Calibration method of robot base frame using unit quaternion form

A fine method to calibrate the pose of the robot base frame with respect to (w.r.t.) the world frame is proposed by using the unit quaternion form. The inconsistency of the frame description can be avoided in the task of the off-line programming, multi-arm coordination and identification of kinematic parameters. Five different TCPs (Tool Center Points) are measured, and a group of four incompatible equations is solved by the least-square method to obtain the preliminary pose of the base frame. To improve the orthogonality of the rotation matrix, an objective equation is established by the penalty function with only one multiplier. After the objective equation is solved by Newton's iteration method, the preliminary rotation matrix is updated to an orthogonal unit one. The stability of the calibration method has been demonstrated by the numerical simulation involving a certain amount of noise. The verification experiment has been accomplished, and has proved that the positioning errors of robot are reduced and distributed evenly.