Optimal Linear State Feedback Time-varying Regulator For A Unicycle Mobile Robot

Abstract

This paper proposes an optimal time-varying linear state feedback control for wheeled mobile robot of the unicycle type. The control law that stabilizes exponentially the motion of the robot to a given desired trajectory is found, after transformation of the cinematic model of the robot into a well-known Brocket integrator [1] Numerical simulations are presented in order to demonstrate the effectiveness of the proposed control design. Copyright © 2008 by ASME.4423429Petroleum Division, ASMEBrockett, R., Asymptotic stability stabilization (1983) Differential Geometric Control Theory, pp. 181-191. , R. Brockett, R. Millman & H. Sussmann,eds, Boston, BirkhauserKolmanovsky 1. & N.H. McClamroch, Developments in nonholonomic control problems. IEEE Control Systems Magazine 15 (1995) 20-36Dixon, W.E., Jiang, Z.P., Dawson, D.M., Global exponential setpoint control of wheeled mobile robots: A Lyapunov approach (2000) Automatica, 36, pp. 1741-1746Canudas de Wit, C., Sördalen, Exponential Stabilization of mobile robots with nonholonomic constraints (1992) IEEE Transactions on Automatic Control, 37 (11), pp. 1791-1797Walsh, G., Tilbury, D., Sastry, S., Murray, R., Laumond, J.P., Stabilization of trajectories for systems with nonholonomic constraints (1994) IEEE Transactions on Automatic Control, 39 (1), pp. 216-222Rafikov, M., Balthazar, J.M., On control and synchronization in chaotic and hyperchaotic systems via linear feedback. control (2008) Communications in Nonlinear Science and Numerical Simulation, 13, pp. 1246-1255Astolfi, A., Exponential stabilization of wheeled mobile robot via discontinuous control (1999) Journal of Dynamic systems, Measurements and Control, 121, pp. 121-126Kim, B.M., Tsiotras, P., Controllers for unicycle-type wheeled robots: Theoretical results and experimental validation (2002) IEEE Trans. on Robotics and automation, 18 (3), pp. 294-307Oriolo, G., Luca, A., (2002) de, WMR Control via Dynamic Feedback Linearization: Design, implementation, and Experimental Validation, IEEE Transaction on Control System Tecnology, 10 (6)Bryson A.E. and Y. Ho. Applied Optimal Control. Hemisphere Publ. Corp., Washington D.C., 1975Anderson, B.D.O., Moor, J.B., (1990) Optimal Control Linear Quadratic Methods, , Prentice-Hall, NYAlekander, J.C., Maddocks, J.H., On the kinematics of wheeled mobile robots (1989) Int. J. Robot. Res, 8 (5), pp. 15-27Reeds, J.A., Shepp, L.A., Optimal paths for a car that goes both forwards and backwards (1990) Pacific J. Math, 145 (2), pp. 367-393Samson, C., Control of Chained systems: Application to path following and time-varying point-stabilization of mobile robots (1995) IEEE Transactions on Automatic Control, 40 (1), pp. 64-77Godhan, J.M., Egeland, A., Lyapunov approach to exponential stabilization of nonholonomic systems in power form (1997) IEEE Transactions on Automatic Control, 42 (7), pp. 1028-103