JOINT SPACE TRAJECTORY PLANNING FOR FLEXIBLE MANIPULATORS

A trajectory planning approach for controlling flexible manipulators i s proposed. It is demonstrated that choosing actual joint angles as th e generalized rigid coordinates is the key to applying the proposed ap proach. From the observation of the special structure of the input mat rix, the concepts of motion-induced vibration and inverse dynamics und er a specified motion history of the joints are formed naturally. Base d on the above concepts, trajectory planning in joint space is propose d by using the optimization technique to determine the motion of joint s along a specified path in joint space or work space and for general point-to-point motion. The motion for each joint is assumed to be in a class consisting of a fifth-order polynomial and a finite terms of Fo urier series. This parameterization of motion allows the optimal traje ctory planning to be formulated as a standard nonlinear programming pr oblem, which avoids the necessity of solving a two-point-boundary-valu e problem and using dynamic programming. Setting the accelerations to zero at the initial and the final times is used to obtain smoother mot ion to reduce the spillover energy into unmodeled high-frequency dynam ics. A penalty term on vibration energy contained in the performance i ndex is used to minimize the vibration of the system modeled by lower frequency only. The final simulation results show the effectiveness of the proposed approach and the advantage for proper trajectory plannin g. (C) 1995 John Wiley & Sons, Inc.