A novel simultaneous calibration method with radius constraint for 3D robot measurement

The utilization of 3D robot measurement systems, which integrate 2D profile scanners with industrial robots, is prevalent in manufacturing industries. Nonetheless, the measurement precision of such devices is often compromised due to inaccuracies in the robot kinematic parameters and the handeye matrix. This paper presents a novel simultaneous calibration methodology that concurrently resolves the issues related to robot kinematic parameters and the hand-eye relationship through the application of radius constraint. By integrating the hand-eye matrix into the robotic kinematic chain, an integrated model of the robot measurement system is formulated. Combining the spherical equation with the integrated kinematic model, a radius error model is established. The Jacobian matrix associated with the radius error is approximated using Taylor expansion. An iterative approach is proposed to identify the values of system parameters, which include both joint twists and hand-eye twist. Simulation results validate the effectiveness of the proposed algorithm, demonstrating its robustness to measurement noise. In practical applications, the maximum radius error was reduced from 4.480 mm to 1.721 mm, representing an accuracy improvement of 61.58%. Additionally, the average radius error decreased from 2.680 mm to 0.092 mm, indicating a substantial accuracy enhancement of 95.56%.