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An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles

Authors:

Pankaj K. Agarwal,

Oren SalzmanAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 14, Issue 4

Article No.: 46, Pages 1 - 21

https://doi.org/10.1145/3230650

Published: 21 August 2018 Publication History

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Abstract

We study a path-planning problem amid a set O of obstacles in R², in which we wish to compute a short path between two points while also maintaining a high clearance from O; the clearance of a point is its distance from a nearest obstacle in O. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem. Let n be the total number of obstacle vertices and let ε ∈ (0, 1]. Our algorithm computes in time O(n²/ε² log n/ε) a path of total cost at most (1 + ε) times the cost of the optimal path.

References

[1]

Pankaj K. Agarwal and Hongyan Wang. 2000. Approximation algorithms for curvature-constrained shortest paths. SIAM J. Comput. 30, 6 (2000), 1739--1772.

Digital Library

[2]

Franz Aurenhammer, Rolf Klein, and Der-Tsai Lee. 2013. Voronoi Diagrams and Delaunay Triangulations. World Scientific.

Digital Library

[3]

John F. Canny and John H. Reif. 1987. New lower bound techniques for robot motion planning problems. In Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science. IEEE, 49--60.

Digital Library

[4]

Nicholas J. Cavanna and Donald R. Sheehy. 2016. Adaptive metrics for adaptive samples. In Proceedings of the Canadian Conference on Computational Geometry. Simon Fraser University, Vancouver, British Columbia, Canada.

[5]

Danny Z. Chen, Ovidiu Daescu, and Kevin S. Klenk. 2001. On geometric path query problems. Int. J. Comput. Geometry Appl. 11, 6 (2001), 617--645.

[6]

Danny Z. Chen and Haitao Wang. 2013. Computing shortest paths among curved obstacles in the plane. In Proceedings of the 29th Annual IEEE Symposium on Foundations of Computer Science. IEEE, 369--378.

Digital Library

[7]

Howie Choset, Kevin M. Lynch, Seth Hutchinson, George Kantor, Wolfram Burgard, Lydia E. Kavraki, and Sebastian Thrun. 2005. Principles of Robot Motion: Theory, Algorithms, and Implementation. MIT Press.

[8]

Kenneth L. Clarkson. 2006. Building triangulations using epsilon-nets. In ACM Symposium on Theory of Computing. 326--335.

Digital Library

[9]

Michael B. Cohen, Brittany Terese Fasy, Gary L. Miller, Amir Nayyeri, Donald R. Sheehy, and Ameya Velingker. 2015. Approximating nearest neighbor distances. In Proceedings of the 14th Annual Symposium on Algorithms and Data Structures. Springer, 200--211.

[10]

Michael L. Fredman and Robert Endre Tarjan. 1987. Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34, 3 (1987), 596--615.

Digital Library

[11]

Dan Halperin, Oren Salzman, and Micha Sharir. 2017. Algorithmic motion planning. In Handbook of Discrete and Computational Geometry (3rd ed.), C. D. Tóth, J. O’Rourke, and J. E. Goodman (Eds.). CRC Press LLC, 1311--1342.

[12]

Monika Rauch Henzinger, Philip N. Klein, Satish Rao, and Sairam Subramanian. 1997. Faster shortest-path algorithms for planar graphs. J. Comput. Syst. Sci. 55, 1 (1997), 3--23.

Digital Library

[13]

John Hershberger, Subhash Suri, and Hakan Yıldız. 2013. A near-optimal algorithm for shortest paths among curved obstacles in the plane. In Proceedings of the 29th Annual Symposium on Computational Geometry. 359--368.

Digital Library

[14]

Niel Lebeck, Thomas Mølhave, and Pankaj K. Agarwal. 2013. Computing highly occluded paths on a terrain. In Proceedings of the 21st Annual ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems. ACM, 14--23.

Digital Library

[15]

Joseph S. B. Mitchell. 2017. Shortest paths and networks. In Handbook of Discrete and Computational Geometry (3rd ed.), C. D. Tóth, J. O’Rourke, and J. E. Goodman (Eds.). CRC Press LLC, 811--848.

[16]

Joseph S. B. Mitchell, Günter Rote, and Gerhard J. Woeginger. 1992. Minimum-link paths among obstacles in the plan. Algorithmica 8, 5 8 6 (1992), 431--459.

