Collision Detection for Unions of Convex Bodies With Smooth Boundaries Using Closed-Form Contact Space Parameterization
Sipu Ruan, Xiaoli Wang, Gregory S. Chirikjian
Abstract
This paper studies the narrow phase collision detection problem for two general unions of convex bodies encapsulated by smooth surfaces. The approach, namely <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CFC</i> (Closed-Form Contact space), is based on parameterizing their contact space in closed-form. The first body is dilated to form the contact space while the second is shrunk to a point. Then, the collision detection is formulated as finding the closest point on the parametric contact space with the center of the second body. Numerical solutions are proposed based on the point-to-surface distance as well as the common-normal concept. Furthermore, when the two bodies are moving or under linear deformations, their first time of contact is solved continuously along the time-parameterized trajectories. Benchmark studies are conducted for the proposed algorithms in terms of solution stability and computational cost. Applications of the sampling-based motion planning for robot manipulators are demonstrated.
BibTeX
@inproceedings{ral2022_collisiondetecti,
title = {Collision Detection for Unions of Convex Bodies With Smooth Boundaries Using Closed-Form Contact Space Parameterization},
author = {Sipu Ruan and Xiaoli Wang and Gregory S. Chirikjian},
booktitle = {RA-L 2022},
year = {2022}
}