A two-step solution for robot-world calibration made intelligible by implementing Chasles’ motion decomposition in Ad(SE(3))

Abstract

As a typical kinematic problem, an important criterion for the accuracy of robot-world calibration is whether the rotational and translational parts are calculated separately or not. Solving the kinematic equation separately increases the interest into the decomposition mode of the equation. This paper provides a decomposition mode for Ad(SE(3)) with embedded Chasles’ motion, providing a new decomposition mode for the robot-world equation. Firstly, the Lie algebra ad(se(3)) for Chasles’ rotational and translational motions are constructed and mapped exponentially to the Lie group Ad(SE(3)) separately, thus implementing the Chasles’ motion decomposition of Ad(SE(3)). Subsequently, the robot-world equation in Ad(SE(3)) is derived based on joint kinematics. A new decomposition mode for robot-world equation is proposed through the Chasles’ motion decomposition, and a two-step method based on point set matching is proposed. Finally, the effect of coordinate invariants on the calibration accuracy is discussed, and the superiority of the proposed method is verified with simulation and experimental tests.