influenced by external events.
They concluded that the controller based on Central PatternGenerators (CPGs) per-
formed the best of the three controllers. The robot performed smoothly transition between
its three gaits (”wave gait”, ripple gait and tripod gait).
In [87] they propose an architecture that allows safe and efficient walking in rough terrain.
They add planning that allows the hexapod to anticipate changes in its gait. They develop
a behavior-based controller that allows change arbitrarily among gaits and keep the stability
in rough terrains. Two robot behaviors called ’contact foot’ and ’free foot’ are studied. The
’contact foot’ behavior causes the foot to achieve and maintain contact with the ground while
the ’free foot’ causes the foot to stay free, out-of-contactwith the terrain. They conclude that
the coordination of these two robot behaviors enables transitions between fixed gaits.
In [23] they present methods to correctly transition between different gaits. The processes
of gait transition are applied to smoothly switch from a tripod walking gait to a metachronal
wave gait used to climb stairs. In the proposed mechanisms they define transitions as a series
of phase offset modifications where each changes the parameters of a gait slightly, until
achieving the desired gait. This method results in midway configurations for which some
legs are playing one gait, and the rest the other because legsswitch, one by one, from one
gait to another.
Around the same time, Nishii [120], proposes a method to estimate the cost of transport
for legged locomotion where the resultant locomotor pattern, which makes the appropriate
cost, presenting several features of the pattern observed in legged animals. So, they estimate
the cost for force generation using a simple equation and consider the essential property of
46 CHAPTER 3. STATE OF THE ART
energy cost to trigger a gait transition and the other features of legged locomotion. Their
results indicate that the gait transition occurs when a larger number of stance legs suppress
the total cost to support the body or in other words that gait transition occurs due to the
change in the balance of costs for swinging the leg and supporting the body.
A more recent approach [121] of this problem introduces a newformalism for coordina-
tion of periodic tasks which can be applied on gait transitions for legged robots. They use
’Young Tableaux’ to decompose the space of all periodic legged gaits into a cellular complex
indexed. They find the task of transit between the gaits whilelocomoting over level ground.
With this aim they define a set of dynamical reference generators over the ’Gait Complex’
and develop automated coordination controllers to force the legged system to converge to a
specified cell’s gait. During this process the relative static stability of gaits is verified ap-
proximating their stability margin via transit through a ’Stance Complex’. Integrating these
two mechanisms, ’Gait Complex’ and ’Stance Complex’ they achieved the desired gait tran-
sitions.
3.5 Posture Control
Postural control has been intensively investigated in hexapod robots.
In [89], to improve rough terrain locomotion in a hexapod robot they propose the incor-
poration of biologically based control. Their method consist on use distributed control and
local leg reflexes that enable insects deal with irregular terrain. The application of ’elevator
reflex’ and ’searching reflex’ mechanisms allows the robot toovercome any obstacle that
appear on the terrain and keep the balance.
Wettergreen et al. [87] propose an architecture based on control walking behaviors of the
robot in order to reproduce a correct locomotion in rough terrain. The developed controller
allows transit between the different gaits and maintain balance as well as stability in rough
terrains following the rules based on two robot behaviors called ’contact foot’and ’free foot’.
In [122], they propose and demonstrate a computationally simple algorithm for control-
ling the posture of a complex hexapod robot with several DOFs. In order to keep static
posture and generate body motion the proposed algorithm avoids inverse kinematics by is-
suing feedforward force commands.
[123] proposes a sensorial feedback based control system tohexapod locomotion in
rough terrain. In order to deal with terrain irregularitiesthey use local behaviors such as col-
3.5. POSTURE CONTROL 47
lision reaction and searching for ground only adapting the leg trajectories thus maintaining
the robot balance.
Paolo Arena et al. [32] presented a biologically inspired solution to control an hexapod
locomotion using an analog distributed system that makes the role of a CPG for the loco-
motion control. The attitude control is realized by integrating in the CPG a proportional
integrative controller for each leg.
In [124] they propose two new controllers, one for climbing constant slope inclinations
where the posture control is a very important factor and one for achieving higher speeds using
a gait that incorporates a substantial aerial phase. In order to develop these two controllers
they make use of an underlying open-loop control strategy inparallel with low bandwidth
feedback to modulate its parameters.
The inclination behavior is based in adjusting the angle offsets of individual leg motion
profiles based on inertial sensing of the average surface slope.
Moore et al. [125], propose an open loop controller that allows the RHex robot to reli-
ably climb a wide range of regular, full-size stairs withoutoperator intervention during stair
climbing. The success of any stair climbing algorithm is that the robot must be ’in phase’
with the stairs and this algorithm is defined on finding open loop leg motions, based on linear
trajectory segments connecting angle set points, that maintaining a low pitch, a high constant
body velocity, and a moderate ground clearance.
In [86], they proposed an interesting work that incorporates the concept of postural con-
trol. They propose a control system that provides to the hexapod robot the capacity of walk-
ing with only its two hind legs (bipedal running).
The controller has an hierarchical structure composed by three levels of PD controls for
speed control, inverted pendulum balance control and leg trajectory tracking that enables the
robot walks with only two legs as well as still maintain the balance.
In a more recent approach [126], they propose a control system based on the principles
used by cockroaches to climb obstacles and apply this methodin a bio-inspired hexapod
robot. The proposed control system is composed by two functional parts that work in parallel.
They make use of a Cellular Neural Network for control locomotion and designed an attitude
control system that is based on a Motor Map in order to regulate the posture of the robot to
allow it to overcome obstacles.
Our posture control is based on dynamical systems approach.We compensate lateral
48 CHAPTER 3. STATE OF THE ART
displacement of the body by increasing or decreasing leg height on both sides, performed
by generating discrete trajectories for the femur and tibiajoints correcting the posture and
adapting the locomotion on inclined terrains.
In the next chapter will be detailed described the chosen hexapod robot and its develop-
ment in Webots simulator.
Chapter 4
Development of Chiara Robot usingWebots Simulator
After the realization of an exhaustive state of the art of existing hexapod robots, one of the
most recent hexapod robots caught our attention due their excellent features, which we think
is the best option in order to achieve all the objectives proposed for this work and for future
aims. We have chosen the Chiara robot as the working robot andin this chapter it is described
in detail.
4.1 Chiara Robot
Chiara robot is one of the most recent hexapod platforms provided for several applications.
It is an open source educational robot, developed by the Tekkotsu lab, a research group at
Carnegie Mellon University’s, and is manufactured and soldby RoPro Design, Inc.
It is developed by David S. Touretzky (principal investigator), Gaku Sato (body design),
Ethan Tira-Thompson (software), and David Rice (gripper design).
It is a technological platform that can be used by professorsfor teaching students themes
and subjects of robotics like computer vision, inverse kinematics, map building, navigation,
manipulation, path planning and human-robot interaction.
Chiara is programmed in C++ using the Tekkotsu open source software framework de-
veloped at Carnegie Mellon and available free at www.tekkotsu.org.
The Development of Chiara was funded in part by National Science Foundation award
DUE-0717705.
In figure 4.1 is presented the first Chiara prototype, built July 2008.
49
50 CHAPTER 4. DEVELOPMENT OF CHIARA ROBOT USING WEBOTS SIMULATOR
(a) (b) (c)
(d) (e) (f)
Figure 4.1: First Chiara prototype, built July 2008 (from [10]).
The production version looks somewhat different from the initial prototype (Fig. 4.2) and
under this project, was developed on Webots simulator [127], a simulated Chiara robot based
on this production version.
(a) (b)
(c)
Figure 4.2: Production Chiara Version (from [26]).
4.1.1 Features
In figure 4.3 is provided a complete description of the main Chiara features.
4.1. CHIARA ROBOT 51
Special Leg
Arm with gripper
Dynamixel AX-12 Servo
Logitech webcam
Dynamixel AX-S1 Sensor
OF-12S
OF-12SH
Figure 4.3: Chiara Description.
Chiara is composed by six legs and has a total of 27 DOFs distributed through its body
that is laser-cut acrylic. Each leg has 3 DOFs except the right front leg that has 4 DOFs and
can be considered a special leg, with the ability to manipulate objects. This hexapod has
a 6 DOF arm with gripper that enables grasp and manipulation of several objects. It has a
Logitech webcam and a IR rangefinder for sensor fusion on pan/tilt mount.
A Pico-ITX (x86) computer on board with 1 GHz processor, 1 GB RAM and 80 GB hard
drive is provided with the robot and an Ethernet plus 802.11(b/g) WiFi allows the robot to
communicate with the environment that surrounds.
The robot runs Ubuntu Linux OS and Tekkotsu application development framework using
C++. The Ubuntu Linux OS is free as well as open source and Tekkotsu framework provides
integrated vision/kinematics, teleoperation, and monitoring.
The robot includes audio and LED outputs for human-robot interaction, USB bus allows
extend the robot by adding USB-compatible devices. It has anopen source body design that
lets customize the Chiara by changing component shapes, adding sensors, etc.
52 CHAPTER 4. DEVELOPMENT OF CHIARA ROBOT USING WEBOTS SIMULATOR
The robot comes fully assembled and consists of a set of different parts as motors and
sensors.
4.1.2 Motors
The robot has 24 dynamixel AX-12 servos (Fig. 4.4) with position and force feedback as
well as plus 3 analog microservos in the gripper [10].
(a) (b)
Figure 4.4: Dynamixel AX-12 Servo ( 4.4(b) from [27])..
The Dynamixel AX-12 servo is a small actuator that incorporates a gear reducer, a pre-
cision DC motor and a control circuitry. It produces an high torque, although its small size,
and has the capacity to detect and act upon internal conditions such as changes in internal
temperature or supply voltage.
The Dynamixel AX-12 servo has many advantages as position and speed can be con-
trolled with a resolution of 1024 steps, it is provided with feedback for angular position,
angular velocity, and load torque. This servo is composed byan alarm system that alerts the
user when parameters deviate from user defined ranges (e.g. internal temperature, torque,
voltage, etc) and can also handle the problem automatically(e.g. torque off). The main body
of this unit is constructed with high quality engineering plastic which enables it to handle
high torque loads. In order to avoid no efficiency degradation when subjected to high exter-
nal loads a bearing is included at the final axis. This servo has a status LED that indicates
the error status to the user.
In the mechanical assembly of the Dynamixel AX-12 servo two frames are provided
(Fig. 4.5).
4.1. CHIARA ROBOT 53
(a) (b)
Figure 4.5: The two frames provided with Dynamixel AX-12 Servo. a) OF-12SH (from [27]). b)OF-12S (from [27]).
4.1.3 Sensors
The robot is composed by a Dynamixel AX-S1 infrared rangefinder sensor (Fig. 4.6) that is
mounted directly below the camera and is used for multimodalsensing.
(a) (b)
Figure 4.6: Dynamixel AX-S1 Infrared Rangefinder ( 4.6(b) from [28]).
The Dynamixel Sensor Module AX-S1 is a Smart Sensor Module that integrates impor-
tant features. It makes the task of sound sensor, infrared remote control receiver, infrared
distance sensor, light sensor, buzzer, control unit and network. Although its small size, AX-
S1 is composed by special materials that can withstand even the extreme external force. It
has the capacity of detect subtle changes (alarm system) such as internal temperature, service
voltage and other internal conditions and is able to solve the situations.
