Planning collision-free motions for underactuated manipulators in constrained configuration space

We propose a method to drive an underactuated manipulator among obstacles in its workspace. The method allows for collision-free trajectories to be generated from the dynamic equations of the manipulator. When the passive joints are locked, these trajectories lie on surfaces parallel to the axes of the active joints. When the passive joints are free, the trajectories lie on surfaces determined by the nonholonomic constraints imposed by the lack of actuation at the passive joints. By switching the joint brakes on and off, we obtain a sequence of trajectories that connect the start and the goal configurations. A robust controller is utilized to ensure that the manipulator follows the pre-planned trajectories closely despite modeling errors and external disturbances. Simulation and experimental studies demonstrate the validity of the proposed theory