Approximate minimum-time trajectories for 2-link flexible manipulators

Powell's nonlinear programming code, VF02AD, was used to generate approximate minimum-time tip trajectories for 2-link semi-rigid and flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for an n-link, m-joint system with horizontal-plane bending only. Constraints on the trajectory include boundary conditions on position and energy for a rest-to-rest maneuver, straight-line tracking between boundary positions, and motor torque limits. Trajectory comparisons utilize a change in the link stiffness, EI, to transition from the semi-rigid to flexible case. Results show the level of compliance necessary to excite significant modal behavior. Quiescence of the final configuration is examined with the finite-element model.