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Motion on submanifolds of noninvariant holonomic constraints for a kinematic control system evolving on a matrix Lie group

TitleMotion on submanifolds of noninvariant holonomic constraints for a kinematic control system evolving on a matrix Lie group
Publication TypeJournal Article
Year of Publication2003
AuthorsAltafini, C, Frezza, R
JournalSyst. Control Lett. 50 (2003) 241-250
Abstract

For a control system on a matrix Lie group with one or more configuration constraints that are not left/right invariant, finding the combinations of (kinematic) control inputs satisfying the motion constraints is not a trivial problem. Two methods, one coordinate-dependent and the other coordinate-free are suggested. The first is based on the Wei-Norman formula; the second on the calculation of the annihilator of the coadjoint action of the constraint one-form at each point of the group manifold. The results are applied to a control system on SE(3) with a holonomic inertial constraint involving the noncommutative part in a nontrivial way. The difference in terms of compactness of the result between the two methods is considerable.

URLhttp://hdl.handle.net/1963/3018
DOI10.1016/S0167-6911(03)00168-3

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