A Novel Algorithm for Robust Calibration of Kinematic Manipulators and its Experimental Validation

Kinematic calibration of manipulators is an efficient and fundamental way to ensure reliability and high performance of robots. Research on kinematic calibration has a long tradition, and a common strategy used for calibration is to guarantee the least errors in the sense of root-mean-square deviation. However, the absolute positioning accuracy is determined by the maximum error of manipulators, and it is a key indicator for evaluating performance. For example, using manipulators to print machine elements, obviously where the error is the most, may likely cause inaccurate fit. Hence, it is crucial to study a robust calibration strategy. Considering the calibration problem, both positioning and orientation accuracy are ensured by minimizing the maximum positioning errors of three spherical mounted retro-reflectors (SMRs) on the end effector of manipulators. Unfortunately, traditional optimization methods based on gradient cannot be directly employed to solve the minimax problem. Due to the recent progress on optimization, researchers found that the minimax can be transformed into sequence quadratic programming problems under inequality conditions, thus providing solutions for solving the robust calibration. This paper applied this method to convert the calibration problem into constrained quadratic subproblems, and the subproblems can be solved through the primal-dual subgradient method. Then, convexity and robustness analysis is given to prove that these subproblems can quickly converge to a local minimum. Finally, to verify the validity of the proposed algorithm, the experiments are conducted on an IRB 2600 manipulator, and the results show that, with the minimax search algorithm, both the positioning and orientation accuracy is enhanced by 67.34% and 73.14%, respectively, which is significantly higher than the performance of the single-SMR calibration algorithm widely used in the field of industry