用双四元数构建运动学置信区域
Constructing Kinematic Confidence Regions With Double Quaternions.
作者信息
Ge Q Jeffrey, Yu Zihan, Purwar Anurag, Langer Mark P
机构信息
Department of Mechanical Engineering, Stony Brook University, Stony Brook, New York, USA.
Department of Radiation Oncology, Indiana University, Indianapolis, Indiana.
出版信息
Proc MSR RomanSy 2024 (2024). 2024;159:215-230. doi: 10.1007/978-3-031-60618-2_18. Epub 2024 May 29.
A spatial displacement as an element of can be approximated by a 4D rotation, which is an element of . In this way, the problem of constructing confidence regions of uncertain spatial displacements may be studied as that of constructing confidence ellipsoids in . In this light, a double-quaternion formulation of kinematic confidence regions is presented that approximately preserve the geometry of . Examples are provided to demonstrate the efficacy of this approach in comparison with the dual-quaternion formulation.
作为 的一个元素的空间位移可以由作为 的一个元素的四维旋转来近似。通过这种方式，构建不确定空间位移的置信区域的问题可以作为在 中构建置信椭球体的问题来研究。鉴于此，提出了运动学置信区域的双四元数公式，该公式近似地保留了 的几何形状。提供了示例以证明该方法与对偶四元数公式相比的有效性。
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