In this paper, we present a new approach for maximizing the coverage path planning while minimizing the path length of an aerial robot in agriculture environment with concave obstacles. For resolving this problem, we propose a new cellular decomposition which is based on a generalization of the Boustrophedon variant, using Morse functions, with an extension of the representation of the critical points. This extension leads to a decrease of the number of cells after decomposition. The results show that this new cellular decomposition works well even with several concave obstacles inside the environment. Furthermore, for path planning, the cells are divided again into two classes, leading to have a cell set better suited for use of the traveling salesman problem (TSP) to get complete coverage. Genetic Algorithm (GA) and TSP algorithm are applied to obtain the shortest path. Then, an approach is also proposed to maximize the scanned area on the working area with obstacles. The proposed method can be applied in precision agriculture for monitoring insects and other crop pests. The effectiveness of the proposed method has been verified on Matlab/Simulink.