# A Trajectory Generation Method for Multi-Rotor UAV Based on Adaptive Adjustment Strategy
## 1 Introduction  
Unmanned aerial vehicles (UAVs) are small in size and light in weight, so they perform an important role in military, agriculture, industry, and other fields. In order to enable UAVs to perform various tasks such as detection and tracking, it is necessary to allow them to have autonomous motion ability in complex environments. Motion planning is the core to achieving autonomous motion of UAVs. In order to realize the autonomous motion of UAVs and other robots, researchers have proposed various motion planning methods in the past decades. In the framework of the classical motion planning method, motion planning can be divided into two parts: front-end path searching and back-end trajectory generation. The task of the front-end path-searching method is to search for a feasible path from the starting point to the target point. It can be divided into three categories: search-based, sampling-based, and learning-based. Representatives of the search-based method are Dijstra [1] and \(A^{*}\)[2], which represent space as a search graph and then searches for a safe path based on the graph search method. Representatives of the sampling-based method are PRM [3] and RRT [4], which obtain feasible paths through random sampling in the state space. In recent years, deep learning and reinforcement learning are also widely used in path-planning tasks. At present, all kinds of path-searching methods can find a feasible path in real-time, but there are two problems: (1) the path is too close to obstacles, and (2) the path obtained by searching is not smooth, which is not suitable for UAVs and robots to execute. Therefore, optimizing the path through the trajectory generation method is also necessary to obtain a smooth and continuous trajectory convenient for the UAV to execute. Researchers propose various methods to optimize the path to obtain a better trajectory. Trajectory smoothing is simple and widely used in trajectory optimization. It takes thesmoothing loss item of the trajectory point and the distance from the original point as the optimization objective, obtains the smooth trajectory by solving the optimization problem, and then controls the UAV to follow the trajectory based on the control algorithm to avoid the obstacle moving to the target point. However, the trajectory smoothing method may cause the collision-free trajectory to collide with the obstacle. At the same time, because it does not consider the UAV dynamic characteristics, the trajectory obtained is not optimal. In order to optimize the trajectory, polynomial curves are widely used in trajectory representation. We can optimize the parameters of polynomial curves to obtain the optimal trajectory. Reference [5] introduces the differential flatness property of the multi-rotor UAV; that is, the trajectory of the multi-rotor UAV can be indicated as the polynomial curve. According to the representation of obstacle and dynamic constraints, the trajectory optimization method can be divided into unconstrained, hard-constrained, and soft-constrained trajectory optimization methods. The minimum-snap trajectory generation method [5] is representative of the unconstrained trajectory generation method. After obtaining a feasible path, it selects sub-target points in the path and then represents the trajectory as a piecewise polynomial curve passing through each sub-target point. It makes the trajectory continuous by adding continuity constraints of position, velocity, and acceleration. It then obtains the minimum-snap trajectory by solving the optimization problem to minimize the energy required to obtain the trajectory. Researchers also improved the minimum-snap method: The Closed-form [6] method proposed a trajectory optimization method for closed-form solutions so that continuity constraints do not need to be considered in the solution process, thus improving the efficiency of problem-solving. At the same time, a time allocation method was proposed to optimize the time allocation of each trajectory segment of the minimum-snap to achieve faster flight [7].