Collision Detection for Unions of Convex Bodies With Smooth Boundaries Using Closed-Form Contact Space Parameterization

Abstract

This paper studies the narrow phase collision detection problem for two general unions of convex bodies encapsulated by smooth surfaces. The approach, namely CFC (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 timeparameterized 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.

Marching-Primitives: Shape Abstraction from Signed Distance Function

“…Therefore, researchers turn to exploring the possibility of interpreting complex objects and scenes with basic geometric primitives. Taking advantage of the primitive-based representation, many higher-level tasks, such as segmentation [14,16,21,30], scene understanding [29,31,41,47], grasping [33,44,45] and motion planning [35,36], are able to be solved efficiently.…”