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 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.

中文翻译：

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解决手眼标定问题的正则化修补双四元数优化方法

摘要

手眼标定问题是机器人研究中的一个重要应用问题。基于对偶四元数向量的2-范数，我们针对手眼校准问题提出了一种新的对偶四元数优化方法。对偶四元数优化问题分解为两个四元数优化子问题。第一个四元数优化子问题控制机器人手的旋转。它可以通过特征值分解或奇异值分解有效地求解。如果第一个四元数优化子问题的最优值为零，则系统是旋转无噪声的，即存在完全满足所有旋转测试姿势的“完美”机器人手运动。在这种情况下，我们应用正则化技术来解决第二个子问题，以最小化平移距离。否则，我们应用修补技术来解决第二个四元数优化子问题。那么求解第二个四元数优化子问题就是求解二次约束二次规划。这样，我们就给出了手眼标定问题的解集的完整描述。这是手眼校准文献中的新内容。数值结果也显示了所提出方法的效率。