Optimal any-angle path planning in static and dynamic environments

2026-06-30

AI Summary

Existing any-angle path planning methods struggle to simultaneously achieve optimality and computational efficiency in dynamic environments. This work proposes a unified optimal any-angle planning framework, Zeta*, along with its dynamic extension Zeta*-SIPP. The approach restricts the search space through elliptical forward expansion, replaces conventional line-of-sight checks with a Field of View (FoV) formulation, and accelerates visibility computation by integrating backward and forward sweep strategies. In static environments, Zeta* matches the performance of Anya, while in dynamic scenarios, Zeta*-SIPP achieves speedups of over 20× compared to TO-AA-SIPP—all while rigorously preserving solution optimality.

Abstract

Any-angle path planning extends traditional graph-based path planning by allowing movement between any pair of vertices, rather than being restricted by predefined edges. It can find straighter and shorter paths in continuous space with graphs, making it particularly suitable for navigation in open areas such as airspaces, warehouses, and oceans. Many any-angle path-planning algorithms have been proposed, but only a few can guarantee optimal solutions, especially in the presence of dynamic obstacles. To address this challenge, this article focuses on optimal any-angle path planning on grids and introduces two general techniques that accelerate computation while preserving optimality in both static and dynamic environments: 1) elliptical forward expansion, which leverages ellipse-based neighborhoods to restrict the search space, and 2) field of view, which replaces traditional line-of-sight methods to speed up visibility checks. To integrate these two techniques, inverted and forward scanning are introduced. Inverted scanning establishes visual connections from open nodes, whereas forward scanning initiates scans from closed nodes. Building on the proposed techniques, Zeta* and Zeta*-SIPP are developed for static and dynamic environments respectively. Zeta*, when combined with forward scanning, is similar to the state-of-the-art algorithm Anya and attains comparable performance. Unlike Anya, Zeta* can be readily extended to other settings, such as dynamic environments (e.g., Zeta*-SIPP). Zeta*-SIPP, with either scanning method, is more than 20 times faster than the corresponding state-of-the-art optimal planner TO-AA-SIPP. Overall, this research identifies the key requirements for achieving optimal any-angle path planning and introduces a unified approach suitable for different environments.

Problem

• any-angle path planning
• optimal path planning
• dynamic obstacles
• static environments
• grid-based navigation

Innovation

• any-angle path planning
• elliptical forward expansion
• field of view
• Zeta*-SIPP
• optimal path planning