Calibration of encoder indexing of a redundantly actuated parallel mechanism to eliminate contradicting control forces

摘要

This paper presents the kinematic calibration of a two degree-of-freedom redundantly actuated parallel mechanism (RAPM), with the aim of eliminating contradicting control forces (CCF). The kinematic errors in the RAPM induce CCFs, especially in the case of decentralized individual position control, which is the standard control method used in industrial applications. The encoder indexing errors of the actuated joints are known to be of strong influence on the CCFs. Therefore, it is believed that the CCFs will be eliminated if the encoder indexing errors are corrected. We proved this through experiments. We performed the calibration using a projection technique, wherein we projected tracking error terms onto orthogonal complementary terms of the constraint Jacobian between the independent joints and actuated joints. Using this projection technique, the effect of tracking error terms from the joint stiffness and external force is eliminated. During the calibration process, the tracking errors in the actuated joints are measured. Using these errors, we derived the optimal values of the encoder indexing error by minimizing the objective function. We verified the calibration result by comparing the CCFs measured before calibration with those measured after calibration, for the case of individual PID position control. Our results confirmed that the calibration procedure of encoder indexing errors successfully reduces the average norm value of CCFs from 366 N to 13 N.