2013 13th International Conference on Control, Automation and Systems (ICCAS 2013) Oct. 20-23, 2013 in Kimdaejung Convention Center, Gwangju, Korea

Synchronized Coordination for Omni-directional Mobile Robot with

Hemi-circular Wheels using Neural Oscillator

Sajjad Manzoor, Seonghan Lee, and Youngj in Choi*

Electronic Systems Engineering, Hanyang University, 426-791, South Korea (E-mail: sajjadm266@hanyang.ac.kr.areafort@hanyang.ac.kr.cyj@hanyang.ac.kr ) * Corresponding author

Abstract: The paper presents an application example of neural oscillator for synchronized wheel coordination of omni-directional mobile robot with hemi-circular wheels. In this paper, a six neuronal network drives three hemi-circular wheels of the robot. The velocity of each wheel is controlled by coupled neuron firing. These neurons are synchronized, activated, and suppressed according to the required motion. Unlike usual motion, the movement generated from the neural oscillator is normally oscillatory one for the hem i-circular wheels.

Keywords: Neural Oscillator, Coupled oscillator, Central Pattern Generator (CPG), Omni-directional Mobile Robot.

1. INTRODUCTION

These days the CPG-based motion generation for legged robots [1], crawling robots [2], and modular robots [3] has been utilized for the robot control. The CPG gives us the bio-inspired movements that are human-like or resemble some animals or insects. All these robots exhibit rhythmic locomotion, which is the feature of daily life locomotion. But, in mobile robots, the motions can be classified with turning, moving to goal in straight line and turning to final orientation [4,5]. There is rare possibility of rhythmic movement in the wheeled robot systems, but recently in order to get bio-inspired movement and to achieve the motion with the constrained wheels, the CPG-based control method for differential-driven mobile robots has been used in [5,6]. This also makes easy for the mobile robots to move in the confined space or in the non-smooth environment.

In this paper we have achieved rhythmic movements for the omni-directional mobile robot with three hemi-circular wheels. The coupled neural oscillator controls the movement of each wheel. Thus the robot is operated by six-neuron network that has been suggested by Matsuoka [7] (with some slight modifications). As a small result, the repetitive and oscillatory locomotion of robot is obtained. If we apply the different sequences to the six-neuron oscillators, then the different types of robot movements are achieved. This kind of work will also be helpful in hybrid wheel-legged robots as in [8].

The paper is organized as follow; section 2 gives the kinematics of the omni-directional mobile robot with three hemi-circular wheels; section 3 explains the neural oscillator dynamics with six-neuron model, the neuron firing sequences are also given in the same section; simulation results are given in section 4 and section 5 concludes the paper and gives the future work.

2. KINEMATICS OF OMNI-DIRECTIONAL

MOBILE ROBOT WITH HEMI-CIRCULAR

WHEELS Since the omni-directional mobile robot is able to

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perform three degree-of-freedom motions on the ground, it can move in straight line and rotate at any direction. The simple model of omnidirectional mobile robot with hemi-circular wheels is given in Fig. 1, where ex, y) denotes the center position of the robot and 8 implies the orientation of the robot (the orientation of first wheel is represented with respect to the x-axis). The rate kinematic model of the omni-directional mobile robot is given as [4]:

- sin 8z cos 8z

z (1)

where 81 = 8 , 8z = 8 + 120", 83 = 8 + 240", Vv Vz and V3 denote linear (or translational) velocities of three wheels.

Fig. I Omni-directional mobile robot with hemi-circular wheels

The hemi-circular wheels cannot rotate full revolution as seen in Figs. I and 2. It can only rotate a half cycle. To move a robot having such a wheel,

the neural oscillator based control would be a good choice. Such a control only makes the wheel to move back and forth. Thus it results in the different kinds of robot movements. This kind of moment can also be used in full wheel robot in order to avoid obstacles. In such case the neural oscillators can only be used for a small interval (during obstacle avoidance), and in absence of obstacle robot moves in straight line, without oscillation.

Fig. 2 Hemi-circular wheel

3. NEURAL OSCILLATOR

3.1 Model of neural oscillator

Neural oscillator provides the rhythmic control to each wheel, so the oscillating movement to the goal is achieved. The neural oscillator form used here is taken from the reference [2] and it has been used to control the walking and swimming of the salamander robot. The mathematical model is given as:

(2)

(3)

(4)

where {)i and Ti represents i-th oscillator phase and amplitude, wij and C/Jij are coupling weight and phase differences between i-th andj-th oscillators. Each wheel is controlled by the oscillator. C/Jij is used to control the phase difference in the wheels. The robot will only rotate about its center if C/Jij = 0'. On the other hand, if C/Jij = 180' for two wheels and V3 = 0 for the third wheel, then the robot only moves back and forth in [5,6].

3.2 Neuron network

Useful types of neural oscillator networks were proposed by Matsuoka [7]. This paper makes use of six neuron models as suggested in Fig. 3. Each coupled neuron ((Nv N4), (N2' Ns) and (N3' N6)) is utilized for the motions of the hemi-circular wheels. In many cases, the movement is achieved by three-neuron network. The input 'd' is the drive input for each neuron.

