Robotics: Science and Systems XV

Proximity Queries for Absolutely Continuous Parametric Curves

Arun Lakshmanan, Andrew Patterson, Venanzio Cichella, Naira Hovakimyan


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.



    AUTHOR    = {Arun Lakshmanan AND Andrew Patterson AND Venanzio Cichella AND Naira Hovakimyan}, 
    TITLE     = {Proximity Queries for Absolutely Continuous Parametric Curves}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2019}, 
    ADDRESS   = {FreiburgimBreisgau, Germany}, 
    MONTH     = {June}, 
    DOI       = {10.15607/RSS.2019.XV.042}