Formation of High-Speed Motion Pattern of a Mechanical Arm by Trial

Abstract

High-speed motion of a mechanical arm is necessary to speed up a job done by the arm. In high speed, however, the desired trajectory of motion of the arm cannot be obtained simply by applying the trajectory function to the servo system as the reference function because the time lag in the servo system is not negligible. A solution to this problem is to apply dynamically compensating computed torques to the servo system. By this method, however, for increasing the accuracy of the mathematical model of the arm necessary to compute the compensating torques, a very large effort would be required. To avoid this difficulty, an alternative method of correcting the reference function by trial will be useful. Repeating a proper process of trial and correction, the reference function which realizes the desired pattern of trajectory may be obtained. In this paper, correcting algorithm of a reference function for this method is investigated theoretically from the standpoint of stability or convergency of the process of trial and correction, and a stable correcting algorithm is obtained. Through the experiment using a mechanical arm of six degrees of freedom controlled by a digital computer, it is confirmed that the process of trial and correction by this algorithm is stable and the response of the servo system converges rapidly to the desired pattern of trajectory. Faculty of Engineering, Tohoku University, Sendai (Received August 5, 1977)-94