The Application of The Steepest Gradient Descent for Control Design of Dubins Car for Tracking a Desired Path

Miswanto; I. Pranoto; H. Muhammad; D. Mahayana

Authors

Miswanto Mathematics, Institut Teknologi Bandung, Indonesia
I. Pranoto Mathematics, Institut Teknologi Bandung, Indonesia
H. Muhammad Aeronautics and Astronautics, Institut Teknologi Bandung, Indonesia
D. Mahayana Control System and Computer (STEI), Institut Teknologi Bandung, Indonesia

Keywords:

Dubins Car System, Hamiltonian system, Gradient Descent, Numerical Simulation

Abstract

In this paper, we consider the control design of the Dubins car system to track a desired path. We design the control of the Dubins car system using optimal control approach. The control of the Dubins car system is designed for tracking the desired path. Instead of the usual quadratic cost function, a special type of cost functional which includes a tracking error term will be considered. By this special cost functional, the minimum tracking error of path of the Dubins car toward a desired path using Pontryagin Maximum Principle is obtained. The analytical solution of the Hamiltonian system is di±cult to obtain. So, a numerical solution with the steepest gradient descent method is proposed. The numerical results are given at the last section of this paper.

Downloads

Download data is not yet available.

References

Z-P. Jiang and H. Nijmeijer, 1997, Tracking Control of Mobile Robots:a Case Study in Backstepping, Automatica, vol. 33, no. 7, pp. 1393-1399.

Z-P. Jiang and H. Nijmeijer, 1999b, A Recursive Technique for Tracking Control of Nonholonomic Systems in Chained Form, IEEE Transaction on Automatic Control, vol. 44, no. 2, pp. 256-279.

E. Lefeber And H. Nijmeijer, December 1999, Adaptive Tracking Control of Nonholonomic Systems: an example, Proceedings of the 38th Conference on Decision and Control, Phoenix, Arizona USA.

Miswanto, I. Pranoto, and H. Muhammad, 2006, A Model of Swarm Movement with The Presence of A Leader, Proceeding , International Conference on Mathematics and Natural Sciences, pp. 740-742, ITB, Bandung.

E. Panteley, E. Lefeber, A. Loria, and H. Nijmeijer, September 1998, Exponential Tracking Control of a Mobile Car Using a Cascaded Approach, Proceeding of the IFAC Workshop on Motion Control, pp. 221-226, Grenoble France.

G.Y. Tang, Y.D. Zhao and Hui Ma, 2006, Optimal Output Tracking Con- trol for Bilinear Systems, Transactions of the Institute of Measurement and Control 28, 4, pp. 387-397.

H. Tjahjana, I. Pranoto, H. Muhammad, and J. Naibourho, 2007, On the optimal control Computation of linear system, preprint.