This sensor comes with other important features such as three directions infrared sensors
that allow to detect left/center/right distance angle as well as the light and allows to transmit
and receive infrared data between sensor modules due the built-in remote control sensor in
center. Moreover allows to detect current sound level and maximum loudness as well as it
has an ability to count the number of sounds due the built-in micro internal microphone.
In the mechanical assembly of the Dynamixel AX-S1 sensor twoframes are also provided
54 CHAPTER 4. DEVELOPMENT OF CHIARA ROBOT USING WEBOTS SIMULATOR
and are the same used in Dynamixel AX-12 Servo (Fig. 4.5).
For this work was modeled the real Chiara robot for the Webotssimulator. The developers
available the Chiara Solidworks model (Fig. 4.7) to the student community. This model was
used to the development of the robot in the Webots simulator.The aim is that almost all
features of the simulation model are as close as possible to the real model.
Figure 4.7: Chiara Solidworks Model.
4.2 Shape Simplification using Solidworks
The Solidworks platform is a three dimensional mechanical software where is possible to
design a lot of products and things like cars, robots and is employed in several applica-
tions [128]. With this tool was possible model the body partsof the robot and export it to
VRML (Virtual Reality Modeling Language) file format. In Webots it is possible import the
model of the robot in VRML format and use it for the desired simulations.
The ”body parts” of the Chiara Solidworks model are too complex, mainly the legs, they
have a lot of details. With these details, the model of the robot becomes very heavy to render
and simulate on the Webots which could make the simulation very slow taking too long time
to repeat each simulation. For the aim of this work is not necessary this level details.
So, the body parts of the model were simplified on Solidworks platform [128] by re-
moving the minor details, as holes and rough surfaces that only occupy space and are not
fundamental for the simulation environment. The figure 4.8(a) shows the ”OF-12SH” shape
of the robot before simplification where we can verify its certain complexity and figure 4.8(b)
demonstrates the body frame of the robot after the simplification.
4.3. WEBOTS MODEL OF THE HEXAPOD ROBOT 55
(a) (b)
Figure 4.8: a) OF-12SH shape before simplification. b) OF-12SH shape after simplification.
4.3 Webots Model of the Hexapod Robot
The Webots platform was developed by Cyberbotics Ltd and it is a robotics simulation soft-
ware for modeling, programming and simulating different kinds of robots (wheeled robots,
legged robots or flying robots). This simulator provides several properties very important for
modeling such as shape, color, mass, friction, density. It is also possible to add many kinds of
sensors and actuator devices such as distance sensors, motor wheels, cameras, servos, touch
sensors, grippers, emitters, receivers, etc.. Further, itis possible to transfer the developed
code to the real robot.
Webots simulator is based on the Open Dynamics Engine (ODE),an excellent and pow-
erful open source physics engine that works as a library to provide more realistic simulations
and improve the results [127].
A Webots project is composed by a world file that is a 3D virtualenvironment in which
we can create objects and robots to the simulation, and a controller that makes possible
control the robot movement and act on all its servos and sensors. In Webots, a world can
include one or more robots and their environment.
A Scene Tree (Fig. 4.9(a)) is composed by all necessary information to define the graphic
representation and simulation of the 3D world.
The Scene Tree of Webots is structured as a VRML file and contains a list of nodes, each
containing fields. Each field can contain values (text string, numerical values) or nodes.
The Webots simulator supports an important number of VRML nodes such as Back-
ground, PointLight, Viewpoint, WorldInfo, CustomRobot, Shape, Sphere, Transform....etc
In figure 4.9(b) is demonstrated the hierarchy of operation in the Webots environment
containing the different nodes and the controller of the robot.
56 CHAPTER 4. DEVELOPMENT OF CHIARA ROBOT USING WEBOTS SIMULATOR
(a)
Webots
ODE Engine
WorldInfo (…)
Viewpoint (…)
Background (…)
PointLight (…)
CustomRobot
(…)
controller…....
Scene Tree
(b)
Figure 4.9: Webots diagram. a) Scene Tree. b) Webots operation.
4.3. WEBOTS MODEL OF THE HEXAPOD ROBOT 57
The Webots simulator follows the VRML language and the Chiara model simplified in
Solidworks can be easily imported without losing the most important features.
Several modifications were done to simplify the Chiara model, by removing the 6 DOF
arm with gripper and its camera that is used for robot vision programming in order to simplify
the model and the simulation environment.
In Figure 4.10(a) and 4.10(b) is possible to visualize the complete and final hexapod
robot model rendered in Webots.
(a)
(b)
Figure 4.10: Chiara Developed Model. a) Model of the Chiara robot rendered in Webots platform. b)Chiara model rendered in Webots with his bounding objects highlighted.
4.3.1 Servo Node
A Servo node is one of the several existing nodes that is supported by Webots and is used to
add one (active or passive) degree of freedom (DOF) in a mechanical simulation.
58 CHAPTER 4. DEVELOPMENT OF CHIARA ROBOT USING WEBOTS SIMULATOR
There are two types of servos: rotational or linear. A rotational servo is applied to sim-
ulate a rotating motion as the most electric motors, hinges,and other. On the other hand
a linear servo is applied to simulate a sliding motion such aslinear motors, pistons, hy-
draulic/pneumatic cylinders, springs, dampers, etc..
Through these servos we can manipulate all joints of the model and change their position
every moment making the robot move how we wish but according to the servo specifications.
The simulation model of Chiara is developed with only three rotational servos on each
leg except on right front leg that is composed by four rotational servos.
In figure 4.11(a) are demonstrated the directions of rotation of each joint that compose
the hexapod model where the orange lines represent the rotation axes for each joint. The
three rotational joints of each leg are called coxa, femur and tibia following the biological
systems. The right front leg has an additional joint called trochanter (Fig. 4.11(b)).
(a) (b)
Figure 4.11: Developed model of the Chiara robot. a) Directions of rotation of each joint. b) Chiarajoints description.
In Tables 4.1 and 4.2 are presented the chosen values for eachenumerated parameter of
Servos nodes.
Leg maxVelocity (rad/s) maxForce (N*m) MinPosition (rad)
Coxa Femur Tibia
L1 4 1.15 −0.92 −1.74 −1.05L2 4 1.15 −0.92 −1.74 −1.05L3 4 1.15 −1.27 −1.74 −1.05R1 4 1.15 −1.78 −1.74 −1.05R2 4 1.15 −0.92 −1.74 −1.05R3 4 1.15 −0.92 −1.74 −1.05
Table 4.1: Specification of Servos nodes parameters for Chiara simulation model.
4.3. WEBOTS MODEL OF THE HEXAPOD ROBOT 59
Leg maxVelocity (rad/s) maxForce (N*m) MaxPosition (rad)
Coxa Femur Tibia
L1 4 1.15 1 1.74 2.79L2 4 1.15 0.92 1.74 2.79L3 4 1.15 0.92 1.74 2.79R1 4 1.15 1.17 1.74 2.79R2 4 1.15 0.92 1.74 2.79R3 4 1.15 0.92 1.74 2.79
Table 4.2: Specification of Servos nodes parameters for Chiara simulation model (Continuation).
The Figure 4.12 demonstrates the construction of one Servo node (for left front leg coxa
joint) of the developed model in Webots simulator where eachparameter is chosen following
the Dynamixel AX-12 servo specifications.
The effectiveness of the simulation can be best achieved setting the adequate parameters
to the servo nodes.
Figure 4.12: Specification of the Servo node in Webots.
60 CHAPTER 4. DEVELOPMENT OF CHIARA ROBOT USING WEBOTS SIMULATOR
4.3.2 Physics Node
The body of the robot model must comply the physics and features of the real robot. With
the Physics node we can define a number of physics parameters of the robot to be used by
the physics simulation engine.
In simulation of legged robots this node is very important todefine mass repartition and
friction parameters, thus allowing the physics engine to simulate a legged robot accurately.
In this node we choose each value for the different parameters following the features of
the real robot Chiara.
The Physics node is composed by a set of important parameterssuch as mass, density,
bounce, bounceVelocity, coulombFriction, centerOfMass that specify the physical character-
istics of robot model.
The density and mass parameters are used to specify the totalmass of the solid that can
be not only the total robot but also their several parts such as the legs. The body of the robot
weights about 2.280 Kg.
The ”bounce” parameter specifies the bounciness of a solid and it is a value ranging from
0 to 1 where 0 means that the surfaces are not bouncy at all and 1is maximum bounciness.
We set this parameter with value 0.5 for each leg of the robot and its body.
The ”bounceVelocity” parameter specifies the minimum speedof entry indispensable for
bounce and we choose the value 0.01 m/s for all legs of robot and its body considering it to
be an appropriate value.
The ”coulombFriction” parameter defines the friction parameter applied to the solid rang-
ing from 0 to infinity and all of these fields of robot model has the value 0.99.
The ”centerOfMass” parameter defines the position of the center of mass (in meters) of
each solid of the robot and we try follow the specifications ofthe real robot.
In Tables 4.3 and 4.4 are presented the physics parameters ofthe model.
Figure 4.13 demonstrates the construction of a Physics nodeof the developed model in
Webots simulator where each parameter is chosen following the specifications of the real
robot.
4.3. WEBOTS MODEL OF THE HEXAPOD ROBOT 61
Leg Mass (Kg) bounce bounceVelocity (m/s)
Trochanter Coxa Femur Tibia 0.5 0.01
L1 − 0.020 0.150 0.055 0.5 0.01L2 − 0.020 0.150 0.055 0.5 0.01L3 − 0.020 0.150 0.055 0.5 0.01R1 0.0775 0.020 0.150 0.055 0.5 0.01R2 − 0.020 0.150 0.055 0.5 0.01R3 − 0.020 0.150 0.055 0.5 0.01
Table 4.3: Specification of Physics nodes parameters for Chiara simulation model.
Leg coulombFriction centerOfMass
Trochanter Coxa Femur Tibia
X Y Z X Y Z X Y Z X Y Z
L1 0.99 − − − 26 0 0 41.5 0 0 50 12 0L2 0.99 − − − 26 0 0 41.5 0 0 50 12 0L3 0.99 − − − 26 0 0 41.5 0 0 50 12 0R1 0.99 5 0 26.5 26 0 0 41.5 0 0 50 12 0R2 0.99 − − − 26 0 0 41.5 0 0 50 12 0R3 0.99 − − − 26 0 0 41.5 0 0 50 12 0
Table 4.4: Specification of Physics nodes parameters for Chiara simulation model (Continuation).
Figure 4.13: Specification of the Physics node in Webots.
In order to detect collisions were defined ”bounding objects” in the robot model. As the
Chiara model has complex shapes were only used boxes and cylinders as bounding shapes.
The bounding objects are used by the collision detection engine and the figure 4.10(b)
presents the Chiara model in Webots with its bounding shapeshighlighted.
4.3.3 TouchSensor Node
The developed hexapod model has a set of touch sensors, one per leg positioned in the feet.
62 CHAPTER 4. DEVELOPMENT OF CHIARA ROBOT USING WEBOTS SIMULATOR
A TouchSensor node is used to develop two types of touch sensors : ”bumper” and
”force” (pressure) sensors. The bumper sensors simply detect collisions with objects and
return a boolean status while force sensors return the magnitude of the force exerted on their
body by external objects.
