On trajectory control of multi-link robots with flexible links and joints

A technique based on numerical optimization is presented in this paper for solving the inverse dynamics and kinematics of multi-link robot arms with flexible links and joints. This technique finds the joint torques required to move the end point of flexible manipulators through specified trajectories while avoiding tip oscillations. Since the point for which the prescribed motion is specified and the application points of control torques are connected by elastic bodies, the inverse dynamics of flexible manipulators is non-causal. The proposed algorithm takes into account the non-causality of such systems by considering pre-actuation and post-actuation in the solution procedure