Motion on submanifolds of noninvariant holonomic constraints
for a kinematic control system evolving on a matrix Lie group
Claudio Altafini and Ruggero Frezza
Systems and Control Letters, 50(3):241-250, 2003.
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
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
The difference in terms of compactness of the result between the two
methods is considerable.