A Bi-Directional Coupling Calibration Model and Adaptive Calibration Algorithm for a Redundant Serial Robot with Highly Elastic Joints

This paper proposes a calibration method for redundant robot arms with highly elastic joints. The method uses the second-order Chebyshev polynomial to characterize the variation in the error with the poses of all joints. This error model is consistent with the variation in the gravitational torque on each joint and demonstrates good generalization. Based on this, the calibration model includes both kinematic errors and non-kinematic errors. For this high-dimensional model, an adaptive iterative identification algorithm is proposed for a large number of small error parameters of various types. The algorithm sets specific iteration rules for different types of error parameters and adjusts the convergence amplitude in each iteration, ensuring that the iterative algorithm converges to the global optimum. The simulation results show that for a redundant robot arm with 12 highly elastic joints, even with large linearization modeling errors, the new identification algorithm can gradually eliminate them during iteration, achieving an identification accuracy higher than 99.975% for all of the error parameters. The experimental results indicate that on a redundant robot arm with eight cable-driven elastic joints, the new model and identification algorithm reduce the 96.6% absolute positioning errors of the robot arm, enabling it to perform precise and flexible operations. It takes 40.534 s and 29.077 s to run the identification algorithm on MATLAB (R2023b, 2.10 GHz CPU) in the simulation and experiment, respectively.