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Controllability of the kinematic equations describing pure rolling of Grassmannians
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Resumo(s)
This paper studies the controllability properties of
certain nonholonomic control systems, describing the rolling
motion of Grassmann manifolds over the affine tangent space
at a point. The control functions correspond to the freedom of
choosing the rolling curve. The nonholonomic constraints are
imposed by the no-slip and no-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 addressed
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Grassmann manifold Lie group of isometries rolling motions no-slip, no-twist Lie algebras bracket generating property controllability