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Finding curvature-constrained paths that avoid polygonal obstacles

Authors:

Jonathan Backer,

David KirkpatrickAuthors Info & Claims

SCG '07: Proceedings of the twenty-third annual symposium on Computational geometry

Pages 66 - 73

https://doi.org/10.1145/1247069.1247080

Published: 06 June 2007 Publication History

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Abstract

We describe an algorithm to find a unit-curvature path between specified configurations in an arbitrary polygonal domain. Whenever such a path exists, the algorithm returns an explicit description of one such path in time that is polynomial in n (the number of features of the domain), m (the precision of the input) and k (the number of segments on the simplest obstacle-free Dubins path connecting the specified configurations). Our algorithm is based on a new normal form for unit-curvature paths and a dynamic path filtering argument that exploits a separation bound for distinct paths in this normal form.The best result known for the feasibility of bounded-curvature motion in the presence of arbitrary polygonal obstacles involves a reduction to the first-order theory of the reals. It just determines if a feasible path exists (it does not return a path) and requires exponential time and space.

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Cited By

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Díaz JAyala J(2019)Census of bounded curvature pathsGeometriae Dedicata10.1007/s10711-019-00444-2Online publication date: 12-Apr-2019
https://doi.org/10.1007/s10711-019-00444-2
Upadhyay SRatnoo A(2018)On Existence and Synthesis of Smooth Four Parameter Logistic Paths Inside Annular PassagesIEEE Robotics and Automation Letters10.1109/LRA.2018.28670693:4(4375-4382)Online publication date: Oct-2018
https://doi.org/10.1109/LRA.2018.2867069
Takei RTsai R(2018)Optimal Trajectories of Curvature Constrained Motion in the Hamilton---Jacobi FormulationJournal of Scientific Computing10.1007/s10915-012-9671-y54:2-3(622-644)Online publication date: 30-Dec-2018
https://dl.acm.org/doi/10.1007/s10915-012-9671-y
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Index Terms

Finding curvature-constrained paths that avoid polygonal obstacles
1. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

SCG '07: Proceedings of the twenty-third annual symposium on Computational geometry

June 2007

404 pages

ISBN:9781595937056

DOI:10.1145/1247069

Program Chair:
Jeff Erickson
University of Illinois, Urbana-Champaign, USA

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 06 June 2007

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Díaz JAyala J(2019)Census of bounded curvature pathsGeometriae Dedicata10.1007/s10711-019-00444-2Online publication date: 12-Apr-2019
https://doi.org/10.1007/s10711-019-00444-2
Upadhyay SRatnoo A(2018)On Existence and Synthesis of Smooth Four Parameter Logistic Paths Inside Annular PassagesIEEE Robotics and Automation Letters10.1109/LRA.2018.28670693:4(4375-4382)Online publication date: Oct-2018
https://doi.org/10.1109/LRA.2018.2867069
Takei RTsai R(2018)Optimal Trajectories of Curvature Constrained Motion in the Hamilton---Jacobi FormulationJournal of Scientific Computing10.1007/s10915-012-9671-y54:2-3(622-644)Online publication date: 30-Dec-2018
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Paden BCap MYong SYershov DFrazzoli E(2016)A Survey of Motion Planning and Control Techniques for Self-Driving Urban VehiclesIEEE Transactions on Intelligent Vehicles10.1109/TIV.2016.25787061:1(33-55)Online publication date: Mar-2016
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Maini PSujit P(2016)Path planning for a UAV with kinematic constraints in the presence of polygonal obstacles2016 International Conference on Unmanned Aircraft Systems (ICUAS)10.1109/ICUAS.2016.7502625(62-67)Online publication date: Jun-2016
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Su BWang TWu RWang J(2015)Infimum of Path Length of Nonholonomic Vehicle with Finitely Bounded Curvature RadiusJournal of Intelligent and Robotic Systems10.1007/s10846-014-0053-679:2(197-210)Online publication date: 1-Aug-2015
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Cowlagi RTsiotras P(2014)Curvature-Bounded Traversability Analysis in Motion Planning for Mobile RobotsIEEE Transactions on Robotics10.1109/TRO.2014.231571130:4(1011-1019)Online publication date: Aug-2014
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Singh AAggarwal AVashisht MSiddavatam R(2011)Robot motion planning in a dynamic environment using offset Non-Uniform Rational B-Splines (NURBS)2011 IEEE International Conference on Industrial Technology10.1109/ICIT.2011.5754393(312-317)Online publication date: Mar-2011
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Bakolas ETsiotras P(2008)On-line, kinodynamic trajectory generation through rectangular channels using path and motion primitives2008 47th IEEE Conference on Decision and Control10.1109/CDC.2008.4738712(3725-3730)Online publication date: Dec-2008
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Approximation Algorithms for Curvature Constrained Shortest Paths

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