Robot measurement systems with a binocular planar structured light camera (3D camera) installed on a robot end-effector are often used to measure workpieces' shapes and positions. However, the measurement accuracy is jointly influenced by the robot kinematics, camera-to-robot installation, and 3D camera measurement errors. Incomplete calibration of these errors can result in inaccurate measurements. This paper proposes a joint calibration method considering these three error types to achieve overall calibration. In this method, error models of the robot kinematics and camera-to-robot installation are formulated using Lie algebra. Then, a pillow error model is proposed for the 3D camera based on its error distribution and measurement principle. These error models are combined to construct a joint model based on homogeneous transformation. Finally, the calibration problem is transformed into a stepwise optimization problem that minimizes the sum of the relative position error between the calibrator and robot, and analytical solutions for the calibration parameters are derived. Simulation and experiment results demonstrate that the joint calibration method effectively improves the measurement accuracy, reducing the mean positioning error from over 2.5228 mm to 0.2629 mm and the mean distance error from over 0.1488 mm to 0.1232 mm.
Keywords: Lie algebra; binocular planar structured light camera; joint calibration method; robot measurement system.