Steering Nonholonomic Control Systems Using Sinusoids
This paper revises and extends our earlier work in using sinusoids to steer systems with nonholonomic constraints. We show that simple sinusoidal input trajectories are not easily applied to some classes of nonholonomic systems. This leads to the definition of a form of systems which can be steered using our earlier methods. We describe this form in detail and present preliminary efforts towards understanding when systems can be converted into this form.
KeywordsVector Field Nonholonomic System Chained Form Canonical System Growth Vector
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- [BM89]A. M Bloch and N. H. McClamroch. Control of mechanical systems with classical nonholonomic constraints. In IEEE Control and Decision Conference ,pages 201–205, 1989.Google Scholar
- [BM90]A. M Bloch and N. H. McClamroch. Controllability and stabilizability properties of a nonholonomic control system. In IEEE Control and Decision Conference ,1990.Google Scholar
- [Bro81]R. W. Brockett. Control theory and singular Riemannian geometry. In New Directions in Applied Mathematics ,pages 11–27. Springer-Verlag, New York, 1981.Google Scholar
- [GG87]M. Grayson and R. Grossman. Models for free nilpotent Lie algebras. Technical Memo PAM-397, Center for Pure and Applied Mathematics, University of California, Berkeley, 1987. (to appear in J. Algebra).Google Scholar
- [LMR89]Z. Li, R. Montgomery, and M. Raibert. Dynamics and optimal control of a legged robot in flight phase. In IEEE International Conference on Robotics and Automation ,pages 1816–1821, 1989.Google Scholar
- [LS90]G. Lafferriere and H. J. Sussmann. Motion planning for controllable systems without drift: a preliminary report. Technical Report SYCON-90-04, Rutgers Center for Systems and Control, 1990.Google Scholar
- [LS91]G. Lafferriere and H. J. Sussmann. Motion planning for controllable systems without drift. In IEEE International Conference on Robotics and Automation ,pages 1148–1153, 1991.Google Scholar
- [MS90a]R. M. Murray and S. S. Sastry. Grasping and manipulation using multifingered robot hands. In R. W. Brockett, editor, Robotics: Proceedings of Symposia in Applied Mathematics, Volume 41 ,pages 91–128. American Mathematical Society, 1990.Google Scholar
- [MS90b]R. M. Murray and S. S. Sastry. Steering nonholonomic systems using sinusoids. In IEEE Control and Decision Conference ,1990.Google Scholar
- [MS91]R. M. Murray and S. S. Sastry. Nonholonomic motion planning: Steering using sinusoids. Technical Report UCB/ERL M91/45, Electronics Research Laboratory, University of California at Berkeley, 1991.Google Scholar
- [Mur90]R. M. Murray. Robotic Control and Nonholonomic Motion Planning. PhD thesis, University of California at Berkeley, 1990.Google Scholar
- [Sam90]C. Samson. Velocity and torque feedback control of a nonholonomic cart. In International Workshop in Adaptive and Nonlinear Control: Issues in Robotics ,1990.Google Scholar