Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems

We introduce the notion of kinematic controllability for second-order under actuated mechanical systems. For systems satisfying this property, the prob lem of planning fast collision-free trajectories between zero velocity stat es can be decoupled into the computationally simpler problems of path plann ing for a kinematic system followed by time-optimal time scaling. While thi s approach is well known for fully actuated systems, until now there has be en no way to apply it to underactuated. dynamic systems. The results in thi s paper form the basis for efficient collision-free trajectory planning for a class of underactuated mechanical systems including manipulators and veh icles in space and underwater environments.