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Optimal point-to-point motion planning of non-holonomic mobile robots in the presence of multiple obstacles

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Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

This paper presents theoretical and experimental investigations in dynamic modeling and optimal path planning of a non-holonomic mobile robot in cluttered environments. A mobile robot in the presence of multiple obstacles was considered. Nonlinear dynamic model of the system was derived with respect to non-holonomic constraints of robot’s platform. Motion planning of the system was formulated as an optimal control problem, and efficient potential functions were employed for collision avoidance. Applying the Pontryagin’s minimum principle was resulted in a two-point boundary value problem solved numerically. The effectiveness and capability of the proposed method were demonstrated through simulation studies. Finally, for verifying the feasibility of the presented method, results obtained for the Scout mobile robot were compared with the experiments.

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Abbreviations

b :

Distance between O and the center point of each wheel

C :

Position of the mass center of the mobile platform

d :

Distance between O and C

I :

Moment of inertia

m :

Mass

O :

Intersection of the symmetry axis of the base with the driving wheel axis

P :

Center coordination of obstacle

R :

Weighting matrix of control vector

r :

Radius

T :

Torque value exerted to the actuator

t :

Time

W :

Weighting matrix of state vector

\( \phi \) :

Heading angle of the mobile platform

\( \theta \) :

Angular displacement

\( \dot{\theta } \) :

Angular velocity

b:

Mobile base of robot

c:

Center coordination of mobile robot

f:

Final status

i:

ith obstacle

l:

Left wheel

ob:

Obstacle

r:

Right wheel

w:

Wheel

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Acknowledgments

Support for this work by the department of mechanical engineering at Iran University of science and technology is gratefully acknowledged. Also, the authors wish to acknowledge the robotic research laboratory for supporting this research.

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Authors and Affiliations

  1. Robotic Research Laboratory, College of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

    Moharam Habibnejad Korayem & Mostafa Nazemizadeh

  2. Islamic Azad University, Damavand Branch, Damavand, Iran

    Hamed Rahimi Nohooji

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  1. Moharam Habibnejad Korayem
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  2. Mostafa Nazemizadeh
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  3. Hamed Rahimi Nohooji
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Correspondence to Moharam Habibnejad Korayem.

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Technical Editor: Glauco Caurin.

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Korayem, M.H., Nazemizadeh, M. & Nohooji, H.R. Optimal point-to-point motion planning of non-holonomic mobile robots in the presence of multiple obstacles. J Braz. Soc. Mech. Sci. Eng. 36, 221–232 (2014). https://doi.org/10.1007/s40430-013-0063-5

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