Approximation Algorithms for the UAV Path Planning with Object Coverage Constraints

2025-04-11

AI Summary

This paper addresses the shortest-path planning problem for unmanned aerial vehicles (UAVs) under multi-objective observational constraints, balancing both data quality and coverage completeness. It supports two operational paradigms: offline near-optimal approximation and online dynamic target discovery. Methodologically, the authors formulate the problem as a combinatorial optimization model and propose the first offline algorithm with a provable $(2+2n)(1+varepsilon)$-approximation ratio. For online settings, they design multiple efficient algorithms achieving solution times of only 0.01–200 seconds—over 99% faster than Gurobi’s exact solver (which requires ~30,000 seconds)—while attaining solution quality comparable to both the offline approximation and Gurobi’s optimal solutions. Through rigorous theoretical analysis and comprehensive experimental evaluation, the work demonstrates significant advantages in timeliness, practical deployability, and theoretical guarantees.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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 $(2+2n)(1+epsilon)$ where $epsilon>0$ 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.

Problem

• Optimize UAV path for object coverage with quality constraints
• Develop offline and online algorithms for shortest path planning
• Compare algorithm performance in execution time and solution cost

Innovation

• Offline algorithm with $(2+2n)(1+ε)$ approximation
• Online algorithms for dynamic object discovery
• Fast execution times from 0.01 to 200 seconds