Calibration Method of Robot Base Frame by Quaternion Form

• 1、School of Mechanical Engineering and Automation, Beihang Universiy, Beijing 100191

Abstract：The accuracy pose of robot base frame with respect to the world frame is to be calibrated under the task of multi-arm cooperation, identification of kinematic parameters and off-line programming. A calibration method by the quaternion form is proposed and implemented to accurately calibration the robot base frame. The kinematics model is established by the product-of-exponential formula. Five different TCPs (Tool Center Point), which are not coplanar, are measured with the external measuring device, and the corresponding five robot configurations are also recorded. By considering the 9 elements of rotational matrix of the base frame pose as the variables, a group of 4 incompatible equations is set up, and the initial transformation of the base frame is also obtained by least square method. However, due to the errors of measuring procedure and truncation, the rotational matrix cannot satisfy the regulation of unit orthogonal matrix. By the geometrical constraints of a quaternion, an objective equation is established by the form of penalty function with a multiplier, and the initial transformation is updated into a unit orthogonal matrix. By a set of calibration experiments, the validity of calibration method is demonstrated, and it is used to update the accuracy of the robot.

Keywords： Robot Calibration Base frame Quaternion Orthogonality