Improved and modified geometric formulation of POE based kinematic calibration of serial robots

The authors proposed in this paper an improved geometric formulation of POE (product of exponential) based kinematic calibration of serial robots. We use both joint offset-free formulation and adjoint transformation errors of joint screws, and apply it to the calibration of an elbow manipulator. Our formulation explains why the original POE calibration always fails with the existence of joint offset errors; the adjoint formulation of joint screw errors eliminates joint screw constraints that was imposed in the original iterated least square calibration algorithm. The second contribution of this paper is the proposal of a modified POE formulation which adopts point measurement data instead of frame measurement data of the end-effector, which can be more realistic and convenient for practical implementation. Simulation results show that the proposed method is plausible and effective. An experiment is under preparation to verify the effectiveness of the proposed calibration method on an elbow manipulator built by Googol Technology.

I. INTRODUCTION

Due to existence of manufacturing error, assembly error, and mechanical wear, the kinematics model of a serial robot will always deviate away from its nominal one, which creates problems in planning and control of the robot. For example, pure rotation or pure translation joint axis of a serial robot may have direction and/or position error, which can be modeled by the change of its joint screw coordinate; imperfect installation of joint encoders will also introduce errors in the reading of joint angles, known as the joint offset errors. A kinematic calibration is usually needed and implemented after the manipulator's assembly as an effective means to improve manipulator accuracy. Alternatively, kinematic calibration can be avoided through improved level of precision manufacturing, but at a rather higher cost. Judging from the scale of industrial robot production, kinematic calibration excels over quality control in terms of cost-effectiveness.