A novel kinematic calibration method for robot based on the Levenberg–Marquardt and improved Marine Predators algorithm

The task of precision manufacturing with serial robots requires high pose accuracy. Kinematic calibration with monocular camera and chessboard is a common method to improve the pose accuracy of robots. However, the inaccurate hand-eye and base-world parameters, the ease with which cameras capture incomplete checkerboard images, as well as the slow speed and low accuracy of parameter identification, can adversely affect the results of kinematic calibration. For these reasons, this study proposes corresponding solutions to address these issues. Firstly, this study establishes a kinematic error model that takes into account not only the DH parameters of the robot, but also the hand-eye and base-world parameters. This model effectively mitigates the influence of inaccuracies in the hand-eye and base-world parameters on robot calibration, eliminating the need for additional hand-eye calibration. Secondly, to enhance the robustness of parameter identification, a fusion identification algorithm is introduced that combines the Levenberg–Marquardt algorithm (LM) and the improved Marine Predators algorithm (IMPA). This fusion method combines LM and IMPA algorithm, and has the advantages of chaos strategy and Logical opposition-based learning strategy. It can effectively address the low convergence accuracy of the LM algorithm when tackling high-order nonlinear problems, as well as the slow convergence speed of the MPA algorithm, and accurately and quickly identify kinematic parameters. Thirdly, leveraging the concept of constraints, a method is proposed to ensure that the camera captures complete images of the chessboard, guaranteeing that each measured image can be used for calibration. Finally, the proposed calibration method is verified by experiments. The experiments show that the error of the end position and orientation of the robot is effectively reduced. The mean position error along x-axis, y-axis and z-axis and the mean absolute position error decreased from 1.5071 mm, 3.5425 mm, 2.2587 mm and 4.6599 mm to 0.2927 mm, 0.2999 mm, 0.3956 mm and 0.6470 mm, respectively. The mean orientation errors of the x-axis, y-axis and z-axis decreased from 0.6083°, 0.2026°and 0.6343°to 0.1147°, 0.0325°and 0.1439°, respectively. Compared with the error model without hand-eye and base-world parameters, the average absolute position error of the robot after calibration using our error model is 0.3446 mm lower. When comparing the proposed LM-IMPA algorithm with LM, MPA, Parti