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Stabilization of trajectories for systems with nonholonomic constraints

Walsh, G. and Tilbury, D. and Sastry, S. and Murray, R. and Laumond, J. P. (1994) Stabilization of trajectories for systems with nonholonomic constraints. IEEE Transactions on Automatic Control, 39 (1). pp. 216-222. ISSN 0018-9286.

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A new technique for stabilizing nonholonomic systems to trajectories is presented. It is well known that such systems cannot be stabilized to a point using smooth static-state feedback. In this note, we suggest the use of control laws for stabilizing a system about a trajectory, instead of a point. Given a nonlinear system and a desired (nominal) feasible trajectory, the note gives an explicit control law which will locally exponentially stabilize the system to the desired trajectory. The theory is applied to several examples, including a car-like robot.

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Murray, R.0000-0002-5785-7481
Additional Information:© 1994 IEEE. Reprinted with permission. Manuscript received March 14, 1992; revised November 17, 1992. This work was supported in part by the NSF under grants ECS-87-1998 and IRI 90-14490, and by the CNRS. G. Walsh was supported in part by an NSF fellowship. Part of this research was done at the Laboratoire d’Automatique et d’Analyse des Systèmes in Toulouse, France during the summer of 1991. G. Walsh, D. Tilbury, and S. Sastry are grateful for the warm welcome they received there. The authors would like to thank Dr. Georges Giralt for many inspiring discussions and Andrew Teel for suggesting the two remarks after proposition one.
Funding AgencyGrant Number
NSFIRI 90-14490
Centre National de la Recherche Scientifique (CNRS)UNSPECIFIED
NSF Graduate Research FellowshipUNSPECIFIED
Subject Keywords:mobile robots; nonlinear control systems; path planning; stability; car-like robot; local exponential stabilization; nonholonomic systems; nonlinear system; trajectories
Issue or Number:1
Record Number:CaltechAUTHORS:WALieeetac94
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Official Citation:G. Walsh, D. Tilbury, S. Sastry, R. Murray and J. P. Laumond, "Stabilization of trajectories for systems with nonholonomic constraints," in IEEE Transactions on Automatic Control, vol. 39, no. 1, pp. 216-222, Jan. 1994. doi: 10.1109/9.273373
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7314
Deposited By: Archive Administrator
Deposited On:29 Jan 2007
Last Modified:12 Dec 2019 17:06

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