# Adaptive Path Planning for UAV-Based Pollution Sampling
## 4 Experiments and Results
### General Form of a Measurement Mission  
The placement of global waypoints along with mission-specific parameters, such as those defining the measurement path, is optimized by GPP. Nevertheless, the resulting path must comply with the UAV's kinematic limitations. To minimize computational complexity, the GPP focuses solely on optimizing global waypoints, serving as control points that are connected using Dubins airplane paths to generate a smooth and kinematically feasible trajectory. For any given pair of control waypoints, the algorithm calculates all possible Dubins paths and selects the shortest one. Taking into account the above, consider the following example mission scenario:  
1. The UAV initiates its flight and proceeds to the region identified as having the highest pollution levels.
2. It navigates the specified area following a predefined parametric measurement trajectory.
3. The aircraft completes the mission by returning to the designated landing site and safely landing.  
Takeoff and landing procedures are controlled separately, either manually by a human operator or via a specialized autonomous system, functioning independently from the planning algorithm.  
A parametric polygon, which defines the area designated for data collection, can represent the measurement path. This measurement polygon is subsequently transformed into a path using an area coverage algorithm tailored to the UAV's kinematic limitations. For instance, the maximum coverage algorithm proposed by [PERSON] et al. [41] can be utilized for this purpose.  
To cover the area uniformly in all directions, the measurement polygon should be a circle. It results from the assumption that the shape of the polluted area is not known a priori. The circle is approximated by a regular polygon to facilitate computation. Consequently, the optimized variables are ultimately expressed as  
\[\mathbf{p}=\begin{bmatrix}\mathbf{W}^{S}&\mathbf{W}^{G}&N_{S}&N_{G}&\mathbf{w} ^{M}\end{bmatrix}, \tag{7}\]  
where \(\mathbf{W}^{S}\) and \(\mathbf{W}^{G}\) represent the vectors of global waypoints leading from the takeoff endpoint to the start of the measurement path, and from the end of the measurement path to the landing initiation point, respectively. The start and goal points denote the locations where control is transferred to or from the path planner.  
Maintaining a uniform structure of the optimization vector throughout the process involves introducing variables \(N_{S}\) and \(N_{G}\), which determine the number of waypoints utilized in \(\mathbf{W}^{S}\) and \(\mathbf{W}^{G}\). The minimum value is 0, which applies when the start or goal waypoint can be directly connected to the measurement path using a single Dubins path. The maximum number of waypoints is specified by \(N_{S}\) and \(N_{G}\). Additionally, the variable \(\mathbf{w}^{M}\) denotes the geometric center of the measurement polygon. Exact polygon shape is determined by parameters excluded from the GPP optimization process.  
The GPP can utilize a predefined preliminary path established by a human expert before the optimization begins. Moreover, the expert provides initial values for the optimization vector \(\mathbf{p}\), leveraging their knowledge and experience. The GPP subsequently improves upon this initial template by solving the optimization problem outlined earlier.