Based on product of exponentials (POE) formula, three explicit error models are given in this paper for kinematic calibration of serial robot through measuring its end-effector positions. To obtain these error models, the tool frame should be chosen as reference frame at first, and then each position–error-related segment in the error models using pose measurement should be selected. And during kinematic parameter identification, all the errors in joint twists are identifiable, and the initial transformation errors and the joint zero-position errors can be identified conditionally. Namely, the initial transformation errors are identifiable if they do not contain orientation errors. And the joint zero-position errors are identifiable when a robot only consists of prismatic joints and the coordinates of its joint twists are linearly independent.
The effectiveness of this calibration method has been validated by simulations and experiments. The results show that: (1) the identification algorithms are robust and practical. (2) The method of position measurement is superior to that of pose measurement.