Approximate Minimum-Time Trajectories for Two-link Flexible Manipulators

The method of recursive quadratic progamming has been used to generate approximate minimum-time tip trajectories for two-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 bending only in the horizontal-plane. 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 compare a semirigid configuration to a flexible one. The level of compliance necessary to excite significant modal behavior is demonstrated. Applied torques for minimum-time maneuvers are shown to be very similiar between configurations and retain much of the qualitative character of rigid-body slewing motion.