Digital Library

[17]

Colm Ó’Dúnlaing and Chee-Keng Yap. 1985. A “retraction” method for planning the motion of a disc. J. Algo. 6, 1 (1985), 104--111.

[18]

Guang Song, Shawna Miller, and Nancy M. Amato. 2001. Customizing PRM roadmaps at query time. In Proceedings of the IEEE International Conference on Robotics and Automation. IEEE, 1500--1505.

[19]

Ron Wein, Jur P. van den Berg, and Dan Halperin. 2007. The visibility-Voronoi complex and its applications. Comput. Geom. 36, 1 (2007), 66--87.

Digital Library

[20]

Ron Wein, Jur P. van den Berg, and Dan Halperin. 2008. Planning high-quality paths and corridors amidst obstacles. I. J. Robot. Res. 27, 11--12 (2008), 1213--1231.

Cited By

Hsieh MShell DFu MSolovey KSalzman OAlterovitz R(2023)Toward certifiable optimal motion planning for medical steerable needlesInternational Journal of Robotics Research10.1177/0278364923116581842:10(798-826)Online publication date: 1-Sep-2023
https://dl.acm.org/doi/10.1177/02783649231165818
Strub MGammell J(2022)Adaptively Informed Trees (AIT*) and Effort Informed Trees (EIT*)International Journal of Robotics Research10.1177/0278364921106957241:4(390-417)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1177/02783649211069572
Ramamurthi YAgarwal TChattopadhyay A(2022)A Topological Similarity Measure Between Multi-Resolution Reeb SpacesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.308727328:12(4360-4374)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1109/TVCG.2021.3087273
Show More Cited By

Index Terms

An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles
1. Computing methodologies
  1. Artificial intelligence
    1. Planning and scheduling
      1. Robotic planning
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
  2. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 14, Issue 4

October 2018

445 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3266298

Editor:
Aravind Srinivasan
University of Maryland, USA

Issue’s Table of Contents

Copyright © 2018 ACM.

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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 August 2018

Accepted: 01 May 2018

Revised: 01 May 2018

Received: 01 June 2017

Published in TALG Volume 14, Issue 4

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National Science Foundation
United States-Israel Binational Science Foundation
German-Israeli Foundation
Office of Naval Research
Hermann Minkowski Minerva Center for Geometry at Tel Aviv University
Israel Science Foundation
Toyota Motor Engineering & Manufacturing

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Cited By

Hsieh MShell DFu MSolovey KSalzman OAlterovitz R(2023)Toward certifiable optimal motion planning for medical steerable needlesInternational Journal of Robotics Research10.1177/0278364923116581842:10(798-826)Online publication date: 1-Sep-2023
https://dl.acm.org/doi/10.1177/02783649231165818
Strub MGammell J(2022)Adaptively Informed Trees (AIT*) and Effort Informed Trees (EIT*)International Journal of Robotics Research10.1177/0278364921106957241:4(390-417)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1177/02783649211069572
Ramamurthi YAgarwal TChattopadhyay A(2022)A Topological Similarity Measure Between Multi-Resolution Reeb SpacesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.308727328:12(4360-4374)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1109/TVCG.2021.3087273
Kuntz AFu MAlterovitz R(2022)Planning High-Quality Motions for Concentric Tube Robots in Point Clouds via Parallel Sampling and optimization2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)10.1109/IROS40897.2019.8968172(2205-2212)Online publication date: 28-Dec-2022
https://dl.acm.org/doi/10.1109/IROS40897.2019.8968172
Fu MSolovey KSalzman OAlterovitz R(2022)Resolution-Optimal Motion Planning for Steerable Needles2022 International Conference on Robotics and Automation (ICRA)10.1109/ICRA46639.2022.9811850(9652-9659)Online publication date: 23-May-2022
https://dl.acm.org/doi/10.1109/ICRA46639.2022.9811850
Salzman O(2020)RoadmapsEncyclopedia of Robotics10.1007/978-3-642-41610-1_168-1(1-7)Online publication date: 30-Mar-2020
https://doi.org/10.1007/978-3-642-41610-1_168-1
Li MLi SGe Y(2019)High-quality trajectory planning for heterogeneous individuals针对异质群体的高质量轨迹规划方法Journal of Central South University10.1007/s11771-019-4036-426:3(654-664)Online publication date: 22-Apr-2019
https://doi.org/10.1007/s11771-019-4036-4

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