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arXiv · 1902.05027

Proximity Queries for Absolutely Continuous Parametric Curves

Arun Lakshmanan·Andrew Patterson·Venanzio Cichella·Naira Hovakimyan
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Abstract

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 of several proximity problems.

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Arun Lakshmanan, Andrew Patterson, Venanzio Cichella, Naira Hovakimyan. 2019-02-13. Proximity Queries for Absolutely Continuous Parametric Curves. https://doi.org/10.15607/rss.2019.xv.042

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