| This paper is concerned with
analysis on controllability for a class of nonholonomic systems. We discuss
controllability of underactuated planar manipulators with one unactuated
joint. We show that if the first joint (in the base side) is actuated, these
systems are completely controllable, namely, there exists an admissible
trajectory from any given initial point to any given final point. In order
to prove this, we use global stabilizing feedback control law to converge
the state to a manifold, where the system is locally controllable. By this
controller, we have two trajectories, one starting at the given initial
position and the other starting at the given final position. Then we connect
them using a kind of bi-directional approach to show the existence of the
whole admissible trajectory. Finally, we give some simulation results to
discuss controllability of more general cases, the first joint being actuated
and all other joints being unactuated. |
