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

作     者：Chen, Zhongming Ling, Chen Qi, Liqun Yan, Hong 

作者机构：Department of Mathematics School of Science Hangzhou Dianzi University Hangzhou310018 China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong Center for Intelligent Multidimensional Data Analysis Science Park Shatin Hong Kong Department of Electrical Engineering City University of Hong Kong Kowloon Hong Kong 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Numerical methods 

摘      要：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 for the solution set of hand-eye calibration problems. This is new in the hand-eye calibration literature. The numerical results are also presented to show the efficiency of the proposed method. © 2022, CC BY.