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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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