Trajectory Tracking Using Artificial Potential Fields

Authors: Krishna S. Raghuwaiya, Shonal Singh, Jito Vanualailai

Abstract:

In this paper, the trajectory tracking problem for carlike mobile robots have been studied. The system comprises of a leader and a follower robot. The purpose is to control the follower so that the leader-s trajectory is tracked with arbitrary desired clearance to avoid inter-robot collision while navigating in a terrain with obstacles. A set of artificial potential field functions is proposed using the Direct Method of Lyapunov for the avoidance of obstacles and attraction to their designated targets. Simulation results prove the efficiency of our control technique.

Keywords: Control, Trajectory Tracking, Lyapunov.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081227

References:

[1] Y.U. Cao, A.S. Fukunaga, and A.B. Kahng, "Cooperative Mobile Robotics", Autonomous Robots,1997, vol 4, pp. 7-27.
[2] P. Morin and C. Samson, "Motion control of wheeled mobile robot," in Springer Handbook of Robotics (B. Siciliano and O. Khatib, eds), Springer Berlin Heidelberg, 2008, pp. 799-826.
[3] R. W. Brockett, "Differential Geometry Control Theory," chapter Asymptotic Stability and Feedback Stabilisation, Springer-Verlag, 1983, pp. 181-191.
[4] A. P. Aquiar, J. P. Hespanha, and P. V. Kokotovic, "Path-Following for nonminimum phase systems removes performance limitations," IEEE Transactions on Autonomous Control, 2005, 50(2): pp. 234-239.
[5] G. Klancar, and I. Skrjanc, "Tracking-error model based predictive control for mobile robots in real time," Robotics and Autonomous Systems, Elsevier, 2007, 55, pp. 460-469.
[6] Y. Kanayama, Y. Kimura, F. Miyazaki, T. Noguchi, "A stable tracking control method for an autonomous mobile robot," In Proceedings 1990 IEEE International Conference on Robotics and Automation, Los Alamitos, CA, USA, 1990, vol. 1, pp. 384-389.
[7] C. Samson, K. Ait-abderrahim, "Feedback control of a nonholonomic wheeled cart in Cartesian space," In Proceedings of the 1991 IEEE International Conference on Robotics and Automation, vol. 2,Sacramento, CA, 1991, pp. 1136-1141.
[8] C. Samson, "Time-varying feedback stabilization of car like wheeled mobile robot," International Journal of Robotics Research, 1993, 12 (1), pp. 55-64.
[9] G. Oriolo, A. De Luca, and M. Vendittelli, "Wmr control via dynamic feedback linearization: Design, implementation and experimental validation," IEEE Trans. Control Syst. Technol., 2002, 10(6), pp. 835- 852.
[10] Z.-P. Jiang, and H. Nijmeijer, "Tracking control of mobile robots: a case study in backstepping," Automatica, 1997, 33 (7), pp. 1393-1399.
[11] G. Klančar, and I. Škrjanc, "Tracking-error model-based predictive control for mobile robots in real time," Robotics and Autonomous Systems, 2007, 55 (6), pp. 460-469.
[12] E.-H. Guechi, J. Lauber, M. Dambrine, G. Klan─ìar, S. Blaži─ì, "Control design for non-holonomic wheeled mobile robots with delayed outputs," Journal of Intelligent& Robotic Systems, 2010, 60 (3), pp. 395-414.
[13] T.H.S. Li, S.J. Chang, "Autonomous fuzzy parking control of a car-like mobile robot," IEEE Transactions on Systems, Man, and CyberneticsÔÇö Part A: Systems and Humans, 2003, 33 (4), pp. 451-465.
[14] Z.-G. Hou, A.-M. Zou, L. Cheng, M. Tan, "Adaptive control of an electrically driven nonholonomic mobile robot via backstepping and fuzzy approach," IEEE Transactions on Control Systems Technology, 2009, 17 (4), pp. 803-815.
[15] R.E.Precup, and H. Hellendoorn, "A survey on industrial applications of fuzzy control," Computers in Industry, 2011, 62(3), pp. 213 - 226.
[16] W. Sheng, Q. Yang, J. Tan, and N. Xi, "Distributed multi-robot coordination in area exploration," Robotics and Autonomous Systems, 2006, vol 54, pp. 945-955.
[17] K. Raghuwaiya, S. Singh, and J. Vanualailai, "Formation Control of Mobile Robots", In Proceedings of the ICCMSDE, WASET, Phuket, Thailand, 2011, pp. 762-767.
[18] B. Sharma, "New Directions in the Applications of the Lyapunov-based Control Scheme to the Find path Problem", PhD Dissertation, Universityof the South Pacific, Fiji, July 2008.