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

Abstract

The hand-eye calibration problem is an important application problem in robot research. Based on the 2-norm of dual quaternion vectors, we propose a new dual quaternion optimization method for the hand-eye calibration problem. The dual quaternion optimization problem is decomposed to two quaternion optimization subproblems. The first quaternion optimization subproblem governs the rotation of the robot hand. It can be solved efficiently by the eigenvalue decomposition or singular value decomposition. If the optimal value of the first quaternion optimization subproblem is zero, then the system is rotationwise noiseless, i.e., there exists a "perfect" robot hand motion which meets all the testing poses rotationwise exactly. In this case, we apply the regularization technique for solving the second subproblem to minimize the distance of the translation. Otherwise we apply the patching technique to solve the second quaternion optimization subproblem. Then solving the second quaternion optimization subproblem turns out to be solving a quadratically constrained quadratic program. In this way, we give a complete description

Modified Hand–Eye Calibration Using Dual Quaternions

“…Furthermore, the equivalence relationship of the basic transformation matrix can be deduced by analyzing the robot vision system as well. Chen studied dual quaternion algebra and proposed an effective regularization-patching optimization method for handeye calibration based on dual quaternion [25]. Huang and Wang studied the camera projection matrix by analyzing the constraints step by step in order to identify the internal and external parameters of the camera, and then, the corresponding transformation matrix could be obtained by using the quaternion algebra [26,27].…”

Motion Addition and Motion Optimization

“…Two classical problems in robot research, i.e., the hand-eye calibration problem [7,9,10,14,19] and the simultaneous localization and mapping (SLAM) problem [1,2,3,4,17,18] were formulated as motion optimization problems, which are actually unconstrained real optimization problems. This approach improved the dual quaternion optimization approach, studied in [11,5].…”