Comparison of the Observability Indices for Robot Calibration considering Joint Stiffness Parameters

Abstract

In this paper, comparisons of the 4 observability indices for robot calibration considering joint stiffness parameters are performed for finding the best robot pose set. 4 observability indices such as the minimum singular value index, the inverse condition number index, the product of singular values index and the noise amplification index were discussed and compared with the conventional calibration Jacobian matrix. Here, we propose the joint stiffness included Jacobian to consider robot joint deflection due to the load. Those indices are evaluated and compared in light of the resulting calibration accuracies. Genetic algorithms customized for a simple 2-link planar robot manipulator with a loading in the end-effector are applied to search optimal robot poses where measurement values are used to calibrate both the robot kinematic parameters and joint stiffness parameters. In this process, 4 observability indices, treated as fitness functions respectively, are evaluated and compared through a 2-link robot manipulator calibration simulation. While the kinematic parameters are well calibrated in all of the 4 observability, in joint stiffness included identification, these 4 observabilities perform differently. The noise amplification index identifies joint stiffness more stably and approximately with very small residual errors than others.