Analysis of unified error model and simulated parameters calibration for robotic machining based on Lie theory

In robotic machining process, the kinematic errors of serial structure and compliance errors caused by external cutter-workpiece interactions can result in considerable deviation of the desired trajectory. Therefore, this paper proposes an efficient calibration methodology by establishing a unified error model about kinematic errors and compliance errors based on Lie theory, which simultaneously calibrates the kinematic parameters and joint compliances of a serial machining robot. In this methodology, the propagation law of kinematic errors is investigated by analysis of the kinematic error model, and the corresponding equivalent kinematic error model is thus obtained, in which the joint offset errors are regarded as one source of twist (joint twist and reference configuration twist) errors. On this basis, with the segmentation and modelling of the joint compliance errors caused by the link self-weight and cutting payloads, the unified error model is developed by linear superposition of configuration errors of the robotic end-cutter, calculated from the kinematic errors and compliance errors respectively. Meanwhile, to improve the accuracy of parameters calibration, the observability index is adopted to optimize the calibration configurations so as to eliminate the twist error constraints. The calibrated kinematic parameters and joint compliances are obtained eventually, and used to compensate the kinematic and compliance errors of the serial machining robot. Finally, to validate the effectiveness of the proposed unified error model, simulation analysis is performed using a 6-DOF serial machining robot, namely KUKA KR500. The comparisons among calibrated parameters show that the unified error model is more computationally efficient with optimal calibration configurations, rendering it suitable for the calibration of kinematic parameters and joint compliances in actual machining applications.