论文标题
运动，单位双季节和运动优化
Motion, Unit Dual Quaternion and Motion Optimization
论文作者
论文摘要
我们将动作作为真正的六维矢量引入。运动意味着旋转和翻译。我们定义了一个运动操作员，该运动操作员将单位双四合一映射到动作，以及一个UDQ操作员，将运动映射到单位双四合一。通过这些运算符，我们介绍了运动优化的配方，这实际上是一个真正的不受限制的优化公式。然后，我们在机器人研究中提出了两个经典问题，即手眼校准问题以及同时定位和映射（SLAM）问题作为运动优化问题。这为通过实际不受约束的优化打开了解决这些问题的新方法。
We introduce motions as real six-dimensional vectors. A motion means a rotation and a translation. We define a motion operator which maps unit dual quaternions to motions, and a UDQ operator which maps motions to unit dual quaternions. By these operators, we present the formulation of motion optimization, which is actually a real unconstrained optimization formulation. Then we formulate two classical problems in robot research, i.e., the hand-eye calibration problem and the simultaneous localization and mapping (SLAM) problem as motion optimization problems. This opens a new way to solve these problems via real unconstrained optimization.
