To cover an area of interest by an autonomous vehicle, such as an Unmanned Aerial Vehicle (UAV), planning a coverage path which guides the unit to cover the area is an essential process. However, coverage path planning is often problematic, especially when the boundary of the area is complicated and the area contains several obstacles. A common solution for this situation is to decompose the area into disjoint convex sub-polygons and to obtain coverage paths for each sub-polygon using a simple back-and-forth pattern. Aligned with the solution approach, we propose a new convex decomposition method which is simple and applicable to any shape of target area. The proposed method is designed based on the idea that, given an area of interest represented as a polygon, a convex decomposition of the polygon mainly occurs at the points where an interior angle between two edges of the polygon is greater than 180 degrees. The performance of the proposed method is demonstrated by comparison with existing convex decomposition methods using illustrative examples.

This paper models an operation problem of an unmanned aerial vehicle for the emergency medical service (UEMS) system. The model is set up as a location-allocation problem. The coverage distance and capacity of the UEMS facility are modeled as functions of UAVs assigned. The allocation of the demand point is constrained by the variable coverage distance of each facility. The robust optimization approach is used over the cardinality-constrained uncertain demand, which leads to a nonlinear optimization problem. The UEMS location-allocation problem (ULAP) is reformulated to a solvable problem. An extended formulation and corresponding branch-and-price (B&P) algorithm are also proposed, which strengthen the linear programming relaxation bound. The subproblem of the B&P algorithm is defined as a robust disjunctively constrained integer knapsack problem. Two solution approaches of mixed-integer linear programming reformulation and decomposed dynamic programming are designed for the subproblem. To provide time-efficient solutions for large-scale problems, a restricted master heuristic (RMH) is proposed based on the extended formulation. In computational experiments, the B&P algorithm provided a strong lower bound, and the RMH could find an effective feasible solution within an applicable computation time.