Any-angle path planning

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The path found by A* on an octile grid vs. the shortest path between the start and goal nodes. Shortest path vs A* on octile grid.png
The path found by A* on an octile grid vs. the shortest path between the start and goal nodes.

Any-angle path planning algorithms are pathfinding algorithms that search for a Euclidean shortest path between two points on a grid map while allowing the turns in the path to have any angle. The result is a path that cuts directly through open areas and has relatively few turns. [1] More traditional pathfinding algorithms such as A* either lack in performance or produce jagged, indirect paths.

Contents

Background

Real-world and many game maps have open areas that are most efficiently traversed in a direct way. Traditional algorithms are ill-equipped to solve these problems:

An any-angle path planning algorithm aims to produce optimal or near-optimal solutions while taking less time than the basic visibility graph approach. Fast any-angle algorithms take roughly the same time as a grid-based solution to compute.

Definitions

Taut path
A path where every heading change in the path “wraps” tightly around some obstacle. For a uniform grid, only taut paths can be optimal.
Single-source
A path-finding problem that seeks to find the shortest path to all parts from the graph, starting from one vertex.

Algorithms

A*-based

So far, five main any-angle path planning algorithms that are based on the heuristic search algorithm A* [3] have been developed, all of which propagate information along grid edges:

There are also A*-based algorithm distinct from the above family:

RRT-based

Besides, for search in high-dimensional search spaces, such as when the configuration space of the system involves many degrees of freedom that need to be considered (see Motion planning), and/or momentum needs to be considered (which could effectively double the number of dimensions of the search space; this larger space including momentum is known as the phase space), variants of the rapidly-exploring random tree (RRT) [23] have been developed that (almost surely) converge to the optimal path by increasingly finding shorter and shorter paths:

Other algorithms

Applications

Any-angle path planning are useful for robot navigation and real-time strategy games where more optimal paths are desirable. Hybrid A*, for example, was used as an entry to a DARPA challenge. [21] The steering-aware properties of some examples also translate to autonomous cars.