In case of omnidirectional mobile robot, the sequence of the neuron activations would be one of important issues because it brings quite different robot motion. We determine the following rhythmic sequence patterns

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(these sequences are a little bit different from those of [7], as those were for the locomotion of the insects):

Nl � N2 � N3 � N4 � Ns � N6 Nl = N2 = N3 N4 = Ns = N6 Nl � N2 � N3 N4 � Ns � N6 Nl = Ns � N2 = N3 N4 = N2 � Ns = N6 Nl � N2,N3 = 0

N2 � N3,N1 = 0

Nl � N3,N2 = 0

N4 � Ns,N6 = 0

N4 � N6,Ns = 0

Ns � N6,N4 = 0

These patterns show that the oscillators are able to work in three kinds of combinations, such as six-neuron network, three-neuron network and two-neuron network. In above sequences, the "=" symbol denotes that the neurons fire at the same time, while "�" implies that the neuron before the symbol fire earlier. First sequence will give the robot the oscillatory movement in straight line, second and third sequences make the robot to be rotated about its center, and next four also give the robot the oscillatory movements that depend on two wheels only, and all the other sequences are for the two wheels movement in straight line and one wheel stationary. The next section will show the simulation result to verify the effectiveness of the proposed method.

d

Fig. 3 Six-neuronal network for omni-directional mobile robots with hemi-circular wheel

4. SIMULATION RESULT

The simulation of the omni-directional mobile robot has been done for first sequence. The radius of robot and the wheel radius are taken to be unit values for simplicity. And we choose C/Jij = 120'. The simulation results for neuronal oscillator are shown in Fig. 4. The movement of the center of mobile robot in two-dimensional plane is shown in Fig. 4(a). It does not

have a straight motion but it has the oscillatory movement. After getting transient (initial) movement, the robot has stable movement as shown in Fig. 4(a)(b). When the neurons are fired correctly at angle of (/Jij = 120°, the movement is stabilized in a particular direction. The Fig. 4(b) gives the firing rate of each neuron and Fig. 4( c) shows the angle for the oscillation of each wheel. The orientation of robot can be controlled by controlling the firing sequence of neurons.

30r-----,-----,---,-------,------,---,------, I I I I I 25 ---1- - - -1- - - - r- ---1- - - -1- --- ---

20 - - - -+ - - - -1- - - -j- - - - -+ - ---

� 15 � >- 10 - - - � - --

10 20

(a)

(b)

30 40 X-axis

I --- 1 ---

50

-N1 - -N2

-N3 -N4 -N5 -N6

1.5·r---�--�----,----_,___-----,�==

0.5 -

-0.5

-1 - lJ1I\I\I\I\II1lI\JIII��IlII��IMIIIII\I\IIIIl\l\IIIlIIIIIIIIlIIi\IIIlI\II�I\I\llflllllllllllllt

-1.501;--------;';-----7-----.;---.;;-------c,0;;-------;,2'

(c)

60

Fig. 4 Simulation results (a) Cartesian motion on x-y plane, (b) neuron firing of all nodes (c) input angle for

each wheel.

5. CONCLUSIONS

The desired motion generation method based on the neural oscillators was proposed in this paper. The wheels were assumed to be hem i-circular shapes. Through the proposed method, we obtained oscillatory movements. This would be helpful in studying robots that have tripod-like properties with hemi-circular wheels in the future.

Acknowledgements This work was supported in part by the National

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Research Foundation (NRF-2013RIAIA2010192), in part by the Ministry of Knowledge Economy (MKE) and Korea Institute for Advancement in Technology (KIAT) through the Workforce Development Program in Strategic Technology, in part by the MKE(The Ministry of Knowledge Economy), Korea, under the Human Resources Development Program for Convergence Robot Specialists support program supervised by the N[PA (National [T Industry Promotion Agency) (NIPA-2013-H1502-13-1001), Republic of Korea.

[1]

[2]

[3]

REFERENCES

G. Taga et ai, "Self-organized control of bipedal locomotion by neural oscillators in un predictable environment" Biological cybernetics, Vol. 65, pp. 147-[59, 1991. A. J. [jspeert et ai, "From swimming to walking with salamander robot driven by a spinal cord model," Science 3 [5, [4 [6 (2007). A. J. [jspeert et ai, "Learning to move in modular robots using central pattern generation and online optimization," International Journal of Robotic Research, Vol. 27, No. 3-4, pp. 423-443, 2008.

[4] DJ. Balkcom et aI, "Time optimal trajectories for an omni-directional vehicle," International Journal of Robotic Research , Vol. 25, No. 10, pp. 985-999, 2006.

[5] I. Urziceanu et aI, "Central pattern generator control of a differential wheeled robot," International Conference on System Theory Control and Computing, 2011, Sinaia, Romania.

[6] J. Gonzalez et ai, "Motion control of differential wheeled robots with joint limit constraints," International Conference on Robotics and Biomimetic, Dec. 2007, Phuket, Thailand.

[7] K. Matsuoka, "Mechanisms of frequency and pattern control in the neural rhythmic generators," Biological cybernetics, Vol. 56, pp. 345-353, 1987.

[8] S. Y. Shen et ai, "Design of leg-wheel hybrid mobile platform", IEEE/RSJ International conference on intelligent robots and systems, Oct 2009 St. Louis, USA.