Calibration of stewart platforms and other parallel manipulators by minimizing inverse kinematic residuals

Abstract

This paper focuses on the accuracy enhancement of Stewart platforms through kinematic calibration. The calibration problem is formulated in terms of a measurement residual, which is the discrepancy between the measured leg length and the computed leg length. With this formulation, one is able to identify kinematic error parameters of the Stewart platform without the necessity of solving the forward kinematic problem; thus avoiding the numerical problems associated with any forward kinematic solution. By this formulation, a concise differential error model with a well-structured identification Jacobian, which relates the pose measurement residual to the errors in the parameters of the platform, is derived. Experimental studies confirmed the effectiveness of the method. It is also shown in this paper that the proposed approach can be applied to other types of parallel manipulators, assuming that their inverse kinematic solution is simpler than its forward kinematic solution. Because this condition is satisfied by almost all parallel manipulators, the method is very useful for kinematic calibration of such machines. © 1998 John Wiley & Sons, Inc.