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Approximation Algorithms for the UAV Path Planning with Object Coverage Constraints

Jiawei Wang, Vincent Chau, Weiwei Wu

TL;DR

The paper tackles UAV path planning under object-coverage constraints, focusing on observing all sides of rectangular objects while minimizing flight length. It develops an offline $(1+\epsilon)(2+2n)$-approximation algorithm and three online heuristics that adapt as objects are discovered, all grounded in a Steiner-tree–based framework and TSP approximations. Empirical results show the offline and online methods achieve costs close to a Gurobi ILP solver (within approximately 1.2–1.3×) but with dramatically shorter runtimes, whereas a vanilla Best Available TSP approach performs worse, especially as the number of objects increases. The work demonstrates practical, scalable solutions for coverage-constrained UAV routing with provable guarantees and competitive performance.

Abstract

We study the problem of the Unmanned Aerial Vehicle (UAV) such that a specific set of objects needs to be observed while ensuring a quality of observation. Our goal is to determine the shortest path for the UAV. This paper proposes an offline algorithm with an approximation of $(2+2n)(1+ε)$ where $ε>0$ is a small constant, and $n$ is the number of objects. We then propose several online algorithms in which objects are discovered during the process. To evaluate the performance of these algorithms, we conduct experimental comparisons. Our results show that the online algorithms perform similarly to the offline algorithm, but with significantly faster execution times ranging from 0.01 seconds to 200 seconds. We also show that our methods yield solutions with costs comparable to those obtained by the Gurobi optimizer that requires 30000 seconds of runtime.

Approximation Algorithms for the UAV Path Planning with Object Coverage Constraints

TL;DR

The paper tackles UAV path planning under object-coverage constraints, focusing on observing all sides of rectangular objects while minimizing flight length. It develops an offline -approximation algorithm and three online heuristics that adapt as objects are discovered, all grounded in a Steiner-tree–based framework and TSP approximations. Empirical results show the offline and online methods achieve costs close to a Gurobi ILP solver (within approximately 1.2–1.3×) but with dramatically shorter runtimes, whereas a vanilla Best Available TSP approach performs worse, especially as the number of objects increases. The work demonstrates practical, scalable solutions for coverage-constrained UAV routing with provable guarantees and competitive performance.

Abstract

We study the problem of the Unmanned Aerial Vehicle (UAV) such that a specific set of objects needs to be observed while ensuring a quality of observation. Our goal is to determine the shortest path for the UAV. This paper proposes an offline algorithm with an approximation of where is a small constant, and is the number of objects. We then propose several online algorithms in which objects are discovered during the process. To evaluate the performance of these algorithms, we conduct experimental comparisons. Our results show that the online algorithms perform similarly to the offline algorithm, but with significantly faster execution times ranging from 0.01 seconds to 200 seconds. We also show that our methods yield solutions with costs comparable to those obtained by the Gurobi optimizer that requires 30000 seconds of runtime.

Paper Structure

This paper contains 29 sections, 5 theorems, 3 equations, 12 figures, 2 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. UAV path planning
  4. UAV coverage
  5. Travelling Salesman Problem (TSP)
  6. System Model and Problem Formulation
  7. System Model
  8. Discretization of observation points
  9. Integer Linear Programming representation
  10. Methodology
  11. An approximation algorithm
  12. Construction of graph
  13. Selection of the observation points
  14. Construction of the path
  15. Online solutions
  16. ...and 14 more sections

Key Result

Lemma 2

The gross error of the discretization process does not exceed $\epsilon*D$.

Figures (12)

  • Figure 1: Efficient observation that satisfies both the distance and the angle constraints.
  • Figure 2: Area discretization of the observation range
  • Figure 3: Graph construction
  • Figure 4: A possible Steiner tree connecting the selected observation points that observes all faces of all objects
  • Figure 5: Approximation algorithm
  • ...and 7 more figures

Theorems & Definitions (7)

  • Definition 1: Efficient observation
  • Lemma 2
  • Definition 5: Steiner Tree
  • Lemma 7
  • Lemma 8
  • Lemma 9
  • Theorem 10