In this work were only used ”bumper” sensors in the feet allowing to know if the robot is
really in contact with the world. It returns 1 when a collision occurs and 0 otherwise.
It is important refer that collisions between a TouchSensorand other parts of the same
robot are not considered.
In Figure 4.14 it is possible to visualize the touch sensor node that was used for each leg
of the robot (in this case we can see the TouchSensor node of the left front leg).
Figure 4.14: Specification of the TouchSensor node in Webots.
In this chapter all steps related to the development of Chiara model in Webots were
detail presented. In next chapter a bio-inspired controller able to generate locomotion in the
hexapod robot will be proposed and described.
Chapter 5
Hexapod Locomotion Generation
In this chapter we start the locomotion of the hexapod robot.The most important actions of
animal locomotion as gaits will be described.
We propose a bio-inspired controller able to generate locomotion and reproduce the dif-
ferent type of gaits. Motor patterns are generated by coupled Central Pattern Generators,
formulated as nonlinear oscillators. The results are performed in simulation and described in
detail.
5.1 Gait Description
During animal locomotion one of the most important actions is the coordinated cyclic man-
ner of lifting and placing the legs on the ground. This action, called a gait, is a periodic
relationship among the movement of all limbs during locomotion.
A gait can be characterized [129] by the concepts of cycle time (T), duty factor (β ) and
relative phase (θ ij ).
A gait is defined by the sequence that the legs are lifted and placed, named events of
the gait. The sequence in which the legs are lifted and placedis called a gait event se-
quence [130]. A gait is normally cyclic because the same sequence of lifting and placing
the legs is repeated. The complete cycle of limb movements inwhich all legs have been
lifted and placed exactly once, is a step cycle or also named stride and the necessary time to
complete a step cycle is the cycle time(T).
A stride can be divided into two phases, the stance phase (also called support phase)
and the swing phase (also called transfer phase) where they have independent durations and
their sum gives the cycle time,T. Basically, the stance phase corresponds to the time inter-
val in which the limb is in ground contact and the body is propelled. The duration of the
63
64 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
stance phase determines the overall period of the step cycleand is defined by the following
expression,
Tst = (β )T (5.1)
In swing phase the leg is swung up and moved to the starting point of the next standing
phase. The next equation presents the expression of the duration of the swing phase,
Tsw= (1−β )T (5.2)
The relationship between the stance phase duration (Tst) and the cycle time (T=Tst + Tsw)
is the duty factorβ ∈ [0,1],
β =Tst
Tst+Tsw(5.3)
The duty factorβ is defined as the fraction of the duration of the step cycle forwhich a
foot is on the ground.
In general, animals increase their locomotion velocity by decreasing the step cycle dura-
tion, increasing the number of steps per second [29]. Observations of animal locomotion led
to the conclusion that this decrease of the cycle time is mainly due to a decrease in the stance
phase duration,Tst. While the stance phase duration is decreased, the swing phase duration,
Tsw, remains practically constant throughout all velocities of locomotion.
We focus our work in the most common hexapodal gaits, used forstraightforward walk-
ing [131]. We follow usual limb conventions [109], the limbsof the left (L) and right (R)
sides of the insect are numbered from front to back. The subindexs stand for the limb num-
ber: 1 is the front leg, 2 is the middle leg and 3 is the rear leg (Fig. 5.1).
R3
L2
L3
L1
R2
R1
Contralateral Limbs
Adjacent Limbs
Figure 5.1: Legs Description.
5.1. GAIT DESCRIPTION 65
It is considered that the first event, and the start of the stride, is chosen as the reference
event when an arbitrary chosen reference limb is set down. The convention used here is that
the reference limb is the right rear leg(R3).
The relative phase of legi is defined as the time elapsed from the setting down of a chosen
reference foot until the foot of legi is set down, given as the fraction of the cycle time. Thus,
consider as reference the right rear limb(R3), the relative phase for all the limbs is given by
θi =∆tiT, (5.4)
whereθi ∈ [0,1], because∆ti ≤ T is the time delay between the placing events of the right
rear leg limb and limbi.
Many of the usual hexapod gaits possess a degree of symmetry,which can in general be
described according to the two following assumptions [132]: 1) no leg moves forward until
the one behind is placed in a supporting position; and 2) legsof the same girdle are always in
strict alternation, performing the step cycle out of phase from each other (0.5 out of phase).
Figures 5.2 and 5.3 depict the gait diagrams and the relativephases for the most common
hexapodal gaits [109]. In Figure 5.2 the white color indicates that the foot is in ground
contact and the black color otherwise.
(a)
(b)
(c)
Figure 5.2: Gait diagram depicting event sequences for three different hexapodal gaits. White colorindicates that the foot is in ground contact. a) Metachronal(low - speed) Gait. b) Ripple (medium -speed) Gait. c) Tripod (fast - speed) Gait.
66 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
The Metachronal gait, illustrated in Fig. 5.2(a), is adopted by the hexapod when it moves
slowly, usually with a duty factor ofβ = 34 meaning that during this fraction of the dura-
tion of the step cycle each foot is on the ground. This gait canbe described as a back to
front propagating ”wave”, first moving the limbs on the rightside (with black color in the
figure 5.2(a)) and then the limbs on the left side (with black color in the figure 5.2(a)).
The adjacent limbs of each half of the hexapod body (R3 and R2,R2 and R1) are 600 out
of phase and contralateral limbs (e.g. R3 and L3) are half a period (or 1800) out of phase
(Fig. 5.3(a)). In this gait each leg is lifted of the ground after 16 of the cycle time the reference
leg (R3) be placed in the ground as demonstrated in figure 5.3(a) .
The Ripple Gait (Fig. 5.2(b)) is used by the hexapod to move with a medium speed and
duty factorβ = 58 where each foot is on the ground during this fraction of the cycle time.
The contralateral anterior and posterior legs,i.e. L1 and R3, L3 and R1 move together in
phase (as we can verify in figure 5.2(b) with black color).
Contralateral legs in each segment are half a period (1800) out of phase and the consec-
utive movements of the limbs are one quarter of a period (900) out of phase (Fig. 5.3(b)).
During this gait L1 and R3 start together the movement, then after one quarter of a period
moves R2, more a quarter of a cycle begin their movement R1 andL3 and finally after more
one quarter of a period moves L2 as possible to verify in figure5.3(b).
When an hexapod moves rapidly, it normally uses the tripod gait (Fig. 5.2(c)), with a duty
factor ofβ = 12 meaning that each foot is on the ground during this fraction of the duration
of the step cycle and if the value ofβ is less than12 the hexapod robot is running. At each
move, ipsilateral anterior and posterior legs, and the contralateral middle leg move together
in phase.
At each time, three legs (L1, L3, R2 and R1, R3, L2) move together in phase as demon-
strated with black color in figure 5.2(c). On each segment, contralateral limbs are half a
period (1800) out of phase. The adjacent limbs on the right and left sides are also half a
period (1800) out of phase (Fig. 5.3(c)).
5.2 Locomotor Model
Each leg of the hexapod robot has 3 DOFs, one per joint, exceptthe right front leg that has
4 DOFs. The names of the joints of the hexapod model are definedas coxa, femur and tibia
following the biological inspiration but as the right frontleg is a special leg has more one
5.2. LOCOMOTOR MODEL 67
5/6
4/6
3/6
2/6
1/6
0
(a)
0
3/4
1/2
1/2
1/4
0
(b)
1/2
0
1/2
0
1/2
0
(c)
Figure 5.3: Relative phases for the most common hexapodal gaits. a) Metachronal gait. b) Ripplegait. c) Tripod gait.
joint called trochanter (see Fig. 4.11).
We present a two-layer architecture able to generate the motions of hexapodal locomotion
and able of changing the walking velocity through continuous gait change (fig. 5.4).
Coxa
Femur
Tibia
Robot
En
vir
on
me
ntCentral Pattern
Generators
Lateral posture
control
Lower
layer
Upper
layer
m
¯
¹xi
yF,i
yT,i
Pa
ram
ete
r
mo
du
lati
on
Figure 5.4: System’s overall architecture. The network of CPGs generate the motions of locomotionfor the coxa joints. The posture control mechanism generates the necessary discrete movements onthe femur and tibia, to correct the robot’s body orientation.
We also include a lateral posture mechanism that automatically corrects the body orien-
tation of the robot in respect to lateral inclination.
The lower layer generates the required motions of the limbs for locomotion, using a
network of CPGs, on-line generating coordinated trajectories for the coxa joints, which we
can modulate through simple and predictable parameter changes. These trajectories encode
the values of the joint’s angles and are sent online for the lower level PID controllers of each
coxa joint (fig. 5.4).
The parametersβ andµ are determined by the upper layer, specified through the value of
a single descending command. We are able to change between three basic hexapodal gaits,
controlling the velocity and behaviour of the robot, as locomotion initiation, gait switching
and stopping.
68 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
Next will be described the network of CPGs used in the lower layer and the lateral posture
control mechanism will be discussed later in this report.
5.3 CPGs
Movements for all coxa joints are generated by a single nonlinear Hopf oscillator, as follows
xi = α(µ − r2i )(xi −yi)−ωzi (5.5)
zi = α(µ − r2i )zi +ω(xi −yi) (5.6)
wherexi andzi are the state variables,r i =√
(x2i +z2
i ), amplitude of the oscillations is given
by A=√µ , ω specifies the oscillations frequency and relaxation to the limit cycle is given
by 12α µ .
This oscillator generates harmonic solutions for the statevariablesxi andzi where the
variableyi controls the offset for the solution in thexi state variable.
Herein, we consider that the descending phase of thexi trajectory, in which the coxa joint
value is decreasing, corresponds to the stance step phase inwhich the limb moves backwards,
thus propelling the robot forward. The ascending phase is the movement that places the foot
in a more advanced position, ready for the next step, and corresponds to the swing step phase.
This oscillator contains an Hopf bifurcation from a fixed point at xi = yi (whenµ < 0
(Fig. 5.5)) to a structurally stable, harmonic limit cycle,for µ > 0 (Fig. 5.6).
−0.2 −0.1 0 0.1 0.2 0.3 0.4
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
x
z
i
i
(a)
0 1 2 3 4 5 6 7 8
−0.4
−0.2
0
0.2
T ime ( s )
x ,
z
ii
(b)
Figure 5.5: a) Fixed point at (0, 0) withµ =−1, yi = 0, α = 0.5 andω = π. b) Oscillatory harmonicsolution. The initial condition (xo,yo) = (0,−0.5), xi (solid blue line) andzi (solid red line).Theoscillator relaxes toxi = 0 andzi = 0.
5.3. CPGS 69
−1 −0.5 0 0.5 1
−1
−0.5
0
0.5
1z
xi
i
(a)
0 1 2 3 4 5 6 7 8−1
−0.5
0
0.5
1
T ime (s)
x ,
z ii
(b)
Figure 5.6: Solutions of the oscillator (4.2, 4.3). a) Limit-cycle with amplitude of 1,µ = 1, yi = 0.The initial condition (xo,yo) = (0,−0.5), α = 0.5 andω = π. b) Harmonic solution where thexvariable is the solid blue line andz is the solid red line.
