A general approach for geometric error modeling of over-constrained hybrid robot

The geometric error model is critical to improve the absolute accuracy of an over-constrained hybrid robot, with the structure combining serial and parallel robots. Due to common constraints or redundant constraints in over-constrained mechanism, the motion of passive joints is always over-determined, which would destroy the rationality of previous error model. In this article, a geometric error modeling method of over-constrained hybrid robot based on the product of exponential formula is proposed. For any over-constrained robot, the existence and expression of constraint equations among geometric errors are deduced, thus above over-determined problem is solved. In addition, redundant errors are eliminated to ensure the minimality of error model. Due to constraint equations, the maximal number of identifiable errors is less than previous results, 4r+2p+6, where r and p denote the number of equivalent revolute and prismatic joints. Due to the standard modeling process, the method can be applied in any over-constrained hybrid robot. The method is validated by kinematic calibration of a 5-DOF 2UPU/SP-RR hybrid robot, and the results show that pose errors of this robot decrease by about 90%.