Averaging for Attitude Control and Motion Planning
N.E. Leonard and P.S. Krishnaprasad
In Proceedings of the 32nd IEEE Conference on Decision and
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
we prove a second-order averaging theorem applicable to systems evolving
general matrix Lie groups. Using this theorem, we show how to construct
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
two controls available and to
the unicycle motion planning problem.
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