A regularization-patching dual quaternion optimization method for solving the hand-eye calibration problem

The hand-eye calibration problem is an important part of robot calibration, which has wide applications in aerospace, medical, automotive and industrial fields [15, 10]. The problem is to determine the homogeneous matrix between the robot gripper and a camera mounted rigidly on the gripper or between a robot base and the world coordinate system. In 1989, Shiu and Ahmad [29] and Tsai and Lenz [30] used one motion (two poses) to formulate the hand-eye calibration problem as solving a matrix equation AX = XB, (1) where X is the unknown homogeneous transformation matrix from the gripper (hand) to the camera (eye), A is the measurable homogeneous transformation matrix of the robot hand from its first to second position, and B is the measurable homogeneous transformation matrix of the attached camera and also, from its first to second position. To allow the simultaneous estimation of both the transformations from the robot base frame to the world frame and from the robot hand frame to sensor frame, Zhuang, Roth and Sudhaker [38] derived another homogeneous transformation equation AX = ZB, (2) where X is the transformation matrix from the gripper to the camera, Z is the transformation matrix from the robot base to the world coordinate system, A is the transformation matrix from the robot base to the gripper and B is the transformation matrix from the world base to the camera. It is worth mentioning that there are other kinds of mathematical models for hand-eye calibration problem.