An SVD-based projection method for interpolation on SE(3)
An SVD-based projection method for interpolation on SE(3)
复制标题
一种基于 SVD 的 SE(3) 插值投影方法
DOI：
10.1109/tra.2002.1019463
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Vijay R. Kumar
中科院分区：
文献类型：
--
作者：
C. Belta;Vijay R. Kumar
本文提出了一种生成具有特定边界条件的运动刚体光滑轨迹的方法。我们的方法包括两个关键步骤：1)在GA/sup+/(N)中生成最优轨迹，这是R/sup n/中仿射群的一个子群；2)轨迹在SE(3)上的投影，SE(3)是刚体位移的李群。整个过程对于流形上的局部坐标和惯性系的选择都是不变的。这种方法的好处有三个方面。首先，可以应用各种众所周知的有效技术中的任何一种来生成GA/sup+/(N)上的最优曲线。其次，该方法给出了SE(3)上一般黎曼度量选择的最优解的近似解。第三，从计算的角度来看，我们提出的方法比传统方法代价更低。
This paper develops a method for generating smooth trajectories for a moving rigid body with specified boundary conditions. Our method involves two key steps: 1) the generation of optimal trajectories in GA/sup +/ (n), a subgroup of the affine group in R/sup n/ and 2) the projection of the trajectories onto SE(3), the Lie group of rigid body displacements. The overall procedure is invariant with respect to both the local coordinates on the manifold and the choice of the inertial frame. The benefits of the method are threefold. First, it is possible to apply any of the variety of well-known efficient techniques to generate optimal curves on GA/sup +/ (n). Second, the method yields approximations to optimal solutions for general choices of Riemannian metrics on SE(3). Third, from a computational point of view, the method we propose is less expensive than traditional methods.