Controllability of the Kinematic Equations Describing Pure Rolling of Grassmannians

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.