The generated trajectory results in a superposition of two types of movements, rhythmic
and discrete, where the rhythmic motion can be switched on oroff by simply settingµ to
positive or negative values, respectively. When the rhythmic motion is switched off by setting
µ to a negative value, the attractor of the Hopf oscillator is no longer a limit cycle but a fixed
point specified by the offset, i.e. byyi variable.
The generated trajectories using the Hopf oscillator can besummarized as
[xi (t)zi (t)
]=
[yi0
],µ < 0
[yi +
√µ cos(ωt)√µ sin(ωt)
],µ > 0
(5.7)
This oscillator generates smooth trajectories due to stable solutions, despite small changes
in the parameters. We motivate the choice of this Hopf oscillator because it can be com-
pletely analytically solved, which facilitates the smoothmodulation of the generated trajec-
tories with respect to their amplitude and frequency (for speed change) according to small
parameter changes, while keeping the general features of the original movements.
With this oscillator we can only turn on its oscillatory activity (Fig. 5.7), stop the oscilla-
tor and generate a discrete movement (Fig. 5.8) by continuously changing the offsetyi where
the resultingxi trajectory follow this change and combining both (Fig. 5.9)by turn on the
oscillator and change the offset where the resulting harmonic xi trajectory oscillates around
the offset (yi) value.
By modifying the offset values (yi variable), we can easily modulate the generated trajec-
70 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
tories. Whatever the change is, the system converges almostimmediately to the new solution
of the system where it is easily possible verify the smoothness of the trajectory when the
parameters are changed.
0 2 4 6 8 10 12−2
−1
0
1
2
T ime(s)
xi
Figure 5.7: Oscillatory solution with an amplitude of 2.
0 2 4 6 8 10 12−4
−2
0
2
4
y
0 2 4 6 8 10 12−4
−2
0
2
4
T ime (s)
i x
,y
ii
Figure 5.8: Trajectory modulation through changes in theyi values (offset) when rhythmic motionis turned off (µ < 0). The solid blue line is thexi solution and the dashed red line isyi where theresultingxi trajectory converges asymptotically to the current value of yi .
The amplitude of oscillations, is defined by the value of√µ whenµ > 0 and it is possible
to modulate it by changing theõ value (Fig. 5.10). Att = 3 swe set the
õ value to 4 and
the generated trajectoriesxi andzi follow this change oscillating with the same amplitude.
At t = 6 sõ returns to its initial value (2) and the amplitude of the generated trajectories
are also modulated to their initial state (2). Finally, att = 8 sasõ is again changed to 4,xi
andzi are also again modulated following theõ value.
5.3. CPGS 71
0 1 2 3 4 5 6 7 8 9 10−4
−2
0
2
4y
0 2 4 6 8 10 12
−5
0
5
T ime ( s)
i x
,y
ii
Figure 5.9: Trajectory modulation through changes in theyi values (offset) when rhythmic motionis turned on (µ > 0). The solid blue line is thexi solution and the dashed red line isyi where theresulting harmonicxi trajectory oscillates around the offset (yi value).
0 2 4 6 8 10 12−4
−2
0
2
4
0 2 4 6 8 10 12
2
3
4
T ime(s)
õ
6
6
me
8
8
x ,
z ii
Figure 5.10: Amplitude modulation of the generated trajectoriesxi andzi (top) by modifying theµparameter (bottom). Thexi variable is the solid blue line and thezi is the solid red line (top figure).
Theω parameter defines the frequency of oscillations and varyingits value we can modu-
late the frequency of the generated trajectories (Fig. 5.11). Beginning with a frequency value
of 5 rad s−1, at t = 3 s its value is changed to 2rad s−1 and the oscillator promptly changes
the frequency of the generated trajectories, resulting in asmooth and responsive trajectories.
The same situations occur att = 6 s andt = 8 s where the oscillator adequately responds to
72 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
changes in frequency values.
0 2 4 6 8 10 12
−1
0
1
0 2 4 6 8 10 12
2
5
10
15
T ime (s)
ω
6
me
8
x ,
z ii
Figure 5.11: Frequency modulation of the generated trajectoriesxi andzi (top) by modifying theωparameter (bottom). Thexi variable is the solid blue line andzi is the solid red line (top figure).
The direction of the limit-cycle is controlled by the signalof parameterω. Whenω > 0
the limit-cycle rotates counter-clockwise (Fig. 5.12(a))and if ω < 0 it rotates clockwise
(Fig. 5.13(a)). This change in the limit-cycles direction results in the inversion of the gener-
ated trajectories in time.
In figure 5.12 the trajectoryxi is generated beforezi and in figure 5.13 the opposite hap-
pens.
−1.5 −1 −0.5 0 0.5 1 1.5−1.5
−1
−0.5
0
0.5
1
1.5
x
z
i
i
(a)
0 1 2 3 4 5 6 7−1
0
1
T ime(s)
x ,
zi
i
(b)
Figure 5.12: Limit-cycle directions and resulting trajectories forω > 0. a) Limit-cycle with amplitudeof 1 with ω = 10. b) Generated trajectoriesxi andzi . Thexi variable is the solid blue line and thezi
is the solid red line.
5.3. CPGS 73
−1.5 −1 −0.5 0 0.5 1 1.5−1.5
−1
−0.5
0
0.5
1
1.5
zi
xi
(a)
0 1 2 3 4 5 6 7−1
0
1
T ime(s)
x ,
z ii
(b)
Figure 5.13: Limit-cycle directions and resulting trajectories forω < 0. a) Limit-cycle with amplitudeof 1 with ω =−10. b) Generated trajectoriesxi andzi . Thexi variable is the solid blue line and thezi
is the solid red line.
The generatedxi andzi trajectories are inverted in time because the limit-cycle direction.
This oscillator generates anxi oscillatory trajectory in which the ascending and descend-
ing parts have equal durations. In order to achieve an independent control of the duration of
these parts, we employ the following equation proposed by [101],
ω =ωst
e−azi +1+
ωsw
eazi +1, (5.8)
whereω alternates between two different values,ωsw andωst, depending on the step phase
identified by the value of thezi variable. The alternation speed between these two values is
controlled bya.
By controlling the durations of the ascending and descending phase of thexi trajectory,
we are controlling the durations of the swing (Tsw) and stance (Tst) step phases, respectively.
This is achieved by settingωsw = πTsw
(swing frequency) andωst =πTst
(stance frequency).
It is thus possible to generate gaits with a desired duty factor, β , by keeping the swing
frequency constant and specifying the stance frequency according to the duty factor value as
follows,
ωst =1−β
βωsw. (5.9)
In the next figure (5.14) are demonstrated the generated trajectoriesxi and zi for two
different values ofβ . At the beginning is used aβ = 0.5 but att = 4 s this value is changed
to 0.9 and we can verify that the duration of the ascending phase (swing) inxi trajectory is
kept constant, only the duration of the descending phase (stance) changes.
74 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
0 1 2 3 4 5 6 7 8−1
−0.5
0
0.5
1
T ime (s)
Swing Stance
4
me
β = 0.5 β = 0.9
x ,
z ii
Figure 5.14: Generated trajectoriesxi (solid blue line) andzi (solid red line). ForTsw= 0.3 and initialβ = 0.5, att = 4 s theβ value is changed to 0.9.
Duringzi < 0, for ω > 0, was defined that the generatedxi trajectory describes the swing
movement of the robot and duringzi > 0 is performed the stance movement. In this situation
the stance phase is the descending trajectory making the robot walk forward.
If ω < 0, the direction of the limit cycle is inverted thus the generatedxi andzi trajectories
are also inverted. In this case the opposite happens where the stance phase is the ascending
trajectory and the robot walks backwards. These differences are better described and demon-
strated in figure 5.15 where it’s possible analyze the changes inxi andzi trajectories whenω
has positive or negative sign.
3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
−1
−0.5
0
0.5
1
T ime(s)
x ,
z ii
(a)
3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
−1
−0.5
0
0.5
1
x ,
z ii
T ime(s)
(b)
Figure 5.15: Generated trajectoriesxi (solid blue line) andzi (solid red line) for different signs ofωandβ = 0.8. a)xi andzi solutions forω < 0. b)xi andzi solutions forω > 0.
5.4. INTERLIMB COORDINATION 75
The femur joints are controlled as simple as possible: by flexing the femur to a fixed
angle during swing phase, and extending to a fixed angle during the stance phase.
5.4 Interlimb coordination
Interlimb coordination is achieved by coupling, in a given manner, the dynamics of the six
CPGs, each controlling a coxa joint. These couplings ensurethat the limbs stay synchro-
nized, and are given by:[xizi
]=
[α(µ − r2
i
)−ω
ω α(µ − r2
i
)][
xizi
]+∑
j 6=i
R(θ ij)
[0
x j+zjr j
]
wherei, j ∈ {L1,L2,L3,R1,R2,R3}. The linear terms are rotated onto each other by the
rotation matrixR(θ ij), whereθ i
j is the required relative phase between thei and j coxa
oscillators to perform the gait (we exploit the fact thatR(θ) = R−1(−θ)).
Figure 5.16 shows the resulting network of six coxa coupled Hopf oscillators, that allows
interlimb coordination for each gait of the hexapod locomotion.
Le� Front Leg Right Front Leg
Right Middle Leg Le� Middle Leg
Right Rear Leg Le� Rear Leg
θ1
2
θ2
1
θ1
3 θ2
4
θ4
6
θ3
4
1 2
3 4
5 6
θ4
2 θ3
1
θ4
3
θ5
3 θ3
5 θ6
4
θ6
5
θ5
6
Figure 5.16: Coupling Network to achieve interlimb coordination.
Table 5.1 lists the relative phases(θ ij) between the oscillators of the coupling network for
metachronal, ripple and tripod gaits [109].
Gait θ12 θ1
3 θ24 θ3
4 θ35 θ4
6 θ56
Metachronal π π3
π3 π π
3π3 π
Ripple −π −3π2
π2 π π
2π2 π
Tripod π π −π −π −π π π
Table 5.1: Relative Phases between oscillators.
76 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
In order to obtain the desired gaits we modulate a set of parameters presented in Table 5.2.
These parameters areβ , µ andωsw previously mentioned.
β µ ωsw (rad s−1)
Table 5.2: Parameter values used in the gait generation experiments.
Using this approach to interlimb coordination we obtain a network of oscillators with
controlled phase relationships, able to generate any type of behavior such as locomotion
with stable and smooth trajectories.
5.5 Gait Generation Experiments
In this work we want to generate the metachronal, ripple and the tripod hexapodal gaits,
according to the CPG-based locomotor generator. All experiments presented in this work
were done in simulation using the Webots simulator.
Parameters for experiments were chosen in regard to stability during the integration pro-
cess and to feasibility of the desired trajectories. The choice toβ , µ andωsw values followed
the Dynamixel AX-12 Servos specifications and also therefore the definitions of the Servo
Nodes for the developed model. Varying theµ andωsw values we can change the velocity of
the hexapod robot.
In these experiments, the robot walks over a plain surface and aTsw= 0.3 s is set for the
three generated gaits. The used cycle time in these experiments was 8 ms and in the three
generated gaits were used same values toβ andµ of the coxa joints.
