# Motion Planning in UAV-Aided Data Collection with Dynamic Jamming
### Prior Work  
We focus on past work from two fields: motion planning and data collection. To generate smooth and safe trajectories for UAVs online, the authors in [7; 8] presented the extraction of free space in the configuration space and utilized a range of convex shapes to represent the free space. The motion planning problem is formulated as restricting motion trajectories to convex graphs through convex optimization, which can be solved directly with a dedicated toolbox. However, the size of the area in which the convex shapes are constructed directly affects the local optimality of the trajectory. The authors in [9] proposed a zoning method that can be combined with a multi-stage optimal control formulation to accommodate complex forms of unobstructed areas in unstructured environments due to the presence of multiple obstacles within the predicted range. This method can effectively increase the free space for UAV planning. Other authors have proposed methods that are simpler and faster to calculate, such as the geometry-based method in [10], which constructs convex polyhedra by means of ellipsoidal expansion.  
Moreover, to constrain effectively the entire trajectory within the convex shape together with its derivatives in the feasible space under the hard constraint, the authors in [11] employed a piecewise Bezier curve on the basis of Bernoulli's polynomial to express the flight trajectory of the UAV. However, the order of the Bezier curve increases with the increase of control points, and a higher order can easily result in an \"ill-conditioned\" trajectory. To solve the problem of pathological Bezier curves under higher-order polynomials, the authors in [12] introduced B-spline curves, which have the advantages of Bezier curves while still being applicable to higher-order polynomial curves.  
Collecting data from ground-based distributed SNs is among the crucial technologies for WSNs. The typical objectives of trajectory optimization are to minimize the mission time of the UAV [13; 14; 15], minimize energy consumption during the flight [16; 17; 18], maximize the amount of collected data [19; 20], and maximize the amount of served sensors [21]. In addition to the basic UAV motion constraint, the data volume constraint is essential in all published research studies of UAV data collection. It is usually a non-convex constraint. In some studies, the communication rate required to meet the demodulation requirements is further considered, which is also non-convex. To deal with these non-convex optimization problems, design equivalence problems or relaxation problems as well as the transformation of constraints into penalty terms into optimization objectives have commonly been used in research. The successive convex approximation (SCA) [21] and some heuristic algorithms (e.g., PSO [22] and GE [23]) are commonly used to solve the trajectory. However, neither the SCA nor the heuristic algorithm can obtain a globally optimal solution, and the resulting local solution is strongly influenced by the initial value.  
Inspired by the problems in past work, we focus on path planning and trajectory optimization considering UAV motion constraints in a dynamic jamming environment, which can be combined as motion planning. In our study, we first analyze the communication link [18; 24] between the UAV and the ground sensors and formulate the optimization problem of minimizing the energy consumption, which considers the collection data demodulation threshold, obstacle avoidance, data collection volume, and motion principle. Then, we relaxed this non-convex optimization problem by introducing relaxation variablesand constructing equivalence constraints. Further, to solve the initial value problem of SCA during replanning in dynamic environments, we propose a communication-flight-corridor (CFC)-based initialized path generation method, which enables the SCA algorithm to converge to the optimal value quickly. Finally, the optimized path points were subjected to a B-spline curve.