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An exact coverage path planning algorithm for UAV-based search and rescue operations

Sina Kazemdehbashi, Yanchao Liu

TL;DR

This work tackles wind-aware coverage path planning for multiple UAVs in SAR, discretizing the search region into an $n\times m$ grid and formulating the problem as a MIP baseline. It introduces a provable lower bound, LB, with $\text{LB} = (n-1)T_s + (\lceil nm/q \rceil - n)T_p$, and a constructive Near-Optimal Path Planning (NOPP) algorithm that guarantees solutions in {LB, LB+Tp} through a four-phase process. The approach extends to Moore neighborhood connectivity and demonstrates strong scalability, achieving near-optimal solutions for large instances (up to 10,000 cells) with negligible relative gaps while dramatically reducing computation compared to the baseline MIP. The practical impact lies in providing SAR teams with a fast, reliable method to coordinate UAV swarms under wind, enabling timely discovery and safer, more efficient missions.

Abstract

Unmanned aerial vehicles (UAVs) are increasingly utilized in global search and rescue efforts, enhancing operational efficiency. In these missions, a coordinated swarm of UAVs is deployed to efficiently cover expansive areas by capturing and analyzing aerial imagery and footage. Rapid coverage is paramount in these scenarios, as swift discovery can mean the difference between life and death for those in peril. This paper focuses on optimizing flight path planning for multiple UAVs in windy conditions to efficiently cover rectangular search areas in minimal time. We address this challenge by dividing the search area into a grid network and formulating it as a mixed-integer program (MIP). Our research introduces a precise lower bound for the objective function and an exact algorithm capable of finding either the optimal solution or a near-optimal solution with a constant absolute gap to optimality. Notably, as the problem complexity increases, our solution exhibits a diminishing relative optimality gap while maintaining negligible computational costs compared to the MIP approach.

An exact coverage path planning algorithm for UAV-based search and rescue operations

TL;DR

This work tackles wind-aware coverage path planning for multiple UAVs in SAR, discretizing the search region into an grid and formulating the problem as a MIP baseline. It introduces a provable lower bound, LB, with , and a constructive Near-Optimal Path Planning (NOPP) algorithm that guarantees solutions in {LB, LB+Tp} through a four-phase process. The approach extends to Moore neighborhood connectivity and demonstrates strong scalability, achieving near-optimal solutions for large instances (up to 10,000 cells) with negligible relative gaps while dramatically reducing computation compared to the baseline MIP. The practical impact lies in providing SAR teams with a fast, reliable method to coordinate UAV swarms under wind, enabling timely discovery and safer, more efficient missions.

Abstract

Unmanned aerial vehicles (UAVs) are increasingly utilized in global search and rescue efforts, enhancing operational efficiency. In these missions, a coordinated swarm of UAVs is deployed to efficiently cover expansive areas by capturing and analyzing aerial imagery and footage. Rapid coverage is paramount in these scenarios, as swift discovery can mean the difference between life and death for those in peril. This paper focuses on optimizing flight path planning for multiple UAVs in windy conditions to efficiently cover rectangular search areas in minimal time. We address this challenge by dividing the search area into a grid network and formulating it as a mixed-integer program (MIP). Our research introduces a precise lower bound for the objective function and an exact algorithm capable of finding either the optimal solution or a near-optimal solution with a constant absolute gap to optimality. Notably, as the problem complexity increases, our solution exhibits a diminishing relative optimality gap while maintaining negligible computational costs compared to the MIP approach.
Paper Structure (20 sections, 9 theorems, 13 equations, 12 figures, 8 tables, 4 algorithms)

This paper contains 20 sections, 9 theorems, 13 equations, 12 figures, 8 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Problem Formulation
  4. Grid-based decomposition
  5. Mathematical formulation - a baseline
  6. Main Method
  7. Lower bound derivation
  8. Near-optimal path planning algorithm (NOPP)
  9. Initial settings
  10. Phase one
  11. Phase two
  12. Phase three
  13. Phase four
  14. Generating paths for UAVs
  15. Extension to Moore Neighborhood Connectivity
  16. ...and 5 more sections

Key Result

Lemma 1

Let $A$, $B$, $K$, $H$, and $N$ be non-negative real numbers satisfying $A \le B \le K$, $A + K \ge 2B$, and $H \ge N$. Then, the optimal value for $(x_1,x_2,x_3)$ in the following linear programming problem is $(x_1^*,x_2^*,x_3^*)=(N,H-N,0)$.

Figures (12)

  • Figure 1: Suppose a SAR team receives a report of a missing mid-age hiker whose last contact was about two hours ago. Assuming an average human walking speed of 5 km/h, the radius of the region of interest would be approximately 10 km.
  • Figure 2: (a) The camera's field of view, aligned with a cell in the grid; (b) Cell indexing convention for an ($n \times m$) rectangular search area.
  • Figure 3: Illustration of cell labeling for neighbors under Assumption 2.
  • Figure 4: Example of calculating the H-value for the first UAV after phase 1 in two cases: (a) Due to $|S^*|=7$ and a $D$ move before $S^*$, the H-value is 6 ($n=8,\ m=9,\ q=5$); (b) Since there is no $U^*$, the H-value is 0 ($n=8,\ m=9,\ q=8$).
  • Figure 5: The flowchart of the NOPP algorithm.
  • ...and 7 more figures

Theorems & Definitions (18)

  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Lemma 2
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • ...and 8 more