5.5.1 Metachronal Gait
In this experiment, we setβ = 56, and the relative phases are set according to first row of
Table 5.1. The chosen parameters values in this experiment are demonstrated in Table 5.3.
β µ ωsw (rad s−1)56 100 10.47
Table 5.3: Parameter values used in metachronal gait generation experiments.
The robot moves with a velocity of≈ 0.058 m/s. It is important to refer that we calculate
the velocity of the robot in the three generated gaits using the same way to calculate the
average speed:Vm =distance(m)
time(s) .
5.5. GAIT GENERATION EXPERIMENTS 77
The planned generated coxa jointsxi trajectories are depicted in figure 5.17 as well as
the recordedxi trajectories from the servos wherei ∈ {1,2,3,4,5,6}. We can verify that the
generated trajectories are coordinated as desired.
Note that the six oscillators have a lag of a sixth of one period (60o) as expected. The
solid blue line represents L1 trajectory, solid dark green is R2 trajectory, solid red line is L2
trajectory, light blue represents R2 trajectory, dashed purple is L3 trajectory and the dashed
light green is R3 trajectory (the same nomenclature is used in the other experiments).
−10
−5
0
5
10
xi (
o)
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10
−5
0
5
10
Time (s)
x~i (
o)
Figure 5.17: Top: Generated coxa jointsxi trajectories. Bottom: Recordedxi trajectories from theservos. Solid blue line represents L1 trajectory, solid dark green is R1 trajectory, solid red line is L2trajectory, light blue represents R2 trajectory, dashed purple is L3 trajectory and dashed light green isR3 trajectory. The recordedxi trajectories are very closely to the generated onesxi .
For this gait the adjacent limbs of each half of the hexapod body (R3 and R2, R2 and R1)
are 600 out of phase and contralateral limbs (e.g. R3 and L3) are halfa period (or 1800) out
of phase.
In figure 5.18 we can verify that each recordedxi trajectory (dashed line) from de servos
is very closely to the generated onesxi (solid line) with a slight delay between them.
Readings from the touch sensors in the robot feet are presented in figure 5.19 where
SW indicates swing phase andST indicates the stance phase. This figure also presents the
recordedxi trajectories from the coxa servos for each corresponding leg.
The diagram shows that the sequence of the footfall is correct where the limbs of the
robot move like a ”wave”, one at a time with R3 striking the ground first, then R2, followed
by R1, then L3,followed by L2 and finally L1. However, L2 and R2touch the ground and
78 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
−5
0
5
10
L1
−5
0
5
10
R1
−5
0
5
10
L2
−5
0
5
10
R2
−5
0
5
10
L3
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20
−5
0
5
10
Time (s)
R3
Figure 5.18: Recordedxi trajectories from the servos (dashed line) and generated coxa jointsxi tra-jectories (solid line) for metachronal gait.
come to lift during the stance phase (see L2 and R2 panels) resulting in a different duty factor
compared with the real value. The glitches that occur are ’ignored’ in order to calculate the
actual duty factor. As our controller network is working open-loop this problem can mean
that we need to close the loop.
L1
L2
L3
R1
R2
R3
−50510
x~1 (o)
−50510
x~3 (o)
−50510
x~5 (o)
−50510
x~2 (o)
−50510
x~4 (o)
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20
−50510
x~6 (o)
Time (s)
SWST
ST
ST
ST
ST
ST
SW
SW
SW
SW
SW
Figure 5.19: Achieved footfall sequence for Metachronal gait. Below each feet sequence are depictedthe corresponding recordedxi trajectories from the coxa servos.
5.5. GAIT GENERATION EXPERIMENTS 79
5.5.2 Ripple Gait
In this experiment, we setβ = 34 and the relative phases are set according to second row
of Table 5.1. The robot moves with a velocity of≈ 0.09 m/s, slightly faster than in the
metachronal gait. For this experiment the chosen parameters values are presented in Ta-
ble 5.4.
β µ ωsw (rad s−1)34 100 10.47
Table 5.4: Parameter values used in ripple gait generation experiments.
Figure 5.20 depicts planned generated coxa jointsxi trajectories as well as the recorded
xi trajectories from the servos.
−10
−5
0
5
10
xi(o)
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10
−5
0
5
10
Time (s)
x~i (
o)
Figure 5.20: Top: Generated coxa jointsxi trajectories. Bottom: Recordedxi trajectories from theservos. Solid blue line represents L1 trajectory, solid dark green is R1 trajectory, solid red line is L2trajectory, light blue represents R2 trajectory, dashed purple is L3 trajectory and dashed light green isR3 trajectory. The recordedxi trajectories are very closely to the generated onesxi .
In this gait, trajectories for L1 (solid blue line) and R3 (dashed light green line ) are in-
phase, as well as R1 (solid dark green line) and L3 (dashed purple line) trajectories. The
adjacent legs are a quarter of a period(90o) lagged.
Figure 5.21 shows each recordedxi trajectory from de coxa servos (dashed line) and we
can verify that is very closely to the generated onesxi (solid line). Among them there is a
slight delay that not affect the generation of the gait.
The diagram of the footfall (Fig. 5.22) shows that the sequence of the footfall is correct
80 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
−5
0
5
10
L1
−10
0
10
R1
−5
0
5
10
L2
−5
0
5
10
R2
−10
0
10
L3
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20
−505
10
Time (s)
R3
Figure 5.21: Recordedxi trajectories from the servos (dashed line) and generated coxa jointsxi tra-jectories (solid line) for ripple gait.
with each leg striking the ground at the desired time. In thisfigure are also demonstrated the
recordedxi trajectories from the coxa servos for each corresponding leg in order to analyze
the behavior in the swing and stance phases.
L1
L2
L3
R1
R2
R3
−50510
x~1 (o)
−50510
x~3 (o)
−10
0
10
x~5 (o)
−10
0
10
x~2 (o)
−50510
x~4 (o)
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 200
−50510
Time (s)
x~6 (o)
o
16 16.5
SWST
SW
SW
SW
SW
SW
ST
ST
ST
ST
ST
Figure 5.22: Achieved footfall sequence for Ripple gait. Below each feet sequence are depicted thecorresponding recordedxi trajectories from the coxa servos.
But, as occur in metachronal gait generation, L2 and mainly R2 touch and come to lift
5.5. GAIT GENERATION EXPERIMENTS 81
several times during the stance phase (see L2 and R2 panels) causing a change in the actual
duty factor. The glitches that occur are also ’ignored’ in order to calculate the actual duty
factor and this situation means that there is a need to close the loop of our controller network.
5.5.3 Tripod Gait
In the tripod gait we have set aβ = 12 and the relative phases are set according to third row
of Table 5.1. A final faster velocity of≈ 0.19 m/s was achieved.
Table 5.5 describes the used parameters values for this experiment.
β µ ωsw (rad s−1)12 100 10.47
Table 5.5: Parameter values used in tripod gait generation experiments.
The planned generated coxa jointsxi trajectories are illustrated in figure 5.23 as well as
the recordedxi trajectories from the servos.
−10
−5
0
5
10
xi (
o)
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10
−5
0
5
10
Time (s)
x~
i (o
)
Figure 5.23: Top: Generated coxa jointsxi trajectories. Bottom: Recordedxi trajectories from theservos. Solid blue line represents L1 trajectory, solid dark green is R1 trajectory, solid red line is L2trajectory, light blue represents R2 trajectory, dashed purple is L3 trajectory and dashed light green isR3 trajectory. The recordedxi trajectories are very closely to the generated onesxi .
Note that, as expected, three legs are in-phase at each time.Adjacent legs are half a
period(180o) lagged. L2 (solid red line), R1 (solid dark green line) and R3(dashed light
green line) trajectories are together in-phase as well as R2(light blue line), L1 (solid blue
line) and L3 (dashed purple line) trajectories.
82 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION
Figure 5.24 shows each recordedxi trajectory from de coxa servos (dashed line) and we
can prove that is very closely to the generated onesxi (solid line) as we desire but with an
insignificant delay between them.
−10
0
10
L1
−10
0
10
R1
−10
0
10
L2
−10
0
10
R2
−10
0
10
L3
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10
0
10
Time (s)
R3
Figure 5.24: Recordedxi trajectories from the servos (dashed line) and generated coxa jointsxi tra-jectories (solid line) for tripod gait.
The feet sequence and the recordedxi trajectories from the coxa servos for each corre-
sponding leg are depicted in figure 5.25. This diagram demonstrates that each time three legs
are in contact with the ground (L1, L3, R2 and R1, R3, L2).
However, we can see that almost all legs, in small instants ofthe stance phase touch the
ground and come to lift resulting in a different duty factor compared with the real value. We
had to ’ignore’ the glitches in order to calculate the actualduty factor. As our controller
network is working open-loop this shows the need of closing the loop.
In next chapter will be discussed the switch between these three gaits using a simple
mechanism.
5.5. GAIT GENERATION EXPERIMENTS 83
L1
L2
L3
R1
R2
R3
−10
0
10
x~1 (o)
−10
0
10
x~3 (o)
−10
0
10
x~5 (o)
−10
0
10
x~2 (o)
−10
0
10
x~4 (o)
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10
0
10
Time (s)
x~6 (o)
o
ST
ST
ST
ST
ST
ST
SW
SW
SW
SW
SW
SW
Figure 5.25: Achieved footfall sequence for Tripod gait. Below each feet sequence are depicted thecorresponding recordedxi trajectories from the coxa servos.
Chapter 6
Gait Transition
An objective of this work is to switch between the three implemented gaits. For this pur-
pose a modulatory drive signal,m, is used to regulate the activity of the CPGs where its
strength initiates, stops and switches among gaits, by adjusting the needed parameters of the
oscillators.
These parameters are the amplitudeµ, the frequencyωst of the stance phase and the gait
phases(θ ij). Both the value of the stance frequency and the gait phases can be expressed as
functions of the duty factorβ .
6.1 Gait Transition Mechanism
One aim of this work is to achieve gait transition between thethree implemented gaits. In
this work a modulatory drive signal,m, is used to regulate the activity of the CPGs. Its
strength initiates, stops and switches among gaits, by adjusting the needed parameters of the
oscillators. Bellow a lower threshold of the modulatory drive,mlow, the robot stops to move.
Them values were chosen arbitrarily as well as its range.
Different values of the drive signal mean different behaviors, that is, locomotion initia-
tion, speed change and gait change. These different behaviors correspond to adjustments of
the CPG parameters, namely: amplitude, stance frequency and coupling parameters.
6.2 Initiating/stopping locomotion
By modifying theµ parameter the system switches between a stable fixed point atxi = 0
(µ < 0) and a rhythmic movement(µ > 0), meaning theµ parameter sets whether or not
there are oscillations generated by the CPG. For am below mlow = 0.2 the oscillators are
shut down and the robot stops its movement.
84
6.3. DUTY FACTOR MODULATION 85
6.3 Duty factor modulation
In this work, the metachronal gait has a duty factor of(56), the ripple gait has a duty factor
of (34) and the tripod gait has a duty factor of(1
2). As the modulatory drive increases in
strength, the duty factor linearly decreases (from(56) until (1
2)). β is defined as a piecewise
linear function of the modulatory drivem,
β =
{−0.083m2+0.166m+0.749 ,mlow < m≤ 3
0.5,m≥ 3. (6.1)
6.4 Gait phases modulation
In order to modulate the gait phases we use the adaptive gait rule from [62]. This rule states
that: 1) in consecutive legs, each leg motion has 1−β phase shift fast to fore side leg; and
2) legs of the same girdle perform the step cycle 0.5 out of phase from each other.
