Skip to Main content Skip to Navigation
Journal articles

A Strictly Convex Hull for Computing Proximity Distances With Continuous Gradients

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 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 con-vex shapes.
Document type :
Journal articles
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01079783
Contributor : Mehdi Benallegue <>
Submitted on : Tuesday, November 4, 2014 - 11:57:31 AM
Last modification on : Thursday, June 10, 2021 - 3:03:12 AM
Long-term archiving on: : Thursday, February 5, 2015 - 10:11:05 AM

File

06710113.pdf
Files produced by the author(s)

Identifiers

Citation

Adrien Escande, Sylvain Miossec, Mehdi Benallegue, Abderrahmane Kheddar. A Strictly Convex Hull for Computing Proximity Distances With Continuous Gradients. IEEE Transactions on Robotics, IEEE, 2014, 30 (3), pp.666-678. ⟨10.1109/TRO.2013.2296332⟩. ⟨hal-01079783⟩

Share

Metrics

Record views

737

Files downloads

2065