Kinematic calibration of a Stewart platform using pose measurements obtained by a single theodolite

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 the solution of the forward kinematic problem. The error parameters are basically the installation errors of the platform ball and U-joints as well as the leg length offsets. 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. A measurement procedure that utilizes a single theodolite was devised to determine the poses of the platform. Experimental studies reveal that the proposed calibration method is effective in enhancing the accuracy performance of Stewart platforms.