The adaptive gait rule is defined as a function of the duty factor. The task of change the
robot walking speed means changing the duty factor, thus this gait rule must be changed as
the walking speed changes. This rule is used because it is very hard to change the leg phases
without stopping the robot and the adaptive gait rule simplifies this process allows achieve
the desired relative phases keeping its synchronized motion.
According to these indications,(θ ij) can be mathematically defined by
θ ij =
{(1−β )2π , adjacent legs
(0.5)π , contralateral legs. (6.2)
In fact we have presented the required relative phases for the network of oscillators based
on this rule in Table 5.1.
6.5 Experiments
In order to demonstrate the implementation of this model to perform the gait transition in the
hexapod robot, several experiments were realized. The aim of these experiments is demon-
strate the smoothness and performance on gait transition when interlimb phase relationships
are progressively adjusted following the previously presented solution. We expect a smoother
locomotion when the interlimb phase relationships are changed according to the proposed
rule.
86 CHAPTER 6. GAIT TRANSITION
An abrupt transition between the gaits it is used in the first experiment, and another
experiment uses a gradual transition between the differentgaits.
In the first experiment (Fig. 6.1) the robot walks forward during the first 20 s perform-
ing the metachronal gait(β = 56) (Fig. 6.1(b)) with an initial modulatory drivem (Top fig-
ure 6.1(a)) of 1 , then att = 20s themvalue is abruptly changed to 2 and the robot performs
the transition to the ripple gait(β = 34) (Fig. 6.1(c)). Finally at instantt = 40s, m drops to 3
forcing the robot to transit to the tripod gait(β = 12) (Fig. 6.1(d)). Thenµ is set to a negative
value and the oscillators stop the movement of the robot.
But in the second experiment (Fig. 6.2), the robot only stabilizes in the ripple gait at about
t = 45sand for tripod gait the hexapod stabilizes betweent = 85sandt = 90s. These facts
occur because the transition is realized in a gradual way thus taking more time.
During this first experiment the duty factor (Bottom figure 6.1(a)) is modulated according
to changes in modulatory drive signalm value, where we can verify that in the first 20 s the
duty factor value is56 because the robot is in metachronal gait, att = 20 s the robot transits
to ripple gait and the duty factor value is abruptly changed to 34. At t = 40 s as the robot
performs the transition to the tripod gait, the duty factor value is quickly changed to12.
In figure 6.1 are demonstrated the obtained results for the abrupt transition between the
gaits, where are presented the modulatory drive signal (m) and duty factor (Fig. 6.1(a)) as
well as recordedxi trajectories from the servos for robot coxa joints (Figures6.1(b), 6.1(c)
and 6.1(d)).
In the second experiment (Fig. 6.2), it is used a gradual transition between the different
gaits.
In this experiment (Fig. 6.2) the modulatory drive signalm (Top figure 6.2(a)) starts at 1
and during the first 20 s the robot performs the metachronal gait (β = 56) (Fig. 6.2(b)) , then
at t = 20s themvalue is gradually increased to 2 with the robot performing the transition to
the ripple gait(β = 34) and the figure 6.2(c) demonstrates the recordedxi trajectories from
the servos betweent = 40 s andt = 45 s when the robot finishes the transition. Ultimately
at instantt = 40 s, m is gradually changed to 3 allowing the robot to transit to thetripod gait
(β = 12) and in figure 6.2(d) we can see the recordedxi trajectories from the servos when
the robot is finishing the transition to tripod gait. Thenµ is set to a negative value and the
oscillators stop the movement of the robot.
6.5. EXPERIMENTS 87
1
2
3
m
0 10 20 30 40 500.5
0.75
0.8
Time (s)
β
20 40
(a)
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20
−5
0
5
Time(s)
x~
i (o)
(b)
35 35.5 36 36.5 37 37.5 38 38.5 39 39.5 40
−5
0
5
Time (s)
x~
i (o)
(c)
55 55.5 56 56.5 57 57.5 58 58.5 59 59.5 60 60.5
−5
0
5
Time (s)
x~
i (o)
(d)
Figure 6.1: Abrupt Transition. a) Top: Modulatory drive,m, is abruptly changed between the gaitstransition. a) Bottom: Duty factor modulation. b) Recordedxi trajectories from the servos betweent = 15sandt = 20 swhere the robot performs the metachronal gait. c) Recordedxi trajectories fromthe servos betweent = 35 s and t = 40 s when the robot finishes the transition to ripple gait. d)Recordedxi trajectories from the servos betweent = 55 s andt = 60 s when the robot finishes thetransition to tripod gait.
For this experiment the duty factor modulation according tochanges in modulatory drive
signalmvalue is presented in bottom figure 6.2(a), where we can see that in the first 20 s the
duty factor is56 because the robot is performing the metachronal gait, att = 20 s the robot
88 CHAPTER 6. GAIT TRANSITION
transits to ripple gait and consequently the duty factor is gradually decreased to34. Finally at
t = 40s the duty factor value is continuously modulated to12 because the robot is performing
the transition to tripod gait.
1
2
3
m
0 10 20 30 40 50 60 70 80 900.5
0.75
0.8
Time (s)
β
20 40
Tim
(a)
15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20
−5
0
5
Time (s)
x~
i (o)
(b)
40 40.5 41 41.5 42 42.5 43 43.5 44 44.5 45
−5
0
5
Time (s)
x~
i (o)
(c)
85 85.5 86 86.5 87 87.5 88 88.5 89 89.5 90
−5
0
5
Time (s)
x~
i (o)
(d)
Figure 6.2: Gradual Transition. a) Top: Modulatory drive,m, is gradually changed between the gaitstransition. a) Bottom: Duty factor modulation. b) Recordedxi trajectories from the servos betweent = 15sandt = 20 swhere the robot performs the metachronal gait. c) Recordedxi trajectories fromthe servos betweent = 40 s and t = 45 s when the robot finishes the transition to ripple gait. d)Recordedxi trajectories from the servos betweent = 85 s andt = 90 s when the robot finishes thetransition to tripod gait. In this situation the robot takesmore time to achieve the desired behaviors.
Next will be described another experiment with a different sequence of gait change. In
this experiment the gait transition not begin in metachronal gait and not finishes in tripod
6.5. EXPERIMENTS 89
gait but is performed in an alternated way.
In this experiment (Fig. 6.3) the modulatory drive signalm (Top figure 6.3(a)) starts at 3
and during the first 10 s the robot performs the tripod gait(β = 12) where in figure 6.3(b)) are
displayed the recordedxi trajectories from the servos for the first 5 s. Then att = 10 s them
value drops to 2 , forcing a quick change from tripod to ripple(β = 34) gait and figure 6.3(c)
demonstrates the recordedxi trajectories from the servos betweent = 10sandt = 15swhen
the robot starts the transition to ripple gait. In figure 6.3(d) are demonstrated the recordedxi
trajectories for final instants (betweent = 25 s andt = 30 s) of the transition to ripple gait.
Finally at instantt = 30 s, m is gradually reduced down to 1, (top fig. 6.3(a)). In fig-
ure 6.3(e) are shown the last moments of the transition to metachronal gait. Thenµ is set to
a negative value and the oscillators stop the movement of therobot.
The duty factor value during the gait transitions is demonstrated in the bottom of fig-
ure 6.3(a), where it is possible to verify that in the first 10 sthe duty factor value is12 because
the robot is in tripod gait, att = 10 s the robot makes the transition to ripple gait and the
duty factor value is abruptly changed to34 and remains in this value untilt = 30 s where the
hexapod switches to metachronal gait and the duty factor value is gradually increased to56.
In the last experiment we can verify that the robot changes its gait by simply adjusting
the modulatory drive signal value and consequently the dutyfactor. However this duty factor
is planned and would be interesting to analyze the real duty factor. With this aim we have
also measured touch sensors from the feet in order to verify the actual duty factor.
In figures 6.4, 6.5, 6.6 and 6.7 are demonstrated the feet sequence for the different instants
of the last experiment.
Analyzing, for example, the last instants (Fig. 6.7) of the experiment (i ∈ {1,2,3,4,5,6}),
following the figure 5.16 that demonstrates the resulting network of six coxa coupled Hopf
oscillators, the robot performs the transition to metachronal gait. We can see that R2 touches
and lifts during the stance phase resulting in a different duty factor compared with the real
value (SW indicates swing phase andST indicates the stance phase). In order to calculate
the actual duty factor we had to ’ignore’ the glitches that occurred. Our controller network
is working open-loop and this shows the need of closing the loop.
90 CHAPTER 6. GAIT TRANSITION
0
1
2
3
m
0 10 20 30 40 50 600.5
0.7
0.8
Time (s)
β
10
e (s)
30
(a)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
−5
0
5
x~
i (o)
Time (s)
(b)
10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15
−5
0
5
Time (s)
x~
i (o)
(c)
25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30
−5
0
5
Time (s)
x~
i (o)
(d)
55 55.5 56 56.5 57 57.5 58 58.5 59 59.5 60
−5
0
5
Time (s)
x~
i (o)
(e)
Figure 6.3: a) Top: Modulatory drive,m, is abruptly changed to 2 att = 10 s when the robot is per-forming the transition between tripod gait and ripple gait.Fromt = 30s, m, is gradually decreased inorder to achieve the metachronal gait. a) Bottom: Duty factor modulation. b) Recordedxi trajectoriesfrom the servos betweent = 0 sandt = 5 swhen the robot is in tripod gait. c) Recordedxi trajectoriesfrom the servos betweent = 10 s andt = 15 swhere the robot is starting the transition to ripple gait.d) Recordedxi trajectories from the servos betweent = 25 s andt = 30 s when the robot is in fullripple gait. e) Recordedxi trajectories from the servos between 55sand 60swhen the robot is alreadyperforming the metachronal gait.
6.5. EXPERIMENTS 91
L1
L2
L3
R1
R2
R3
−10
0
10x~
1 (o)
−10
0
10
x~
3 (o)
−10
0
10
x~
5 (o)
−10
0
10
x~
2 (o)
−100
10
x~
4 (o)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−10
0
10
Time (s)
x~
6 (o)
SWST
11
SW
SW
SW
SW
SW
ST
ST
ST
ST
ST
Figure 6.4: Feet Sequence betweent = 0 s and t = 5 s. L1, L2, L3, R1, R2 andR3 demonstratethe readings from the touch sensors from these legs.x1, x2, x3, x4, x5 and x6 present the recordedtrajectories from coxa servos for the respective legs(L1,L2,L3,R1,R2 and R3).
