institute for software technology

Gerald Steinbauer

Institute for Software Technology

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Mobile Robots - Locomotion

Mobile RobotsLocomotion

Gerald SteinbauerInstitute for Software Technology

Gerald Steinbauer


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Course Outline

1. Introduction to Mobile Robots2. Locomotion3. Sensors4. Localization5. Environment Modelling6. Reactive Navigation

Gerald Steinbauer


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Today’s Agenda

• Motivation for Locomotion• Basic Definitions• Legged Locomotion• Wheeled Locomotion• Properties of Locomotion and their Application• Feedback Control

Gerald Steinbauer


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Literature

Introduction to Autonomous Mobile Robots. 2nd Edition. Roland Siegwart, Illah Reza Nourbakhsh, DavideScaramuzza. MIT Press. 2011.

Springer Handbook of Robotics. Bruno Siciliano and Oussama Khatib.

Springer. 2008.

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Again, Robotics is Easy …

environment/worldsensing

informationextraction

raw data

acting

pathexecution

actuatorcommands

domainmodel

environmentmodel

pathplanning

navigation

perc

eptio

nm

odel

ling

beha

vior

cont

rol

planning reasoning

cognition

task

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Locomotion

• Oxford Dictionary: movement or the ability to movefrom one place to another

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Locomotion

• a mobile robot needs locomotion

• has a long history in nature

• different optimizations for• speed• stability• efficiency

http://www.youtube.com/watch?v=TIFoWAZ0EEg

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Locomotion in Biological Systems[S

iegwart, N

ourbakhsh, Scaram

uzza, 2011, MIT P

ress]

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Inspiration by Nature

• biological locomotion is hard to replicate• mechanical complexity• duplication• miniaturization• actuation• energy storage

[Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press]

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Efficiency I


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Efficiency II[S

icillano, Khatib, 2008, S

pringer]

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Key Issues of Locomotion

• stability• number and geometry of contact points• center of gravity• static/dynamic stability• inclination of the terrain

• characteristics of contact• contact points/path size and shape• angle of contact• friction

• type of environment• structure• medium, e.g. water, air, soft or hard ground

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Dimensionality

• the degree of freedom (DOF) of a workspace is its overall dimensionality• on (flat) ground DOF=3• in the air or below water DOF=6

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Legs versus Wheels[S

iegwart, N

ourbakhsh, Scaram

uzza, 2011, MIT P

ress]

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Zero Moment Point Movement (ZMP)

• commonly used method for stable walking• ZMP is defined as that point on the ground at which

the net moment of the inertial forces and the gravity has no component along the horizontal axes (Vukobratović and Branislav)

[Sicillano, Khatib, 2008, Springer]

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Zero Moment Point Movement

• suppose a legged robot comprising several bodies

• … force vector acing on body (gravity plus external)

• … angular velocity of body • … inertia tensor (∈ ) of

body • … relative position

of body to ZMP [Sicillano, Khatib, 2008, Springer]

≡ 0,0,∗

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Requirements for ZMP

• a robot able to use ZMP needs:• there are at least six

fully actuated joints for each leg

• the joints are positioncontrolled

• the feet are equipped with force sensors, which are used to measure the ZMP

http://www.youtube.com/watch?v=3aOuQ1_e--k

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Wheel Types

Side View

Front View

Top View

standard castor Swedish spherical


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Typical Arrangements (2 and 3 Wheels)2 Wheels

3 Wheels

[Siegw

art, Nourbakhsh, S

caramuzza, 2011, M

IT Press]

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Typical Arrangements ( 4 Wheels)

http://www.youtube.com/watch?v=XzkC4Ez8GYE

[Siegw

art, Nourbakhsh, S

caramuzza, 2011, M

IT Press]

http://www.youtube.com/watch?v=8sH1a511_q4

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Advanced Mechanisms

• NASA Mars Rover - Rocker-Bogie

• hybrid between walking and driving

• allows to climb obstacles

• reduce movement of body

http://www.youtube.com/watch?v=BC441bV1wFc

[Nasa/JPL]

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Other Forms of Locomotion

• in the air • below water

http://www.youtube.com/watch?v=9Vm-gQ9_H9Ihttp://www.youtube.com/watch?v=4ErEBkj_3PY

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Homogeneous Transformation

• we need a transformationbetween the motion in the reference frame and the robot frame

• the transformation depend on the global angle

, ,

, ,

cos sin 0sin cos 00 0 1

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Kinematic Constraints

• an arrangement comprises wheels of differenttypes

• each wheel provides an individual velocity and individual parameters, e.g. steering anlge

• to determine the maneuverability of an attunement we use 2 sorts of constraints• rolling constraints: all motions in the wheel plane have to be

accompanied with the appropriate wheel spin• sliding constraints: the motion orthogonal to the wheel has to be

zero

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Fixed Standard Wheel

sin cos cos 0 RKC

cos sin 0 SKC

, ,

[Siegw

art, Nourbakhsh, S

caramuzza, 2011, M

IT Press]

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Steered Standard Wheel

sin cos cos 0 RKC

cos sin 0 SKC

, ,

same as fixed standard wheel expect steering is now a function of time

[Siegw

art, Nourbakhsh,

Scaram

uzza, 2011, MIT P

ress]

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Swedish Wheel

sin cos cos cos 0 RKC

cos sin sin 0 SKC

[Siegw

art, Nourbakhsh,

Scaram

uzza, 2011, MIT P

ress]

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Spherical Wheel

sin cos cos 0 RKC

cos sin 0 SKC

same as fixed standard wheel expect steering is now a free variable

[Siegw

art, Nourbakhsh,

Scaram

uzza, 2011, MIT P

ress]

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Combining the Constraints I

• the wheel arrangement comprises fixed and steerable wheels,

• denotes the steering angles while denotes all fixed angles

• denotes wheel speed of the fixed wheels while denotes wheel speed of the steered wheels,

denotes the combination

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Combining the Constraints II

0 with and

0 00 ⋱ 00 0

Rolling Constraints

0 with

Sliding Constraints

0

All Together

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Maneuverability

• we can use the constraints to investigate the mobilitypotential of a robot

• the degree of mobility• is defined as: 3• represents the number of DOF that can immediately manipulated

by changes in the wheel velocities• related to the location of the instantaneous center of rotation (ICR)

• the degree of steerability• is defined as: • 0 2 … depends on the number of steerable wheels

• robot maneuverability•• related to the DOF a robot is able to manipulate

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Application of Constraints

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Automatic Reconfigurable Omni-Drive

[Brandstötter, Hofbauer, Steinbauer, Wotawa – IROS 2007]

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Automatic Reconfigurable Omni-Drive

motor 1 fails motor 2 fails motor 3 fails

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(Non)-Holomorphic[S

iegwart, N

ourbakhsh,S

caramuzza, 2011, M

IT Press]

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Feedback Control

• move a differential drive to a goal• non-holonomic constraints – we

need differential inverse kinematics

[Siegw

art, Nourbakhsh,

Scaram

uzza, 2011, MIT P

ress]

⋅

lim→

0

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Control Law

[Siegwart, Nourbakhsh,Scaramuzza, 2011, MIT Press]3, 8, 1.5

⋅+

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Questions?Thank you!

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