Kinematic calibration of over-constrained robot with geometric error and internal deformation

Abstract

In the over-constrained robot with geometric errors, internal forces would occur and lead to deformation due to redundant constraints and common constraints. In current kinematic calibration approaches, since the deformation, geometric errors and pose errors cannot be described in a unified framework, the error propagation fails to be solved intuitively and generically. In this article, a general calibration framework of over-constrained robots is proposed to unify geometric errors and internal deformation through the least action principle. In the framework, considering the interaction between errors and deformation, the difference map between geometric errors and pose errors is explicitly and analytically revealed. The mapping matrix can degenerate to be consistent with the previous research under non-over-constrained robots. In addition, the error forward propagation method and the error identification algorithm are proposed to solve the error nonlinear propagation and the ill-posed identification equations, respectively. Finally, the calibration simulation and experiment results of a 5-DOF over-constrained hybrid robot show that the proposed method can accurately predict the pose of the end-effector under geometric errors robustly and effectively.