A Strictly Convex Hull for Computing Proximity Distances With Continuous Gradients. Escande, A., Miossec, S., Benallegue, M., & Kheddar, A. IEEE Transactions on Robotics, 30(3):666–678, June, 2014. doi abstract bibtex 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.
@article{escande_strictly_2014,
title = {A {Strictly} {Convex} {Hull} for {Computing} {Proximity} {Distances} {With} {Continuous} {Gradients}},
volume = {30},
issn = {1552-3098},
doi = {10.1109/TRO.2013.2296332},
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 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.},
number = {3},
journal = {IEEE Transactions on Robotics},
author = {Escande, A. and Miossec, S. and Benallegue, M. and Kheddar, A.},
month = jun,
year = {2014},
keywords = {Bounding volume, Convergence, Robots, Shape, Vectors, collision avoidance, computing proximity distances, continuous gradients, continuous gradients of proximity distances, convex hull, convex programming, convex shape, convex shapes, distance function, distance queries, gradient methods, optimization, path planning, planning, proximity query, robotic motion planners, smooth and nonsmooth optimization, smooth optimization techniques, sphere tori patches bounding volume, sphere-torus patches, strictly convex hulls, tunable strict convexity},
pages = {666--678}
}
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