Complete, minimal and continuous error models for the kinematic calibration of parallel manipulators based on POE formula

Determination of the identifiable parameters plays an important role in kinematic calibration of robot manipulators. For the conventional serial robots, a consensus has been reached on this problem. However, for the parallel manipulators, there is a lack of effective methods to analyze the parameters' identifiability. This paper presents a systematic approach to establish complete, minimal and continuous error models for kinematic calibration of parallel manipulators. Using the product of exponentials (POE) formula, orthogonal partitioning matrices can be constructed in a straightforward way to determine and eliminate the redundant error components. Hence, error models satisfying completeness, minimality and continuity requirements, can be established for the parallel manipulators. The result shows that the maximal number of identifiable parameters is 4r+2p+6 in a parallel manipulator, where r and p denote the quantities of equivalent revolute and prismatic joints, respectively. And this number is independent of the topology of parallel manipulators, such as the number of limbs, the assignments of actuations, and the geometric constraints within/between the limbs. Furthermore, this conclusion is in agreement with the well-known one for serial robots. Hence, the maximal number of identifiable parameters for both serial and parallel manipulators can be unified by one unique formula.