Approximate Optimal Trajectories for Flexible-Link Manipulator Slewing Using Recursive Quadratic Programming

The method of recursive quadratic programming, coupled with a homotopy method, has been used to generate approximate minimum-time and minimum tracking-error tip trajectories for two-link flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for a multi-link, multi-joint system with bending only in the horizontal-plane. Constraints on the trajectory include boundary conditions on link tip position, final joint velocities, accelerations and torque inputs to complete a rest-to-rest maneuver, straight-line tip tracking between boundary positions, and motor torque limits. Trajectory comparisons demonstrate the impact of torque input smoothness on structural mode excitation. Applied torques retain much of the qualitative character of rigid-body slewing motion with alterations for energy dissipation.