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

Abstract

Angularly accelerating a cantilevered rod which sags under gravity couples the out-of-plane 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 t o suppress the first mode of these vibrations during a horizontal angular move. A load was attached t o 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.

Robotically controlled slosh-free motion of an open container of liquid

“…The horizontal motion using the IIR filter and the rotating slosh-free motion resulted in the responses shown in The non-tilting response in Figure 10 is very similar to the response of the I R filter in that it reduces residual oscillation after the motion is complete. This is because the acceleration time was set equal to the period of oscillation [5].…”