Theta*

Theta*: Any-Angle Path Planning on Grids. Grids with blocked and unblocked cells are often used to represent terrain in robotics and video games. However, paths formed by grid edges can be longer than true shortest paths in the terrain since their headings are artificially constrained. We present two new correct and complete any-angle path-planning algorithms that avoid this shortcoming. Basic Theta* and Angle-Propagation Theta* are both variants of A* that propagate information along grid edges without constraining paths to grid edges. Basic Theta* is simple to understand and implement, fast and finds short paths. However, it is not guaranteed to find true shortest paths. Angle-Propagation Theta* achieves a better worst-case complexity per vertex expansion than Basic Theta* by propagating angle ranges when it expands vertices, but is more complex, not as fast and finds slightly longer paths. We refer to Basic Theta* and Angle-Propagation Theta* collectively as Theta*. Theta* has unique properties, which we analyze in detail. We show experimentally that it finds shorter paths than both A* with post-smoothed paths and Field D* (the only other version of A* we know of that propagates information along grid edges without constraining paths to grid edges) with a runtime comparable to that of A* on grids. Finally, we extend Theta* to grids that contain unblocked cells with non-uniform traversal costs and introduce variants of Theta* which provide different tradeoffs between path length and runtime.


References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Guo, Jinlong; Li, Bin; Ji, Yuandong: A control parametrization based path planning method for the quad-rotor UAVs (2022)
  2. Kaplunova, E. P.; Tochilin, P. A.: The problem of target control for a quadrotor when moving in a horizontal plane avoiding obstacles (2021)
  3. Zambom, Adriano Zanin; Seguin, Brian: Fastest motion planning for an unmanned vehicle in the presence of accelerating obstacles (2021)
  4. Dai, Yanyan; Qian, Dianwei; Lee, SukGyu: Multiple robots motion control to transport an object (2018)
  5. Ivorra, Benjamin: Application of the laminar Navier-Stokes equations for solving 2D and 3D pathfinding problems with static and dynamic spatial constraints: implementation and validation in Comsol Multiphysics (2018)
  6. Andreychuk, A. A.; Yakovlev, K. S.: Two-dimensional path finding subject to geometric constraints (2017)
  7. Harabor, Daniel Damir; Grastien, Alban; Öz, Dindar; Aksakalli, Vural: Optimal any-angle pathfinding in practice (2016)
  8. Yang, Liang; Qi, Juntong; Song, Dalei; Xiao, Jizhong; Han, Jianda; Xia, Yong: Survey of robot 3D path planning algorithms (2016)
  9. Yin, Quanjun; Qin, Long; Liu, Xiaocheng; Zha, Yabing: Incremental construction of generalized Voronoi diagrams on pointerless quadtrees (2014)
  10. De Filippis, Luca; Guglieri, Giorgio; Quagliotti, Fulvia: Path planning strategies for UAVs in 3D environments (2012) ioport
  11. Daniel, Kenny; Nash, Alex; Koenig, Sven; Felner, Ariel: Theta(^*): any-angle path planning on grids (2010)