TL;DR
This paper introduces efficient methods for proximity queries of parametric curves in motion planning, enabling fast collision detection and distance computation crucial for autonomous robot navigation.
Contribution
It provides a novel approach to compute bounds on obstacle proximity for a broad class of curves using convex bounding techniques and closed-form arc length bounds.
Findings
Methods are computationally efficient and accurate.
Applicable to curves with trigonometric or polynomial bases.
Demonstrated effectiveness through numerical simulations.
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…
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Proximity Queries for Absolutely Continuous Parametric Curves
Arun Lakshmanan2, Andrew Patterson2, Venanzio Cichella3 and Naira Hovakimyan2
2University of Illinois at Urbana-Champaign, 3University of Iowa
[email protected], [email protected], [email protected], [email protected]
The reference list from the paper itself. Each links out to its DOI / PubMed record.
- 1Bartoň and Elber [2011] Michael Bartoň and Gershon Elber. Spiral fat arcs–Bounding regions with cubic convergence. Graphical Models , 73(2):50–57, 2011.
- 2Bezanson et al. [2017] Jeff Bezanson, Alan Edelman, Stefan Karpinski, and Viral B Shah. Julia: A fresh approach to numerical computing. SIAM review , 59(1):65–98, 2017.
- 3Boyd and Mattingley [2007] Stephen Boyd and Jacob Mattingley. Branch and bound methods. 2007.
- 4Chakraborty et al. [2008] Nilanjan Chakraborty, Jufeng Peng, Srinivas Akella, and John E Mitchell. Proximity queries between convex objects: An interior point approach for implicit surfaces. IEEE Transactions on Robotics , 24(1):211–220, 2008.
- 5Chang et al. [2011] Jung-Woo Chang, Yi-King Choi, Myung-Soo Kim, and Wenping Wang. Computation of the minimum distance between two Bézier curves/surfaces. Computers & Graphics , 35(3):677–684, 2011.
- 6Chen et al. [2009] Xiao-Diao Chen, Linqiang Chen, Yigang Wang, Gang Xu, Jun-Hai Yong, and Jean-Claude Paul. Computing the minimum distance between two Bézier curves. Journal of Computational and Applied Mathematics , 229(1):294–301, 2009.
- 7Cichella et al. [2018 a] Venanzio Cichella, Isaac Kaminer, Claire Walton, and Naira Hovakimyan. Optimal motion planning for differentially flat systems using Bernstein approximation. IEEE Control Systems Letters , 2(1):181–186, 2018 a.
- 8Cichella et al. [2018 b] Venanzio Cichella, Isaac Kaminer, Claire Walton, Naira Hovakimyan, and Antonio Pascoal. Bernstein approximation of optimal control problems. ar Xiv preprint ar Xiv:1812.06132 , 2018 b.
