Name
Abstract | ||
|---|---|---|
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 ${\\cal C}^1$ 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. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/TRO.2013.2296332 | Robotics, IEEE Transactions |
Keywords | Field | DocType |
convex programming,gradient methods,path planning,robots,computing proximity distances,continuous gradients,convex hull,convex shape,convex shapes,distance function,distance queries,proximity query,robotic motion planners,smooth optimization techniques,sphere tori patches bounding volume,tunable strict convexity,Bounding volume,continuous gradients of proximity distances,smooth and nonsmooth optimization,sphere-torus patches,strictly convex hulls | Bounding volume hierarchy,Topology,Minimum bounding box algorithms,Discrete mathematics,Convex combination,Control theory,Convex hull,Convex set,Proper convex function,Convex optimization,Mathematics,Convex analysis | Journal |
Volume | Issue | ISSN |
30 | 3 | 1552-3098 |
Citations | PageRank | References |
5 | 0.45 | 15 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Adrien Escande | 1 | 273 | 22.91 |
| Sfa Miossec | 2 | 173 | 14.21 |
| Mehdi Benallegue | 3 | 30 | 10.89 |
| Abderrahmane Kheddar | 4 | 1191 | 101.66 |