Averaging for Attitude Control and Motion Planning

N.E. Leonard and P.S. Krishnaprasad

In Proceedings of the 32nd IEEE Conference on Decision and Control, December, 1993, p. 3098-3104.


In this paper we show how to use periodic forcing to solve the constructive controllability problem for drift-free, left-invariant systems on matrix Lie groups with fewer controls than states. In particular, we prove a second-order averaging theorem applicable to systems evolving on general matrix Lie groups. Using this theorem, we show how to construct open loop controls for complete controllability of systems that require up to depth-one Lie brackets to satisfy the Lie algebra controllability rank condition. We apply these results to the attitude control problem with only two controls available and to the unicycle motion planning problem.

Postscript Version (7 pages postscript)

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