Mechanics and Quasi-Static Manipulation of Planar Elastic Kinematic Chains
Mechanics and Quasi-Static Manipulation of Planar Elastic Kinematic Chains
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平面弹性运动链的力学和准静态操纵
DOI：
10.1109/tro.2012.2218911
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发表时间：
2013
影响因子：
7.8
通讯作者：
Zoe McCarthy
中科院分区：
文献类型：
--
作者：
T. Bretl;Zoe McCarthy
本文研究了具有固定基座的平面运动链的准静态操纵问题，其中每个关节是一个线弹性扭转弹簧。这条链处于静态平衡时的形状可以表示为离散时间最优控制问题的解，其边界条件随着最后一环的位置和方向而变化。我们证明了这个问题的所有解的集合是一个光滑的三维流形，它可以用一张图来参数化。仿真实验结果表明，在边界条件空间中，直线路径一致地比直线路径更可行(作为距离的函数)。这些结果与可见性属性的分析相一致，表明我们得出的图表是应用基于采样的算法进行操作规划的更好的空间选择。我们描述了一个这样的算法，并表明它很容易实现。
In this paper, we study quasi-static manipulation of a planar kinematic chain with a fixed base in which each joint is a linearly elastic torsional spring. The shape of this chain when in static equilibrium can be represented as the solution to a discrete-time optimal control problem, with boundary conditions that vary with the position and orientation of the last link. We prove that the set of all solutions to this problem is a smooth three-manifold that can be parameterized by a single chart. Empirical results in simulation show that straight-line paths in this chart are uniformly more likely to be feasible (as a function of distance) than straight-line paths in the space of boundary conditions. These results, which are consistent with an analysis of visibility properties, suggest that the chart we derive is a better choice of space in which to apply a sampling-based algorithm for manipulation planning. We describe such an algorithm and show that it is easy to implement.