Algorithm and Realization of Robotic end Orientation Equivalent Similarity Transformation Based on Rodrigues

In the process of robotic pose measurement, error estimation and online correction, the relative pose transformation and calibration between coordinate frames are required. This paper presented a solution algorithm for measuring and precision evaluating the robot end orientation. Robotic frames transformation relationship was investigated. In view of the measuring space restricted problems of a robot end orientation, the unified description model of the robot end tool orientation transformation and the 3D coordinate measurement parameters of the space target are established. The algorithm of the robot end orientation using multi-point measurement is given with the coordinate frame equivalent similarity transformation. This algorithm utilizes the multi-point laser measurement values of the space rigid body to implement the spatial point coordinate center registration. By the least square optimization algorithm based on Rodrigues matrix transformation, the orthogonal rotation matrix of the orientation relative transformation can be obtained. At last the exact estimation of the robot end orientation z-y-x Euler angle and the orientation error are realized.