“On the location of LQ-optimal closed-loop poles”
Authors: Carlos Canudas de Wit and Ole J. Sørdalen,Affiliation: Laboratoire d´Automatique de Grenoble (France) and NTNU, Department of Engineering Cybernetics
Reference: 1992, Vol 13, No 1, pp. 3-14.
Keywords: Control of mobile robots, piecewise continuous controller, non-holonomic constraints, exponential convergence
Abstract: This paper represents an exponentially stable controller for-a-two-degree-of freedom robot with nonholonomic constraints. Although this type of system is open loop controllable, this system has been shown to be nonstabilizable via pure smooth feedback (Brockett 1983, Samson and Ait-Abderrahim 1991). In this paper, a particular class of piecewise continuous controller is shown to stabilize the system exponentially. This controller has the feature that it does not require infinitely fast switching, as required, for example, by sliding controllers.
PDF (1138 Kb)
DOI: 10.4173/mic.1992.1.1References:
[1] AEYELS, D. (1985). Stabilization of a class of nonlinear systems by smooth feedback, In Syst. Control Letters, no. 5,289-294.
[2] BARRAQUAND, J. LATOMBE, J.-C. (1989). On nonholonomic mobile robots and optimal maneuvering, In 4th International Conference on Intelligent Control, Albany, N.Y.
[3] BLOCH, A.M. MCCLAMROCH, N.H. (1989). Control of mechanical systems with classical nonholonomic constraints, IEEE Conference on Decision and Control, Tampa, Florida, December 1989, pp. 201-205.
[4] BLOCH, A.M., MCCLAMROCH, N.H. REYHANOGLU, M. (1990). Controllability and stabilizability properties of a nonholonomic control system, IEEE Conference on Decision and Control, Honolulu, Hawaii, December 1990, pp. 1312-1314.
[5] BROCKETT, R.W. (1982). Control theory and singular Riemannian geometry, in New Directions in Applied Mathematics, (Springer-Verlag, New York), P.J. Hilton and S. Young (eds), pp. 11-27.
[6] BROCKETT, R.W. (1983). Asymptotic stability and feedback stabilization, in R.W. Brockett, R.S. Millman and H.J. Sussman, editors, Differential Geometric Control Theory.Birkhauser, pp. 181-208.
[7] BYRNES, C. ISIDORI, A. (1991). On the attitude stabilization of rigid spacecraft, Automatica, 27, 87-95 doi:10.1016/0005-1098(91)90008-P
[8] CAMPION, G. D´ANDREA-NOVEL, B. BASTIN, G. (1991). Controllability and state feedback stabilizability of nonholonomic mechanical systems, In Advanced Robot Control, Proc. of the Int. Workshop on Nonlinear and Adaptive Control: Issues in Robotics, Grenoble, Nov. 21-23,1990, vol. 162, C. Canudas de Wit (ed) (Springer-Verlag), pp. 106-124.
[9] CANUDAS DE WIT, C. ROSKAM, R. (1991). Path following of a 2-DOF wheeled mobile robot under path and input torque constraints, Proc. of the IEEE International Conference on Robotics and Automation, Sacramento, California, April 1991.
[10] KAHN, M.E. RUTH, B. (1971). The near-minimum-time control of open loop articulated kinematics chains, Transactions of the ASME, pp. 164-172.
[11] KANAYAMA, V., KIMURA, V., MIYAZAKI, F. NOGUCHI, T. (1990). A stable tracking control method for an autonomous mobile robot, IEEE Conference on Robotics and Automation, Cincinnati, USA, pp. 384-389.
[12] LAFFERRIERE, G. SUSSMANN, H.J. (1991). Motion planning for controllable systems without drift, In Proc. of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, California, April 1991.
[13] MESSAGER, F. (1990). Two nonlinear examples of discontinuous stabilization, In Colloque international sur l´analyse des systemes dynamiques controlés, vol. 1, Lyon, France, July 1990.
[14] MURRAY, R.M. SASTRY, S.S. (1990). Steering nonholonomic systems using sinusoids, Conference on Decision and Control, Honolulu, Hawaii, December 1990.
[15] SAMSON, C. (1991). Velocity and torque feedback control of a nonholonomic cart, In Advanced Robot Control, Proc. of the Int. Workshop on Nonlinear and Adaptive Control: Issues in Robotics, Grenoble, Nov. 21-23, 1990, vol. 162, C. Canudas de Wit (ed) (Springer-Verlag), pp. 125-151.
[16] SAMSON, C. AIT-ABDERRAHIM, K. (1991). Feedback control of a nonholonomic wheeled cart in Cartesian space, In Proc. of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, California, April 1991.
BibTeX:
@article{MIC-1992-1-1,
title={{On the location of LQ-optimal closed-loop poles}},
author={Canudas de Wit, Carlos and Sørdalen, Ole J.},
journal={Modeling, Identification and Control},
volume={13},
number={1},
pages={3--14},
year={1992},
doi={10.4173/mic.1992.1.1},
publisher={Norwegian Society of Automatic Control}
};