Determination of the Identifiable Parameters in Robot Calibration Based on the POE Formula

Abstract

This paper presents an analytical approach to determine and eliminate the redundant model parameters in serial-robot kinematic calibration based on the product of exponentials formula. According to the transformation principle of the Lie algebra se(3) between different frames, the connection between the joints' twist errors and the links' geometric ones is established. Identifiability analysis shows that the redundant errors are simply equivalent to the commutative elements of the robot's joint twists. Using the Lie bracket operation of se(3), a linear partitioning operator can be constructed to analytically separate the identifiable parameters from the system error vector. Then, error models satisfying the completeness, minimality, and model continuity requirements can be obtained for any serial robot with all combinations and configurations of revolute and prismatic joints. The conventional conclusion that the maximum number of independent parameters is 4r + 2p + 6 in a generic serial robot with r revolute and p prismatic joints is verified. Using the quotient manifold of the Lie group SE(3), the links' geometric errors and the joints' offset errors can be integrated as a whole, such that all these errors can be identified simultaneously. To verify the effectiveness of the proposed method, calibration simulations and experiments are conducted on an industrial six-degree-of-freedom (DoF) serial robot.