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COMPLETE CONTROLLABILITY OF THE KINEMATIC EQUATIONS DESCRIBING PURE ROLLING OF GRASSMANNIANS
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This paper studies the controllability properties of certain nonholo nomic control systems, describing the rolling motion of Grassmann manifolds over
the affine tangent space at a point. The control functions correspond to the free dom of choosing the rolling curve. The nonholonomic constraints are imposed by
the non-slip and non-twist conditions on the rolling. These systems are proved to
be controllable in some submanifold of the group of isometries of the space where
the two rolling manifolds are embedded. The constructive proof of controllability
is also partially addressed.
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Palavras-chave
Grassmann manifold Lie group of isometries rolling motions Lie algebras bracket generating property complete controllability