Analysis of feedback control applied with command shaping to minimize residual vibration
Joint flexibility is a physical trait that affects all robotic systems to some degree. This characteristic has been shown to be very detrimental to the performance of these robotic systems when implementing fast point-to-point motion. During such motion, the robot will induce vibrations in its structure that will extend past the completion of the move. Many techniques have been applied over the years in order to minimize these residual vibrations. One such method is known as command shaping, which will construct the input profile so as to avoid exciting the natural frequencies of the system. This work seeks to extend this by analyzing how the feedback controller interacts with the input signal. Since a robotic manipulator is inherently nonlinear, this investigation is begun using a linear three-mass system that mimics the important dynamics of a two-link flexible-joint robot. A model of this three-mass system is derived and simulated in order to provide a new testbed for analyzing the problem of reducing residual vibration. It is shown that by appropriately designing the feedback controller so as to minimize the level of energy at the natural frequencies, lower residual vibration amplitudes are achieved. However, in some instances, these vibrations may take longer to settle out, which is directly correlated to the closed-loop damping of the system. This provides guidelines on how to appropriately construct a feedback controller so as to minimize residual vibration. Using this better understanding of the influence of the feedback, several different controllers are then tested on a two-link flexible-joint robot. The results of these experiments show correlation with the results obtained from the linear system analysis completed, and the trends are now better understood by applying the knowledge gained from the three-mass system. With the influence of the feedback controller on the level of residual vibration that ensues from fast point-to-point motion identified, the separate problems of command shaping and feedback control are tied together so as to achieve even lower levels of residual vibration.^
Peter H. Meckl, Purdue University.