Kinematical error analysis and autonomous calibration of a 5PUS-RPUR parallel robot

Kinematic calibration is essential for improving the absolute accuracy of parallel robots, but conventional identification methods often struggle with the complex, non-linear coupling of their numerous geometric error parameters. This can lead to convergence to local rather than global optima, limiting the effectiveness of the calibration. To address this challenge, this paper proposes a novel self-calibration methodology based on a global optimization strategy. Taking the 5PUS-RPUR parallel robot as an example, its inverse kinematics is established based on screw theory. A sensitivity analysis is performed using the finite difference method to screen for and eliminate error sources with a negligible impact on the moving platform's pose. Measurement points are then selected uniformly throughout the workspace using the farthest point sampling algorithm. An objective function for the GA is constructed by integrating the actuator displacement errors from each kinematic chain with the overall pose error of the moving platform. Non-linear constraints are handled using a penalty function approach. Based on measurement data from an onboard IMU and joint encoders, the identification results are obtained. The experimental results demonstrate that the proposed method significantly improves the robot's positional accuracy across its entire workspace. The superiority and efficacy of this approach are further corroborated by a benchmark comparison with three recent, state-of-the-art calibration methodologies.