*3.7. Path Searching on the Waypoints Graph*

After constructing the WG, the path searching is carried out to find the complete coverage path from the pre-determined location of the UAV. The source point *p* represents the point from where the UAV starts the mission and point *q* represents the endpoint of the mission. Once the complete graph is constructed, the pathfinding process starts from the point *p* and continues until the complete coverage is achieved. We used the ACO algorithm generated order for the collision-free pathfinding over WG with minimum overlapping and informed search. The proposed algorithm keeps track of the locations to be visited along the path by using the order generated for footprints' sweeps visits and their connections. We assume that UAV is able to take turns with sufficient accuracy while switching from one sweep to another during the mission. The proposed approach is able to find the minimum length path with less path overlapping, less number of turns, and reduced computation time compared to the existing methods in most scenarios.

#### **4. Simulation Results and Discussion**

This section presents the simulation results and key findings about the proposed concept. The improvements of the proposed algorithm were compared using four criteria; the improvements in computation time, path lengths, path overlapping, and number of turns with the existing closely related algorithms. To benchmark the proposed algorithm, we compared the proposed algorithm results with decomposition-based CPP methods, BCDH-CPP [53] and CA-CPP algorithm [54]. The simulation results were produced and compared on a PC running Windows 10, with a CPU Intel Core i5 of 2.6 GHz and 8.00 GB of RAM, using MATLAB version 9.4.0.81 (R2018a). In simulations of the proposed CPP algorithm, we consider a 25-kg UAV similar to our previous study [55]. We considered both global constraints that are related to the UAV operating environment and local constraints that are related to the UAV. The numerical values related to the local constraints are: maximum steering angle: p/6 radius and wing span: 1 m. We assumed a zero-wind scenario in our simulations and assumed that there exists no external inference that can impact the established path. We assumed that a UAV has sufficient power to finish the mission successfully in one round. The minimum and maximum UAV flight height limits are 25 m and 150 m (*hmin* = 25 m, *hmax* = 150 m). The safe distance value for collision avoidance with obstacles is set to 10 m (*Dsaf e* = 10 m). The ACO parameters were specified considering the problem size (i.e., no. of sweeps). The sensor footprint sweep width is set to 20 m

(*Fw* = 20 m) and footprint sweep length is set to 30 m (*Fl* = 30 m). We present the overview of the 3D maps used in the experiments and two exemplary coverage path results visually in Figure 8a,b. We compared the proposed algorithm results with the existing methods on two grounds: the varying obstacles densities and shape of the AOI. The relevant details about AOI sizes, obstacles' densities, and the shape of the AOI used in experiments are explained in Sections 4.1 and 4.2.

**Figure 8.** Coverage path planning results from two different types of the area of interest.
