In current robot calibration approaches, the error propagation and identification of serial and parallel robots fail to be solved intuitively and generically, resulting in an inefficient calibration implementation and a low accuracy improvement. In this article, we present a generic error modeling method of serial robots and extend to parallel robots by finite and instantaneous screw (FIS) theory. The differential map and the explicit description of FIS on the robot motions enable a concise error modeling of the serial robot. The identifiability of errors in serial robot is discussed. The maximum independent errors are proved to be 4r + 2p + 6, where r and p are the numbers of revolute and prismatic joints, respectively. Based on the error mapping of serial limbs, reciprocal twist and wrench are introduced to consider the interaction among limbs and reveal the error propagation of the parallel robot. Then, the identification algorithms with high robustness and efficiency are investigated for the serial and parallel robots. Specifically, the conventional ill-conditioning problems of parallel robots are addressed. Finally, the proposed kinematic calibration framework for both types of robots are compared with the existing methods, and verified by simulations and experiments. The results show that our calibration approach improves the robot accuracy in a robust and efficient manner.

Robot calibration to provide an accurate kinematic model is widely adopted in the advanced controller development of articulated serial robot performing complicated tasks. Conventional calibration methods mainly focus on the complete, continuous, and minimal error modeling. The generation and accumulation of errors have not been explicitly explained. In addition, the error identification and compensation sometimes are not practical for controller establishment. This article presents a robot calibration method using finite and instantaneous screw theory. From the differentiation of finite screw, the errors are defined by the deviations of instantaneous screws at initial pose. The error modeling is explicit. We also propose an advanced optimization algorithm based identification method and regard the geometry of redundant errors as constraints. The identified instantaneous screw errors are then converted to the joint actuation errors. Without modifying existing motion controller, errors are compensated by modified inputs. A UR3 robot is taken as an example to illustrate the calibration method. Simulation and experiment are implemented for verification. Comparing with the accuracy before calibration, the position and orientation accuracy of UR3 robot after calibration has improved by 94.75% and 89.29%. The results also show that modified inputs can be conveniently connected to controller development.