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Published May 1992 | Published
Book Section - Chapter Open

Stabilization of trajectories for systems with nonholonomic constraints


A 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. The authors 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, an explicit control law which will locally exponentially stabilize the system to the desired trajectory is given. The theory is applied to several examples, including a car-like robot.

Additional Information

© 1992 IEEE. 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. This research was supported in part by NSF grants ECS-87-19298 and IRI 90-14490, and the CNRS. The first author was also supported in part by an N.S.F. fellowship. The authors would like to thank Dr. Georges Giralt for many inspiring discussions and Andrew Teel for suggesting the first remark after proposition one.

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