TY - GEN
T1 - Averaging for attitude control and motion planning
AU - Leonard, Naomi Ehrich
AU - Krishnaprasad, P. S.
PY - 1993
Y1 - 1993
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0027808635&partnerID=8YFLogxK
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M3 - Conference contribution
AN - SCOPUS:0027808635
SN - 0780312988
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3098
EP - 3104
BT - Proceedings of the IEEE Conference on Decision and Control
PB - Publ by IEEE
T2 - Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4)
Y2 - 15 December 1993 through 17 December 1993
ER -