Experiments in end-point control of manipulators with elastic drives

Abstract

Excitation of lightly-damped drive system resonances severely limits the performance of most present-day robotic manipulators. This dissertation discusses the development of practical high-performance control strategies for manipulators in which the flexibility resides primarily in the drive system. To test the control strategies, an experimental two-link planar manipulator has been constructed that exhibits very lightly-damped drive system resonances, highly nonlinear dynamics, and large variations in payload mass. Three different control strategies are examined. First, a standard collocated proportional-integral-derivative (PID) controller is implemented to demonstrate baseline performance that is characteristic of current industrial robots. What is found is that the control bandwidth is absolutely constrained to less than half the cantilever or fundamental hinged-mode vibration frequency of the manipulator, rejection of disturbances is poor, and large steady-state end-point positioning errors occur due to friction, gravity loading, and other unmodeled dynamics. Linear-quadratic-Gaussian (LQG) control techniques are then used to develop a high-performance controller that employs noncollocated end-point position sensing and a configuration-specific model of the manipulator. When the system is at or near the design configuration, the control bandwidth, disturbance rejection, and steady-state errors are improved by a factor of about four over those for the collocated PID designs. However, the highly tuned LQG controller rapidly loses performance as the arm geometry and payload mass vary from the design point, and deteriorates to instability for some arm geometries and payload masses. To reduce sensitivity to the change in geometry, a constant-gain extended Kalman filter (CGEKF) coupled with a linear-quadratic-regulator (LQR) is developed in which the state estimates are propagated by integrating the full non-linear equations of motion. The nonlinear CGEKF/LQR controller exhibits exceptional robustness to modeling errors, at least a factor-of-four improvement in bandwidth, disturbance rejection, and positioning accuracy over the PID design, excellent command trajectory following with little or no overshoot, and stable control over the entire workspace of the manipulator. An important feature of the CGEKF/LQR is its entirely discrete design. A sample rate of only ten times the closed-loop bandwidth is used to implement the controller.