Guaranteed Collision Detection With Toleranced Motions
This addresses the need for reliable collision detection in robotics or simulations, but it appears incremental as it builds on existing motion analysis methods.
The paper tackles the problem of guaranteed collision detection for toleranced motions by modeling motion as a curve in a 12-dimensional space and covering it with balls, resulting in an algorithm that provides no-collision guarantees with robust and efficient implementation.
We present a method for guaranteed collision detection with toleranced motions. The basic idea is to consider the motion as a curve in the 12-dimensional space of affine displacements, endowed with an object-oriented Euclidean metric, and cover it with balls. The associated orbits of points, lines, planes and polygons have particularly simple shapes that lend themselves well to exact and fast collision queries. We present formulas for elementary collision tests with these orbit shapes and we suggest an algorithm, based on motion subdivision and computation of bounding balls, that can give a no-collision guarantee. It allows a robust and efficient implementation and parallelization. At hand of several examples we explore the asymptotic behavior of the algorithm and compare different implementation strategies.