L1
L2
L3
R1
R2
R3
−10
0
10
x~
1 (o)
−10
0
10
x~
3 (o)
−10
0
10
x~
5 (o)
−10
0
10
x~
2 (o)
−10
0
10
x~
4 (o)
10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15−10
0
10
Time (s)
x~
6 (o)
1111 11.511.5
SWST
SW
SW
SW
SW
SW
ST
ST
ST
ST
ST
Figure 6.5: Feet Sequence betweent = 10 s andt = 15 s. L1, L2, L3, R1, R2 andR3 demonstratethe readings from the touch sensors from these legs.x1, x2, x3, x4, x5 and x6 present the recordedtrajectories from coxa servos for the respective legs(L1,L2,L3,R1,R2 and R3).
92 CHAPTER 6. GAIT TRANSITION
L1
L2
L3
R1
R2
R3
−10
0
10
x~
1 (o)
−10
0
10
x~
3 (o)
−10
0
10
x~
5 (o)
−10
0
10
x~
2 (o)
−10
0
10
x~
4 (o)
25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30−10
0
10
Time (s)
x~
6 (o)
26.
SW
SW
SW
SW
SW
SW
ST
ST
ST
ST
ST
ST
Figure 6.6: Feet Sequence betweent = 25 s andt = 30 s. L1, L2, L3, R1, R2 andR3 demonstratethe readings from the touch sensors from these legs.x1, x2, x3, x4, x5 and x6 present the recordedtrajectories from coxa servos for the respective legs(L1,L2,L3,R1,R2 and R3).
L1
L2
L3
R1
R2
R3
−10
0
10
x~
1 (o)
−10
0
10
x~
3 (o)
−10
0
10
x~
5 (o)
−10
0
10
x~
2 (o)
−10
0
10
x~
4 (o)
55 55.5 56 56.5 57 57.5 58 58.5 59 59.5 60−10
0
10
Time (s)
x~
6 (o)
SW
SW
SW
SW ST
ST
ST
ST
ST
SW ST
SW
Figure 6.7: Feet Sequence betweent = 55 s andt = 60 s. L1, L2, L3, R1, R2 andR3 demonstratethe readings from the touch sensors from these legs.x1, x2, x3, x4, x5 and x6 present the recordedtrajectories from coxa servos for the respective legs(L1,L2,L3,R1,R2 and R3).
Next chapter will be proposed a lateral posture controller using the dynamical systems
approach and will be tested in different situations in whichthe hexapod robot is expected to
6.5. EXPERIMENTS 93
maintain balance. Moreover, a set of biological principlesbased mechanisms that improve
the hexapod locomotion will be also demonstrated and explained.
Chapter 7
Posture Control
In locomotion overall architecture of this work we also include a lateral posture mechanism
to compensate the robot lateral tilt which will be discussedin this chapter.
7.1 Lateral Posture Control
The overall architecture used in this work (fig. 5.4) also includes a lateral posture mechanism
that automatically corrects the body orientation of the robot in respect to lateral inclination.
Parallel to the network of CPGs, a lateral posture mechanismacts on the limbs to correct the
body’s orientation through the value of roll displacement of the body, correcting the posture
and adapting the locomotion on inclined terrains by generating discrete trajectories for the
femur and tibia. The lateral tilt of the robot is measured using accelerometers.
The main aim of this posture control is, by measuring the lateral tilt of the robot body,φ ,
we want to stretch the legs towards which the robot is tilted and fold the other legs (fig. 7.1),
thus reducing the robot lateral tilt and keeping the body parallel to the ground (in this case
a moveable platform). This aim is achieved modulating and adjusting the femur and tibia
joints values that are controlled by dynamical systems.
94
7.1. LATERAL POSTURE CONTROL 95
Hexapod Robot Front View
(a)
(b)
(c)
Figure 7.1: Lateral posture control. Process of stretch andfold the legs. a) Robot stretching the rightlegs and folding the left legs. b) Normal position of the robot. c) Robot stretching the left legs andfolding the right legs.
In our approach we compensate lateral displacement of the body by increasing or de-
creasing leg height on both sides, performed by changing theangles of the femur and tibia
joints. These angles are controlled by discrete movements,generated by a nonlinear dynam-
ical system designed to find the neutral point of lateral posture of the robot, reducing the roll
to a minimum. The dynamical system is given by
˙yo,i = ko, j ,i f (φ)+α(yo,i −Mo,i)e− (yo,i−Mo,i )
2
2σ2
+α(yo,i −Do,i)e− (yo,i−Do,i )
2
2σ2 , (7.1)
is applied to the femur (F) and tibia (T) joints (o = F,T) whereko, j ,i ( j =left,right andi,∈{L1,L2,L3,R1,R2,R3}) is a static gain, set symmetrically for the right and left legs.
Function f (φ) defines a dead zone for the robot’s roll angleφ (fig. 7.2).
96 CHAPTER 7. POSTURE CONTROL
f (φ)
φ00.2- 0.2
0.8 φ
Figure 7.2: Functionf (φ). When−0.2< φ > 0.2, f (φ) has the value zero and elsewheref (φ) hasthe value 0.8φ .
The limits of operation for the system are given by the valuesMi (maximum) andDi
(minimum). These values were chosen following the joints limits values of the real robot.
The correspondence between the system and the leg’s joint isdescribed by the scheme
presented in figure 7.3.
Femur
Tibia
Coxa
yFemur
yTibia
~ xCoxa
Figure 7.3: Posture control scheme where only the used structure to one leg of the hexapod is demon-strated since the procedure for the other legs is the same.
Only the coxa joints perform a rhythmic motion, provided by the six coupled CPGs. The
discrete movements are applied to the femur and tibia joints, changing the height of the leg,
reducing the lateral tilt to a minimum.
7.2. EXPERIMENTS 97
Table 7.1: Parameter values used in the posture control experiments.k j,i α σ MF,i DF,i MT,i DT,i
15 5000 0.1 100o −100o 160o −60o
7.2 Experiments
To demonstrate the role of the lateral posture control, we realize some experiments where
the simulated Chiara robot walks with a metachronal gait on the top of a moveable platform,
subject to different lateral inclinations, reacting to changes in its lateral tilt. The maximum
that the moveable platform could be inclined is 20◦. In Table 7.1 the chosen configuration
parameters are presented.
The robot must counteract the effects of the platform inclination on the robot body, reduc-
ing the sensed roll angle measured by accelerometers to values belonging to a small region
around zero as defined by the dead-zone.
For the first experiment the top panel of figure 7.4 shows the change of the platform
inclination in dashed red line. The robot walks forward during the first 10 s without any
lateral tilt change. Fromt = 10 s tot = 20 s, the platform is gradually inclined to the left up
to 7◦, while the robot remains walking. We can see that the robot successfully counteracts
the platform inclination, maintaining the body roll angle close to 0◦, counteracting the body’s
lateral tilt, stretching the left legs and folding the rightlegs.
Snapshots of the experiment are presented in figure 7.5, showing the inclination that
the robot is subjected and its reaction in order to maintain the body orientation. In fig-
ures 7.5(b), 7.5(c) and 7.5(d) we can visualize the robot stretching the left legs because the
platform is inclined to the left side and folding the right legs.
In figures 7.4(b) and 7.4(c) are demonstrated theyFemur and yTibia trajectories for the
left front leg (solid blue line) and right front leg (dashed red line) that while the platform is
inclined they compensate the robot lateral tilt in order to maintain the body roll angle close to
0◦, exhibiting symmetric trajectories, as expected. In figures 7.4(d) and 7.4(e) are presented
the yFemur and yTibia trajectories for the left front leg (solid blue line) and right front leg
(dashed red line) where as greater the lateral tiltφ change greater is the value of ˙yFemur and
yTibia trajectories.
Betweent = 20 s andt = 30 s the platform is gradually shifted to the right up to 15◦.
Again, the robot successfully maintains its lateral tilt near 0◦, this time, by stretching the
98 CHAPTER 7. POSTURE CONTROL
right legs and folding the left as we can see in figures 7.5(e),7.5(f), 7.5(g) and 7.5(h).
5 10 15 20 25 30 35
−10
−5
0
5
φro
bo
t, p
latf
. (° )
(a)
5 10 15 20 25 30 35
−20020
yF
(° )
(b)
5 10 15 20 25 30 35−20020
yT
(° )
(c)
5 10 15 20 25 30 35−20
0
20
y. F (
° )
(d)
5 10 15 20 25 30 35
−10
0
10
y. T (
° )
(e)
Time (s)
10
10
10
10
20
20
(d
(c
(b
20
20
(a
(e
30
30
30
30
Figure 7.4: Posture control experiments: a) Lateral tiltφ of the robot (solid blue line) and platforminclination (dashed red line). b)yFemur trajectories for the left front leg (solid blue line) and rightfront leg (dashed red line). c)yTibia trajectories for the left front leg (solid blue line) and right frontleg (dashed red line). d) ˙yFemur trajectories for the left front leg (solid blue line) and right front leg(dashed red line). e) ˙yTibia trajectories for the left front leg (solid blue line) and right front leg (dashedred line).
In figure 7.6 we study with more detail the first experiment during t = 20 s untilt = 30 s
in order to demonstrate the response of the system. The vertical dashed lines of the figure
indicate three important instants of time where the changesin lateral tilt of the robot are more
abrupt. In middle and bottom panels of the figure we can verifythat in this three instants
yFemur and yTibia have greater values because as greater the lateral tiltφ change, greater is
the value of these trajectories. This figure also shows that the time to compensate posture is
very low depending of servos features and following the limits of operation for the system.
7.2. EXPERIMENTS 99
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure 7.5: Robot behavior during the posture control in first experiment. a)t = 2 s. b)t = 10 s.c) t = 12 s. d)t = 16 s. e)t = 20 s. f)t = 26 s. g)t = 28 s. h)t = 30 s.
The aim of second experiment (fig. 7.7) is describe a different situation that the robot is
subjected. In this case the robots also walks forward duringthe first 10 s without any lateral
tilt change and fromt = 10 s tot = 20 s, the moveable platform is progressively inclined up
to 7◦ to the left side while the robot remains its normal walking.
In top panel of figure 7.7 we can see that the robot counteractsthe platform inclination,
maintaining the body roll angle close to 0◦, stretching the left legs and folding the right legs
as desired.
100 CHAPTER 7. POSTURE CONTROL
20 21 22 23 24 25 26 27 28 29 30
−10
−5
0
7
φro
bo
t, p
latf
. (° )
20 21 22 23 24 25 26 27 28 29 30
−20
−10
0
10
20
y. F (
° )
20 21 22 23 24 25 26 27 28 29 30
−10
0
10
y.
T (
° )
Time (s)
21
21
Figure 7.6: Posture control experiments: Top figure: Lateral tilt φ of the robot (solid blue line) andplatform inclination (dashed red line); Middle figure: ˙yFemur trajectories for the left front leg (solidblue line) and right front leg (dashed red line); Bottom figure: yTibia trajectories for the left front leg(solid blue line) and right front leg (dashed red line).
In figure 7.8 are presented some snapshots of the experiment where are demonstrated the
different reactions of the robot to maintain the balance when subjected to different inclina-
tions of the platform.
Betweent = 10 s and 20 s the platform is inclined to the left side, the robot reacts stretch-
ing the left legs and folding the right legs as we can verify infigures 7.8(a), 7.8(b) and 7.8(c).
While the platform is inclined the lateral tilt of the robot is compensated in order to maintain
the body roll angle close to 0◦. Figures 7.7(b) and 7.7(c) demonstrate the behavior ofyFemur
andyTibia trajectories for the left front leg (solid blue line) and right front leg (dashed red
line) that exhibit symmetric trajectories and compensate the robot lateral tilt.
