# UAV Formation Trajectory Planning Algorithms: A Review
## 5 Local Trajectory Planning Algorithm
### Artificial Potential Field  
The artificial potential field method (APF) was first proposed by [PERSON] as a virtual force method. The artificial potential field method assumes that each UAV is moving in an artificial potential field. For UAVs, the target point generates an attractive field, and obstacles generate a repulsive force field; under the action of the gravitational field and the repulsive field, the UAV generates a feasible trajectory along the direction of the potential field. In general, in order to simplify the calculation, by calculating the negative gradient of the gravitational potential function and the repulsive potential function, the gravitational and repulsive forces on the UAV in the potential field can be obtained, and then the resultant force on the UAV can be obtained. Then, calculating according to the resultant force, each UAV makes the control amount required for attitude adjustment so as to guide the UAV formation to avoid obstacles and complete trajectory planning. Figure 25 is a schematic diagram of artificial potential field forces. [PERSON] et al. [131] proposed a trajectory planning method in a 3D environment. This method adds a multi-UAV distributed work and inter-machine communication to the artificial potential field method (APF) and solves the problem of multi-UAV coordination and task assignment when exploring disaster areas. [PERSON] et al. [132] proposed a trajectory planning method combining the artificial potential field method (APF) and Dubins curve. This method introduces the virtual leader UAV into the UAV formation and uses the Dubins curve to plan its trajectory. Then, it uses the APF to plan the trajectory of the wingman and finally completes the trajectory planning of the UAV formation by constraining the flight trajectory of the virtual leader. It solves the problem where the lead aircraft may have out-of-control failure and the UAV is restricted by the turning radius. [PERSON] et al. [133] proposed an optimized artificial potential field algorithm. This method simulates other UAVs as dynamic obstacles and at the same time introduces the climbing strategy and dynamic step adjustment method into APF, which solves the problems of inter-machine collision and excessive flight step length in traditional APF under the complex space conditions of multiple UAVs. [PERSON] et al. [134] proposed an improved artificial potential field method (IAPF). This method introduces the judging mechanism of local minimum points and the jump-out  
Figure 25: Schematic diagram of artificial potential field. mechanism of 90\({}^{\circ}\) movement along the target direction into APF; it solves the problems of unreachable targets near obstacles, local minimum points and UAV track oscillations in traditional APF. [PERSON] et al. [135] proposed a trajectory planning algorithm for dense UAV formations based on an artificial potential field (APF). The algorithm improves the APF by improving the repulsive force model, adding the target exchange algorithm and adding constraints, and it solves the problems of traditional APF trajectory oscillation, unreachable targets and local minimum points. [PERSON] and [PERSON] [136] proposed a multi-UAV trajectory planning method based on the improved artificial potential field method (IAPF). This method introduces an improved distance factor potential field function and dynamic step size adjustment method into APF, and at the same time, it considers the influence of the force between UAVs; it solves the problem where the traditional APF target cannot be reached: it is easy to fall into a local minimum, and the trajectory shakes the problem. [PERSON] et al. [137] proposed a collaborative formation distributed trajectory planning method based on the improved artificial potential field (IAPF) and consensus theory. This method introduces the dynamic model and communication network topology, coordination gain factor, repulsion force and planning angle influence factor into APF.