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Flow-Based Path Planning for Multiple Homogenous UAVs for Outdoor Formation-Flying

Mahmud Suhaimi Ibrahim, Shantanu Rahman, Muhammad Samin Hasan, Minhaj Uddin Ahmad, Abdullah Abrar

TL;DR

This work tackles collision-free path planning for outdoor multi-UAV formation flying with unlabeled UAVs by formulating space as a flow network and solving a maximum-flow problem. It discretizes the 3D environment into a grid, constructs a Space Graph $G_s$ and a State Graph $G_x$, then uses a virtual source/sink with unit-capacity edges to derive collision-free routes via the Ford-Fulkerson algorithm, guided by an initial shortest-path step from Bellman-Ford. The approach is validated through software-in-the-loop simulations with up to 64 UAVs and outdoor experiments involving three quadcopters, demonstrating safe, scalable formation flying and efficient computation times. The results indicate the method’s practical viability for real-time formation control and collision avoidance in complex outdoor environments.

Abstract

Collision-free path planning is the most crucial component in multi-UAV formation-flying (MFF). We use unlabeled homogenous quadcopters (UAVs) to demonstrate the use of a flow network to create complete (inter-UAV) collision-free paths. This procedure has three main parts: 1) Creating a flow network graph from physical GPS coordinates, 2) Finding a path of minimum cost (least distance) using any graph-based path-finding algorithm, and 3) Implementing the Ford-Fulkerson Method to find the paths with the maximum flow (no collision). Simulations of up to 64 UAVs were conducted for various formations, followed by a practical experiment with 3 quadcopters for testing physical plausibility and feasibility. The results of these tests show the efficacy of this method's ability to produce safe, collision-free paths.

Flow-Based Path Planning for Multiple Homogenous UAVs for Outdoor Formation-Flying

TL;DR

This work tackles collision-free path planning for outdoor multi-UAV formation flying with unlabeled UAVs by formulating space as a flow network and solving a maximum-flow problem. It discretizes the 3D environment into a grid, constructs a Space Graph and a State Graph , then uses a virtual source/sink with unit-capacity edges to derive collision-free routes via the Ford-Fulkerson algorithm, guided by an initial shortest-path step from Bellman-Ford. The approach is validated through software-in-the-loop simulations with up to 64 UAVs and outdoor experiments involving three quadcopters, demonstrating safe, scalable formation flying and efficient computation times. The results indicate the method’s practical viability for real-time formation control and collision avoidance in complex outdoor environments.

Abstract

Collision-free path planning is the most crucial component in multi-UAV formation-flying (MFF). We use unlabeled homogenous quadcopters (UAVs) to demonstrate the use of a flow network to create complete (inter-UAV) collision-free paths. This procedure has three main parts: 1) Creating a flow network graph from physical GPS coordinates, 2) Finding a path of minimum cost (least distance) using any graph-based path-finding algorithm, and 3) Implementing the Ford-Fulkerson Method to find the paths with the maximum flow (no collision). Simulations of up to 64 UAVs were conducted for various formations, followed by a practical experiment with 3 quadcopters for testing physical plausibility and feasibility. The results of these tests show the efficacy of this method's ability to produce safe, collision-free paths.

Paper Structure

This paper contains 15 sections, 2 equations, 12 figures, 1 table, 5 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Directed Weighted Graphs
  4. Bellman-Ford Algorithm
  5. Flow Network and Maximum Flow Problem
  6. Flow Network generation
  7. Maximum Flow Problem and Ford Fulkerson Algorithm
  8. Conflict resolution using the Ford-Fulkerson Algorithm
  9. Experimental Setup
  10. Simulations
  11. Physical Experiment
  12. Results and Discussions
  13. Simulations
  14. Physical test
  15. Conclusion and Future works

Figures (12)

  • Figure 1: Space Graph showing the nodes and edges
  • Figure 2: A pair of connected nodes in $G_s$ getting converted into Two pairs of nodes and interconnected edges in $G_x$
  • Figure 3: A flow network, G, with four nodes; s indicates the source, and t indicates the sink.
  • Figure 7: Final flow network with the augmented flow
  • Figure 8: Conflict resolution in the Flow Network
  • ...and 7 more figures