## 1 Introduction
### Related Work  
The problem considered in this paper belongs to the classical path planning and secure communication. In this subsection, we first briefly review the typical approaches and then clarify the difference of our work against the existing publications. Graph search based approaches are the well-studied ones for global path planning. They generally need the environment to be modelled by a graph, where a possible link between two vertices of the graph is associated with a weight indicating the cost or time to traverse the link. Then, many popular graph search algorithms, such as [PERSON]'s algorithm [11] and A* algorithm [12], can be applied to compute the shortest path between a start vertex and a destination vertex. Tangent graph based approaches are another type of tools to compute globally optimal paths. For a non-holonomic robot, say a [PERSON] car [13], its angular speed is upper bounded (its minimum turning radius is lower bounded). Then, given the obstacles in an environment, the obstacles can be modelled by circles whose radius should be no smaller than the robot minimum turning radius. Furthermore, a set of tangent lines can be added to link a pair of obstacle circles. The generated graph is called the tangent graph and the robot's path in this tangent graph consists of a number of straight line segments and a number of arcs on the obstacle circle [14; 15]. Optimization algorithms are often used for the path planning problem. Typical optimization algorithms that have been used include but not limited to the particle swarm optimization [16], the genetic algorithm [17], differential evolution [18] gravitational search algorithm [19]. The methods are in general based on a pool of possible trajectories, and follow some updating rules until the optimal path is obtained. A shortcoming of this class of approaches is that they may converge slowly in normal path planning problems. The RRT scheme, a randomized method, usually performs well in terms of the computational efficiency [10]. This method is based on the construction of a random tree of possible actions connecting the start position and the destination. When a node of the tree reaches the destination, a feasible path from the start point to the destination can then be identified. Thanks to its computational efficiency, the RRT scheme is promising to be applied in online path planning. The main task is to dynamically grow and manage the tree. For example, when the destination changes or when mobile obstacles come into proximity, some new nodes may be added to the tree and some existing nodes of the tree may be cut to avoid collision [20; 21]. Moreover, beyond the general RRT framework, some heuristic methods  
Figure 1: Illustration of the considered scenario. have been proposed to guide the tree growth [22; 23], which may generate nearly optimal paths while remaining with a probabilistic planning setting. The considered application scenario is about secure wireless communication. Secure communication is not a new issue in wireless communication, and there are approaches to protecting the security. However, the wireless communication of UAVs brings new challenges. The most important feature is the high probability of LoS with not only the intended node but also malicious nodes (i.e., eavesdroppers). As aforementioned, some strategies have been proposed to increase the security capacity of the UAV wireless communication. Refs. [3; 6; 7] focus on the UAV mobility management to increase the received rate at the intended node and decrease that at the eavesdroppers. Besides this approach, another class of approaches employs UAVs as jammers [24; 25; 26]. Specifically, Ref. [24] considers the optimization of the UAV jammer's trajectory and transmission power. Ref. [25] further takes into account the user scheduling to maximize the secrecy rate. Ref. [26] proposes a strategy where two UAVs send confidential messages to their respective intended node by sharing the same spectrum. A cooperation strategy is designed to maximize the system secrecy rate.