论文标题
用于解决手眼校准问题的正规化二元四元化优化方法
A regularization-patching dual quaternion optimization method for solving the hand-eye calibration problem
论文作者
论文摘要
手眼校准问题是机器人研究中的重要应用问题。基于双重四个载体的2个标准，我们为手眼校准问题提出了一种新的双季节优化方法。双重四基因优化问题分解为两个四元素优化子问题。第一个四个四元优化子问题控制机器人手的旋转。可以通过特征值分解或奇异值分解有效地求解。如果第一个四基金优化子问题的最佳值为零，则系统旋转无噪音，即，存在``Perfect''机器人手动运动，该机器人手动运动完全满足所有测试的旋转。在这种情况下，我们应用正则化技术来求解第二个子问题以最大程度地减少翻译的距离。否则，我们将修补技术应用于解决第二个四基因优化子问题。然后求解第二个四基因优化子问题是解决了二次约束二次程序。通过这种方式，我们为手眼校准问题的解决方案集提供了完整的描述。这在手眼校准文献中是新的。还提出了数值结果以显示所提出方法的效率。
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.
