Murray, Richard M. (1992) Nilpotent Bases for a Class of Non-Integrable Distributions with Applications to Trajectory Generation for Nonholonomic Systems. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1992.002
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This paper develops a constructive method for finding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then used to construct explicit trajectories to drive the system between any two points. A kinematic model of a rolling penny is used to illustrate this approach. The methods presented here extend previous work using "chained form" and cast that work into a coordinate-free setting.
|Item Type:||Report or Paper (Technical Report)|
|Additional Information:||Research supported in part by a grant from the Powell Foundation. The author would like to thank R. Gardner and W. Sluis of the Fields Institute for Mathematical Sciences, Ontario, Canada for many fruitful conversations on the use of exterior differential systems for studying chained systems and for pointing out the connections between Goursat normal form and chained systems. In addition, Sameer Jalnapurliar and Michiel van Nieuwstadt provided invaluable assistance in debugging the proof for Theorem 3.|
|Group:||Control and Dynamical Systems Technical Reports|
|Usage Policy:||You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.|
|Deposited By:||Imported from CaltechCDSTR|
|Deposited On:||16 Jul 2006|
|Last Modified:||26 Dec 2012 14:29|
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