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Air-FAR: Fast and Adaptable Routing for Aerial Navigation in Large-scale Complex Unknown Environments

Botao He, Guofei Chen, Cornelia Fermuller, Yiannis Aloimonos, Ji Zhang

TL;DR

This work tackles real-time 3D navigation in large-scale unknown environments by introducing a hierarchical 3D visibility graph (V-graph) with a layered polygon map and heuristic visibility updates, achieving real-time construction with a complexity of $O\left(K\cdot n^2\log n\right)$. It couples this with an iterative divide-and-conquer path search that yields near-optimal trajectories within strict time limits, demonstrated across extensive simulations and real-world quadrotor experiments. The method outperforms traditional planners (A*, RRT*, BIT*, FAR) in construction speed and path quality, while maintaining robust performance under diverse sensor configurations and environments. Key contributions include the local-global two-layer graph update, the polyhedron-based obstacle representation, and the explorative-optimal planning framework, all released as open-source to accelerate future research and practical deployment.

Abstract

This paper presents a novel method for real-time 3D navigation in large-scale, complex environments using a hierarchical 3D visibility graph (V-graph). The proposed algorithm addresses the computational challenges of V-graph construction and shortest path search on the graph simultaneously. By introducing hierarchical 3D V-graph construction with heuristic visibility update, the 3D V-graph is constructed in O(K*n^2logn) time, which guarantees real-time performance. The proposed iterative divide-and-conquer path search method can achieve near-optimal path solutions within the constraints of real-time operations. The algorithm ensures efficient 3D V-graph construction and path search. Extensive simulated and real-world environments validated that our algorithm reduces the travel time by 42%, achieves up to 24.8% higher trajectory efficiency, and runs faster than most benchmarks by orders of magnitude in complex environments. The code and developed simulator have been open-sourced to facilitate future research.

Air-FAR: Fast and Adaptable Routing for Aerial Navigation in Large-scale Complex Unknown Environments

TL;DR

This work tackles real-time 3D navigation in large-scale unknown environments by introducing a hierarchical 3D visibility graph (V-graph) with a layered polygon map and heuristic visibility updates, achieving real-time construction with a complexity of . It couples this with an iterative divide-and-conquer path search that yields near-optimal trajectories within strict time limits, demonstrated across extensive simulations and real-world quadrotor experiments. The method outperforms traditional planners (A*, RRT*, BIT*, FAR) in construction speed and path quality, while maintaining robust performance under diverse sensor configurations and environments. Key contributions include the local-global two-layer graph update, the polyhedron-based obstacle representation, and the explorative-optimal planning framework, all released as open-source to accelerate future research and practical deployment.

Abstract

This paper presents a novel method for real-time 3D navigation in large-scale, complex environments using a hierarchical 3D visibility graph (V-graph). The proposed algorithm addresses the computational challenges of V-graph construction and shortest path search on the graph simultaneously. By introducing hierarchical 3D V-graph construction with heuristic visibility update, the 3D V-graph is constructed in O(K*n^2logn) time, which guarantees real-time performance. The proposed iterative divide-and-conquer path search method can achieve near-optimal path solutions within the constraints of real-time operations. The algorithm ensures efficient 3D V-graph construction and path search. Extensive simulated and real-world environments validated that our algorithm reduces the travel time by 42%, achieves up to 24.8% higher trajectory efficiency, and runs faster than most benchmarks by orders of magnitude in complex environments. The code and developed simulator have been open-sourced to facilitate future research.
Paper Structure (19 sections, 2 theorems, 3 equations, 6 figures, 5 tables, 2 algorithms)

This paper contains 19 sections, 2 theorems, 3 equations, 6 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Search- or Sampling-based Path Search for 3D Navigation in unknown environments
  4. V-graph-based Navigation
  5. Problem Definition
  6. 3D V-graph Construction and Update
  7. Polyhedron Extraction
  8. Local 3D V-graph Construction
  9. Two-layer Graph Update
  10. Computational Complexity Analysis
  11. Iterative Divide-and-Conquer Path Search
  12. Admissibility, Completeness and Optimality
  13. Experiments
  14. Experiment Setup
  15. Simulation
  16. ...and 4 more sections

Key Result

Theorem 1

Each vertex takes at most $O(k \cdot n\log{n})$ time to update its visibility in $\hat{\mathcal{P}}_{local}$.

Figures (6)

  • Figure 2: Benefits of the proposed algorithm.
  • Figure 3: Illustration of the steps to heuristically construct the 3D V-graph.
  • Figure 4: Illustration for the proposed iterative divide-and-conquer path search algorithm.
  • Figure 5: Experiment setup. The left column shows the simulated drone with a Lidar, overview of the garage and the factory. The right column shows the customized quadroter with a depth camera, overview of the lab and the outdoor space.
  • Figure 6: The resulting map and trajectories of system-level experiment in Garage.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Definition 1
  • Theorem 1
  • Theorem 2