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Stabilization of Nonholonomic Systems                      223

                              in dextrous manipulation), the stabilization of dynamic models of nonholo-
                              nomic systems, and the adaptive stabilization of nonholonomic systems with
                              unknown parameters. Finally, the important problem of trajectory tracking for
                              nonholonomic systems has not been discussed at all. We believe that the list
                              of reference (although by no means complete) provides adequate pointers to
                              investigate and study the above issues.



                              ACKNOWLEDGMENTS
                              The present chapter is the result of collaborative works with D.S. Laila,
                              M.C. Laiou, F. Mazenc, C. Prieur, E. Valtolina, and W. Schaufelberger.



                              REFERENCES
                                 1. Edelen, D. G. B., Lagrangian Mechanics of Nonconservative Nonholonomic
                                    Systems. Noordhoff International Publishing, Leyden, 1977.
                                 2. Brockett, R. W., Asymptotic stability and feedback stabilization, in Differential
                                    Geometry Control Theory, Birkhauser, Boston, p. 181, 1983.
                                 3. Kolmanovsky, I. and McClamroch, N. H., Developments in nonholonomic
                                    control problems, IEEE Control Systems Magazine, 15, 20, 1995.
                                 4. Morin, P., Pomet, J.-B., and Samson, C., Developments in time-varying feed-
                                    back stabilization of nonlinear systems, in Symposium on Nonlinear Control
                                    System Design, Twente, NL, 1998.
                                 5. Lafferriere, G. and Sussmann, H. J., A Differential Geometric Approach
                                    to Motion Planning, Nonholonomic Motion Planning, Kluwer Academic,
                                    Dordrecht, l992.
                                 6. Brockett, R. W. and Dai, L., Non-Holonomic Kinematics and the Role of Elliptic
                                    Functions in Constructive Controllability, Nonholonomic Motion Planning.
                                    Kluwer Academic, Dordrecht, 1992.
                                 7. Murray, R. M. and Sastry, S. S., Nonholonomic motion planning: steering using
                                    sinusoids, IEEE Transactions on Automatic Control, 38, 700, 1993.
                                 8. Lucibello, P. and Oriolo, G., Robust stabilization via iterative state steering with
                                    an application to chained form systems, Automatica, 37, 71, 2001.
                                 9. Samson, C., Velocity and torque feedback control of a nonholonomic cart, in
                                    International Workshop on Adaptive and Nonlinear Control. Grenoble, FR,
                                    p. 125, 1990.
                                10. Pomet, J.-B., Explicit design of time-varying stabilizing control laws for a class
                                    of controllable systems without drift, Systems and Control Letters, 18, 147,
                                    1992.
                                11. Coron, J. M., Global asymptotic stabilization for controllable systems without
                                    drift, Mathematics of Control Signals and Systems, 295, 1992.
                                12. M’Closkey, R. T. and Murray, R. M., Exponential stabilization of driftless
                                    nonlinear control systems using homogeneous feedback. IEEE Transactions on
                                    Automatic Control, 42, 614, 1997.




                              © 2006 by Taylor & Francis Group, LLC



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