Figures 7.7(d) and 7.7(e) present ˙yFemur andyTibia trajectories for the left front leg (solid
blue line) and right front leg (dashed red line). We can verify that the value of these tra-
jectories increases and decreases as the lateral tiltφ change is greater or less varying in a
proportion way.
7.2. EXPERIMENTS 101
5 10 15 20 25 30 35
0
5
10
φrobot, p
latf
. (° )
(a)
5 10 15 20 25 30 35
−200
20
yF
(° )
(b)
5 10 15 20 25 30 35−20
0
20
yT
(° )
(c)
5 10 15 20 25 30 35
−20
0
20
y. F (
° )
(d)
5 10 15 20 25 30 35−20
0
20
y. T (
° )
(e)
Time (s)
10
10
10
10
(e
20
(d
20
20
(b
20
20
(a
30
30
30
30
Figure 7.7: Posture control experiments: a) Lateral tiltφ of the robot (solid blue line) and platforminclination (dashed red line). b)yFemur trajectories for the left front leg (solid blue line) and rightfront leg (dashed red line). c)yTibia trajectories for the left front leg (solid blue line) and right frontleg (dashed red line). d) ˙yFemur trajectories for the left front leg (solid blue line) and right front leg(dashed red line). e) ˙yTibia trajectories for the left front leg (solid blue line) and right front leg (dashedred line).
Fromt = 20 s tot = 22 s the moveable platform is inclined up to 5◦ to the right side and
the robot maintains its lateral tilt near 0◦ but in this case stretching the right legs and folding
the left legs as we can see in figures 7.8(d), 7.8(e) and 7.8(f).
Finally, betweent = 22 s tot = 30 s the platform is again inclined to the left side up to
15◦ and the robot again reacts successfully keeping its lateraltilt near 0◦, by stretching the
left legs and folding the right. In order to achieve a better analysis of this situation we can
visualize figures 7.8(g), 7.8(h) and 7.8(i) where while the platform leans to the left side, the
robot stretches the left legs and folds the right, as expected.
In third experiment the main goals are demonstrate the reaction of the robot when sub-
jected to an abrupt inclination of the moveable platform that sustains its body and verify the
time it takes to respond to the abrupt change as well its behavior during this situation.
During the first 10 s nothing happens in the robot behavior because it walks forward
without any change in platform inclination.
102 CHAPTER 7. POSTURE CONTROL
But, fromt = 10 s tot = 20 s, the moveable platform is gradually inclined up to 7◦ to the
left side. In figure 7.9(a) we can verify that the robot remains its normal walking counter-
acting the platform inclination, keeping the body roll angle close to 0◦ as desired, stretching
the left legs and folding the right legs. Some snapshots of this experiment are shown in fig-
ure 7.10 where are demonstrated the several reactions and behaviors of the robot to keep the
balance when subjected to different inclinations of the platform. In order to verify the behav-
ior of the robot betweent = 10 s andt = 20 s, we can see the figures 7.10(a), 7.10(b), 7.10(c)
and 7.10(d) where the robot reacts stretching the left legs and folding the right legs. Fig-
ures 7.9(b) and 7.9(c) demonstrate the behavior ofyFemur andyTibia trajectories for the left
front leg (solid blue line) and right front leg (dashed red line). These trajectories are sym-
metric and compensate the robot lateral tilt maintaining the body roll angle close to 0◦ while
the platform is inclined. Figures 7.9(d) and 7.9(e) presentyFemur andyTibia trajectories for
the left front leg (solid blue line) and right front leg (dashed red line) where we verify that
vary in a proportion way to the lateral tiltφ change.
7.2. EXPERIMENTS 103
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i)
Figure 7.8: Robot behavior during the posture control in second experiment. a)t = 10 s. b)t = 15 s.c) t = 20 s. d)t = 21 s. e)t = 21.5 s. f) t = 22 s. g)t = 24 s. h)t = 27 s. i)t = 30 s.
At t = 20 s the moveable platform is abruptly inclined up to 7◦ to the right side and the
robot maintains its lateral tilt near 0◦.
From∼ t = 20.1 s to t = 30 s the platform is again inclined to the left side up to 15◦
104 CHAPTER 7. POSTURE CONTROL
and we verify that the robot maintains its lateral tilt near 0◦, by stretching the left legs and
folding the right as demonstrated in figures 7.10(e), 7.10(f), 7.10(g) and 7.10(h).
In figure 7.11 we can visualize and analyze with more detail the reaction of the robot
at t = 20 s when the platform is abruptly inclined. Top panel of thisfigure presents the
lateral tilt φ of the robot (solid blue line) and platform inclination (dashed red line), middle
panel demonstrates ˙yFemur trajectories for the left front leg (solid blue line) and right front
leg (dashed red line) and bottom panel shows the behavior of ˙yTibia trajectories for the left
front leg (solid blue line) and right front leg (dashed red line).
The two vertical dashed lines of the figure indicate the beginning and end of the robot
compensation to the abrupt change in platform inclination in order to keep its lateral tilt near
0◦. We can verify that the compensation begins att ≃ 20.04 s and ends att ≃ 20.08 s. So,
the robot takes about 0.04 s to respond to the abrupt inclination of the moveable platform.
5 15 25 350
5
10
φro
bo
t, p
latf
. (° )
(a)
5 10 15 20 25 35−50
0
50
yF
(° )
(b)
5 10 15 20 25 30 35−40−2002040
yT
(° )
(c)
5 10 15 20 25 30 35
−20
0
20
y. F (
° )
(d)
5 10 15 20 25 30 35
−20
0
20
y. T (
° )
(e)
Time (s)
10
10
10
10
20
20
(d
20
(c
(b
20
(a
(e)
Time (s)
30
30
30
Figure 7.9: Posture control experiments: a) Lateral tiltφ of the robot (solid blue line) and platforminclination (dashed red line). b)yFemur trajectories for the left front leg (solid blue line) and rightfront leg (dashed red line). c)yTibia trajectories for the left front leg (solid blue line) and right frontleg (dashed red line). d) ˙yFemur trajectories for the left front leg (solid blue line) and right front leg(dashed red line). e) ˙yTibia trajectories for the left front leg (solid blue line) and right front leg (dashedred line).
.
7.2. EXPERIMENTS 105
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure 7.10: Robot behavior during the posture control in third experiment. a)t = 10 s. b)t = 15 s.c) t = 19 s. d)t = 20 s. e)t = 23 s. f)t = 26 s. g)t = 28 s. h)t = 30 s.
In the next chapter will presented the conclusions retired from the realization of this work,
through the discussion of the obtained results and comparing with the initial aims. Also, will
be addressed future proposals in order to continue innovating and improving the developed
work.
106 CHAPTER 7. POSTURE CONTROL
5 10 15 20 25 30 35
0
5
10
φro
bo
t, p
latf
. (° )
Time (s)
20 20.01 20.02 20.03 20.04 20.05 20.06 20.07 20.08 20.09 20.1−20
−10
0
10
20
20 20.01 20.02 20.03 20.04 20.05 20.06 20.07 20.08 20.09 20.1
−10
0
10
y. T (
° )
Time (s)
y. F (
° )
20.04
20.04 20.08
20.08
Response time to abrupt inclination
Figure 7.11: Posture control experiments: Top figure: Lateral tilt φ of the robot (solid blue line) andplatform inclination (dashed red line); Middle figure: ˙yFemur trajectories for the left front leg (solidblue line) and right front leg (dashed red line); Bottom figure: yTibia trajectories for the left front leg(solid blue line) and right front leg (dashed red line).
.
Chapter 8
Conclusions
The main goal of this work is, initially, start a detailed study of the type of existing hexapod
robots and the several models of bio-inspired controllers to reproduce their locomotion.
The first step was the choose of a real hexapod robot in order todevelop it simulation
model to perform the all desired tests. We describe the development of a hexapod robot
called Chiara in the Webots simulator.
The development of a simulation model allows us to equip eachrobot with a large number
of available sensors and actuators to program these robots,simulate them and optionally
transfer the resulting programs onto our real robots.
In this work we address the problem of generate the most common hexapodal gaits and
also smoothly switch among these according to changes in thewalking velocity to achieve
stable locomotion.
During this work we only address the three most common hexapodal gaits that are
metachronal gait (”wave gait”) specifying slow walking, ripple gait corresponding to a medium
speed gait and the fast speed tripod gait.
In order to achieve smooth walking from low speed to high speed, robotic gait switching,
similarly to their biological counterparts, should take place continuously with both the duty
factor and the interlimb phase relationships properly adjusted.
The developed architecture is formulated in terms of nonlinear dynamical systems. The
locomotor controller is stratified in three layers, allowing to functionally separate the several
components, facilitating its development.
For the purpose of this work, a model for a CPG was proposed in order to generate the
required movements for each limb of the hexapod robot. It wasdesigned applying nonlinear
dynamical systems approach, which present several advantages which allowed to coordinate
107
108 CHAPTER 8. CONCLUSIONS
all the joints in a limb in order to perform the movements of a step . The movements of each
limb results of trajectories generated on-line in a modularway.
In the first layer (lower level) of this work, is proposed a coordinated network of CPGs
modeled by nonlinear oscillators that it is responsible to control the locomotion of a hexapod
robot for the most common gaits, with independent step phasedurations.
In order to smoothly switch among the different hexapodal gaits, it was also developed a
second layer, which sends the appropriate set of parametersto the first layers CPGs according
to the desired motor programs. These motor programs includeinitiation, regulation and stop
CPGs activity, therefore initiate a walking gait, switch among gaits and stop the locomotion.
This layer receives a modulatory signal that regulates the CPGs activity and its strength is
mapped onto different sets of the CPG parameters resulting in the different motor behaviours.
Further, in this work we also address the situation of loss ofrobot balance due to pertur-
bation situations.
Additionally, in order to solve this problematic we proposea lateral posture control based
on the use of dynamical systems.
The idea is to make it possible to correct the robot posture and keep its balance when
subjected to changes in its lateral tilt (roll). By measuring the roll angle of the robot, the
system uses this information in order to compensate the tiltchanges and reduce them near to
zero.
8.1 Results Discussion
The experiments results were all obtained in simulation environment using Webots simulator.
These results demonstrated that the proposed controller iscapable of successfully gener-
ate the most common hexapodal gaits.
Further, the results demonstrate that using a simple command, a drive signal, allows
velocity control and the switching between three differentgaits.
Results also show that the lateral posture controller is able to maintain the roll angle
around zero, even when the robot walks in planes with a lateral inclination.
To conclude, the objectives initially proposed for this thesis were successfully accom-
plished.
8.2. FUTURE WORK 109
8.2 Future Work
Future work includes to achieve more complex postural control. The aim is to provide all
the capacities to the hexapod robot in order to walk on uneventerrain with different kind of
obstacles such as holes, terrain elevations and rocks. Thisability will require more robustness
to the locomotion controller. Some work and research have been carried in order to solve
this problem using biological inspiration, [89], [123].
Other important aims to future work include to achieve omnidirectional locomotion; par-
tially injured legs; homing and learning in hexapod robots.
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