Motion on submanifolds of noninvariant holonomic constraints for a kinematic control system evolving on a matrix Lie group
✍ Scribed by Claudio Altafini; Ruggero Frezza
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 229 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0167-6911
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✦ Synopsis
For a control system on a matrix Lie group with one or more conÿguration constraints that are not left/right invariant, ÿnding 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 ÿrst 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 di erence in terms of compactness of the result between the two methods is considerable.