A Strictly Convex Hull for Computing Proximity Distances With Continuous Gradients
A Strictly Convex Hull for Computing Proximity Distances With Continuous Gradients
复制标题
用于计算具有连续梯度的邻近距离的严格凸包
DOI：
10.1109/tro.2013.2296332
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发表时间：
2014
影响因子：
7.8
通讯作者：
A. Kheddar
中科院分区：
文献类型：
--
作者：
Adrien Escande;S. Miossec;M. Benallegue;A. Kheddar
我们提出了一种新的包围体，它实现了给定凸壳的可调严格凸性。该几何运算符被命名为球体-环面-面片包围体(STP-BV)，它是由球体和环面面片组成的包围体的首字母缩写。STP-BV的严格凸性保证了一对唯一的见证点和由具有另一个凸形的邻近性查询得到的距离函数的至少c1连续性。随后，距离函数的梯度是连续的。这对于在使用平滑优化技术的机器人运动规划器或控制器中将距离作为约束进行集成非常有用。为了完备性，我们比较了光滑和非光滑优化中的性能，以及当涉及凸形对之间的距离查询时的复杂性不断增加的例子。
We propose a new bounding volume that achieves a tunable strict convexity of a given convex hull. This geometric operator is named sphere-tori-patches bounding volume (STP-BV), which is the acronym for the bounding volume made of patches of spheres and tori. The strict convexity of STP-BV guarantees a unique pair of witness points and at least C1 continuity of the distance function resulting from a proximity query with another convex shape. Subsequently, the gradient of the distance function is continuous. This is useful for integrating distance as a constraint in robotic motion planners or controllers using smooth optimization techniques. For the sake of completeness, we compare performance in smooth and nonsmooth optimization with examples of growing complexity when involving distance queries between pairs of convex shapes.