An Efficient Kinematic Calibration Method for Parallel Robots with Compact Multi-DOF Joint Models

Forward kinematics-based modeling approaches are capable of constructing complete kinematic error models for parallel robots generically. The existing forward kinematics-based modeling methods replace any multiple-degree-of-freedom (multi-DOF) joints with several 1-DOF joints so that any limb of the parallel robot can be modeled like a serial robot. Nonetheless, this substitution complicates the kinematic model and results in additional computation. To overcome this shortcoming, an efficient kinematic calibration method adopting compact multi-DOF joint models is proposed. At first, compact kinematic models for multi-DOF joints are established with the product of exponentials (POE) formula and adopted in the forward kinematic formulation of limbs. Next, error models of limbs are derived by simplifying the forward kinematic formulas' differentials, and the geometric error model for parallel robots is established by further concatenating and reformulating the limb error models. Then, geometric error parameters are identified by using the Levenberg-Marquardt algorithm and the error compensation is accomplished by the inverse kinematics of the calibrated kinematic model. Finally, simulations and an experiment are implemented for validation. Compared with the existing forward kinematics-based modeling approaches, the error modeling procedures are simplified as the equivalent substitution of multi-DOF joints is avoided. The proposed approach also improves the error compensation efficiency without compromising calibration accuracy.