Proximity Queries for Absolutely Continuous Parametric Curves
Arun Lakshmanan, Andrew Patterson, Venanzio Cichella, Naira Hovakimyan · 2019
In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment.However, the problem of evaluating the proximity is generally non-convex and serves as a significant computational bottleneck for motion planning algorithms.In this paper, we present methods for a general class of absolutely continuous parametric curves to compute: (i) the minimum separating distance, (ii) tolerance verification, and (iii) collision detection.Our methods efficiently compute bounds on obstacle proximity by bounding the curve in a convex region.This bound is based on an upper bound on the curve arc length that can be expressed in closed form for a useful class of parametric curves including curves with trigonometric or polynomial bases.We demonstrate the computational efficiency and accuracy of our approach through numerical simulations 1 of several proximity problems.