提出高阶刚体运动插值方法，实现精确轨迹规划。
Geometric Interpolation of Rigid Body Motions
- 基于刚体螺旋理论构造高阶初始/边界条件插值
- 解决1至4阶初始导数及1阶边界导数约束问题
- 适用于机器人轨迹设计，支持零加速度最优路径
刚体运动插值问题旨在求解给定起始与终止位姿之间的空间轨迹。本文研究两类插值问题：一是k阶初值轨迹插值问题（k-IV-TIP），要求满足前k-1阶刚体螺旋导数的初始条件；二是k阶边界值轨迹插值问题（k-BV-TIP），要求在起始和终止位姿处满足螺旋及其前k-1阶导数的条件。本文给出了k=1,...,4时k-IV-TIP的解，即初始螺旋及其至四阶时间导数均被指定。此外，提出一种1-IV-BVP解法，即在起始与终止位姿处指定螺旋。该解为一种新提出的三次插值，能自动退化为零螺旋时的最小加速度曲线。文章还给出了高阶解的一般推导方法，并通过两个数值实例验证了其有效性。
原文摘要 · Abstract (English)
The problem of interpolating a rigid body motion is to find a spatial trajectory between a prescribed initial and terminal pose. Two variants of this interpolation problem are addressed. The first is to find a solution that satisfies initial conditions on the k-1 derivatives of the rigid body twist. This is called the kth-order initial value trajectory interpolation problem (k-IV-TIP). The second is to find a solution that satisfies conditions on the rigid body twist and its k-1 derivatives at the initial and terminal pose. This is called the kth-order boundary value trajectory interpolation problem (k-BV-TIP). Solutions to the k-IV-TIP for k=1,...,4, i.e. the initial twist and up to the 4th time derivative are prescribed. Further, a solution to the 1-IV-TBP is presented, i.e. the initial and terminal twist are prescribed. The latter is a novel cubic interpolation between two spatial configurations with given initial and terminal twist. This interpolation is automatically identical to the minimum acceleration curve when the twists are set to zero. The general approach to derive higher-order solutions is presented. Numerical results are shown for two examples.
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