Parameter-scheduled trajectory planning for suppression of coupled horizontal and vertical vibrations in a flexible rod

Angularly accelerating a cantilevered rod which sags under gravity couples the out-of-lane dynamics of the flexible rod and causes oscillation in both the horizontal and vertical planes. A parameter-scheduled trajectory planner has been analytically developed and experimentally implemented on a commercial robot to suppress the first mode of these vibrations during a horizontal angular move. A load was attached to the tip of the rod and the resulting static, out-of-plane, hub torque was measured with a force-torque sensor. This torque was used to predict the period of the horizontal first mode of vibration of the payload (rod and attached load) from a nonlinear function in order to calculate (schedule) the appropriate control parameters for the angular move. This system has been implemented on a Cincinnati Milacron T3-786 robot, and vibration-suppressed trajectories (which reduce the coupled residual vibrations by over 90%) have been performed by the robot for various payloads