Potential Field Functions for Motion Planning and Posture of the Standard 3-Trailer System

Authors: K. Raghuwaiya, S. Singh, B. Sharma, J. Vanualailai

Abstract:

This paper presents a set of artificial potential field functions that improves upon, in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of 3-trailer systems in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. The effectiveness of the proposed control laws were demonstrated via simulations of two traffic scenarios.

Keywords: Artificial potential fields, 3-trailer systems, motion planning, posture, parking and collision-free trajectories.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337107

References:

[1] O. Khatib, "Real-time obstacle avoidance for manipulators and mobile robots", International Journal of Robotics Research 5 (1): 90–98, March, 1986.
[2] J. Lee, W. Chung, M. Kim, C. Lee, and Jeabok-Song, "A passive multipletrailer system for indoor service robots,” in IEEE/RSJ Int. Conf.Intelligent Robots and Systems, Maui, HI, 2001, pp. 827–832.
[3] Sharma. B, Vanualailai. J, Raghuwaiya. K and Prasad. A, (2008), "New Potential Field Functions for Motion Planning and Posture Control of 1-Trailer Systems”, International Journal of Mathematics and Computing Science, 3(1): 45-71.
[4] Sharma.B, Vanualailai. J, and Chand. U, (2009) "Flocking of Multi-agents in Constrained Environments”, European Journal of Pure and Applied Mathematics, 2(3): 401-425.
[5] K. Raghuwaiya, S. Singh, B. Sharma, and J. Vanualailai, "Autonomous Control of a Flock of 1-Trailer Mobile robots”, Procs of the 2010 International Conference on Scientific Computing, , Las Vegas, USA, 2010, pp 153-158.
[6] K. Raghuwaiya, S. Singh, B. Sharma, G. Lingam, " Formation Types of a Flock of 1-Trailer Mobile Robots,” Procs of The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications, Bangkok, Thailand, 2011, pp 368-382.
[7] B. Sharma, "New Directions in the Applications of the Lyapunov-based Control Scheme to the Findpath Problem”, PhD Dissertation, University of the South Pacific, Fiji, July 2008.
[8] P. C-Y. Sheu and Q. Xue, Intelligent Robotic Planning Systems, World Scientific, Singapore, 1993.
[9] R. W. Brockett, "Differential Geometry ControlTheory”, chapter Asymptotic Stability and Feedback Stabilisation, pages 181-191. Springer-Verlag, (1983).