See also

References

  1. Tansel Uras and Sven Koenig. An Empirical Comparison of Any-Angle Path-Planning Algorithms. Proceedings of the Eighth International Symposium on Combinatorial Search.
  2. 1 2 3 A. Nash. Any-Angle Path Planning. PhD thesis, Department of Computer Science, University of Southern California, Los Angeles (California), 2012.
  3. P. Hart, N. Nilsson and B. Raphael, A Formal Basis for the Heuristic Determination of Minimum Cost Paths, IEEE Trans. Syst. Science and Cybernetics, SSC-4(2), 100-107, 1968.
  4. D. Ferguson and A. Stentz. Field D*: An Interpolation-Based Path Planner and Replanner. Proceedings of the International Symposium on Robotics Research, 2005.
  5. David Ferguson and Anthony (Tony) Stentz, "The Field D* Algorithm for Improved Path Planning and Replanning in Uniform and Non-Uniform Cost Environments," tech. report CMU-RI-TR-05-19, Robotics Institute, Carnegie Mellon University, June, 2005
  6. 1 2 3 4 A. Nash, K. Daniel, S. Koenig and A. Felner. Theta*: Any-Angle Path Planning on Grids. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 1177–1183, 2007.
  7. Carsten, Joseph; Ferguson, Dave; Stentz, Anthony (October 9–15, 2006). "3D Field D*: Improved Path Planning and Replanning in Three Dimensions" (PDF). Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on. Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems. Beijing, China: IEEE. pp. 3381–3386. doi:10.1109/IROS.2006.282516 . Retrieved 2014-11-07.
  8. Carsten, J.; Ferguson, D.; Stentz, A. (2006). "3D Field D: Improved Path Planning and Replanning in Three Dimensions". 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems. p. 3381. CiteSeerX   10.1.1.188.150 . doi:10.1109/IROS.2006.282516. ISBN   978-1-4244-0258-8. S2CID   1845942.
  9. Mitchell, J. S. B.; Papadimitriou, C. H. (1991). "The weighted region problem: Finding shortest paths through a weighted planar subdivision". Journal of the ACM. 38: 18–73. doi:10.1145/102782.102784. hdl: 1813/8768 . S2CID   12673773.
  10. Dave Ferguson and Anthony Stentz. Multi-resolution Field D*. Proceedings of the International Conference on Intelligent, 2006.
  11. 1 2 Daniel, K.; Nash, A.; Koenig, S.; Felner, A. (2010). "Theta*: Any-Angle Path Planning on Grids" (PDF). Journal of Artificial Intelligence Research. 39: 533–579. doi: 10.1613/jair.2994 .
  12. Nash, A.; Koenig, S.; Tovey, C. (2010). "Lazy Theta*: Any-Angle Path Planning and Path Length Analysis in 3D" (PDF). Proceedings of the AAAI Conference on Artificial Intelligence. 24: 147–154. doi:10.1609/aaai.v24i1.7566. S2CID   3754577.
  13. Nash, A.; Koenig, S.; Likhachev, M. (2009). "Incremental Phi*: Incremental Any-Angle Path Planning on Grids" (PDF). Proceedings of the International Joint Conference on Artificial Intelligence: 1824–1830.
  14. Shunhao Oh, Hon Wai Leong, 2016. Strict Theta*: Shorter Motion Path Planning Using Taut Paths. In Proceedings of Twenty-Sixth International Conference on Automated Planning and Scheduling. https://www.aaai.org/ocs/index.php/ICAPS/ICAPS16/paper/view/13049
  15. P. Yap, N. Burch, R. Holte, and J. Schaeffer, Block A*: Database-Driven Search with Applications in Any-angle Path-Planning. Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence, 2011.
  16. Daniel Harabor and Alban Grastien. An Optimal Any-Angle Pathfinding Algorithm. Proceedings of the Twenty-Third International Conference on Automated Planning and Scheduling.
  17. Sinyukov, Dmitry A.; Padir, Taskin (May–June 2017). "CWave: High-Performance Single-Source Any-Angle Path Planning on a Grid". Proceedings of the 2017 IEEE International Conference on Robotics and Automation (ICRA). 2017 IEEE International Conference on Robotics and Automation (ICRA). Singapore: IEEE. pp. 6190–6197. doi:10.1109/ICRA.2017.7989733.
  18. Sinyukov, Dmitry A.; Padir, Taskin (2020). "CWave: Theory and Practice of a Fast Single-source Any-angle Path Planning Algorithm". Robotica. 38 (2). Cambridge University Press: 207–234. doi:10.1017/S0263574719000560. S2CID   182189674.
  19. Oh, Shunhao; Leong, Hon Wai (5 June 2017). "Edge N-Level Sparse Visibility Graphs: Fast Optimal Any-Angle Pathfinding Using Hierarchical Taut Paths". Tenth Annual Symposium on Combinatorial Search. arXiv: 1702.01524 .
  20. Cui, Michael; Harabor, Daniel D.; Grastien, Alban (2017). "Compromise-free Pathfinding on a Navigation Mesh". Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence: 496–502.
  21. 1 2 Junior: The Stanford Entry in the Urban Challenge
  22. Petereit, Janko; Emter, Thomas; Frey, Christian W.; Kopfstedt, Thomas; Beutel, Andreas (May 2012). "Application of Hybrid A* to an Autonomous Mobile Robot for Path Planning in Unstructured Outdoor Environments". ROBOTIK 2012; 7th German Conference on Robotics: 1–6.
  23. LaValle, Steven M. (October 1998). "Rapidly-exploring random trees: A new tool for path planning" (PDF). Technical Report (TR 98–11).
  24. Karaman, Sertac; Frazzoli, Emilio (3 May 2010). "Incremental Sampling-based Algorithms for Optimal Motion Planning". arXiv: 1005.0416 [cs.RO].
  25. Karaman, Sertac; Frazzoli, Emilio (5 May 2011). "Sampling-based Algorithms for Optimal Motion Planning". arXiv: 1105.1186 [cs.RO].
  26. Gammell, Jonathan D.; Srinivasa, Siddhartha S.; Barfoot, Timothy D. (2014). "Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic". 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems. pp. 2997–3004. arXiv: 1404.2334 . doi:10.1109/IROS.2014.6942976. ISBN   978-1-4799-6934-0.