Continuous closed form trajectories generation and control of redundantly actuated parallel kinematic manipulators

This paper deals with continuous closed form trajectories generation and control of redundantly actuated parallel kinematic manipulators. Continuous closed form trajectories are usually given by means of analytical functions of time and show inherent discontinuities in velocity and/or acceleration profiles. In order to solve this problem, we propose an approach consisting of modifying the time function without changing the overall closed shape of the trajectory in the operational space. To deal with the actuation redundancy, an extended version of the PD controller with computed feedforward is proposed. The resulting control torques are projected using a regularization matrix in order to remove internal forces that may be dangerous for the manipulator. The proposed trajectory generator as well as the controller are implemented in real-time on Dual-V; a redundantly actuated parallel manipulator developed in our laboratory.