An algorithm with exact bounds for coverage path planning in UAV-based search and rescue under windy conditions

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 planning the flight paths 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). We derive a precise lower bound for the objective function and develop a fast algorithm with a proven capability 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. The fast execution speed of the algorithms is demonstrated by numerical experiments with area sizes up to 10,000 grid cells.