# A Trajectory Generation Method for Multi-Rotor UAV Based on Adaptive Adjustment Strategy
## 1 Introduction
A trajectory generation method based on the Bezier curve is proposed, which can ensure the continuity of trajectory based on the position of control points, thus simplifying the problem-solving process. This kind of method does not represent obstacles as constraints, so in order to ensure trajectory safety, it is necessary to detect whether the trajectory meets the safety requirements repeatedly. This method adds new control points when a collision happens in the trajectory, so it is time-consuming to solve the problem in a complex environment and cannot meet the real-time requirements. The hard-constrained trajectory generation method represents the obstacles as the constraint condition of the optimization problem so as to ensure the safety of the trajectory obtained by the optimization solution. This kind of method is usually divided into two steps. The first step is representing the safety corridor area based on the geometric shape. The second step is to limit the trajectory in the safety corridor area and solve the safety trajectory that will not collide with the obstacle. Reference [8] generated the safety zone based on the iterative region expansion method and proposed the sum of squares algorithm to ensure that the trajectory is within the safety zone. Reference [9] proposed a safe flight corridor generation method for a 3D environment, which can generate a safe flight corridor composed of a series of ellipsoids. Reference [10] uses a fixed-size square to represent the safe zone and obtains the safe path through the optimization method. Reference [11] proposed a safe corridor generation method based on the point cloud map, which can directly generate feasible paths based on the point cloud map without building an occupancy grid map. Reference [12] propose a motion planning algorithm based on the corridor-constrained minimum control effort trajectory optimization (MINCO) framework, which was finally evaluated on an autonomous LiDAR-navigated quadrotor UAV in wooded environments, achieving flight speeds over 13.7 m/s without any prior map of the environment or external localization facility. The trajectory generation method based on hard constraints can ensure trajectory security, but it still has two problems: first, the generation of safe corridors in a 3D environment is complex; second, the trajectory may be close to the boundary of safe corridors, and thus close to obstacles. The soft-constrained trajectory generation method sets the distance between the trajectory and the obstacle as an optimization item and obtains a safe trajectory away from the obstacle by solving the optimization problem. Reference [13] generates executable smooth trajectories by generating discrete time trajectories and using gradient descent to minimize their smoothness and collision costs. Reference [14] constructed similar optimization terms but used a gradient-free method to solve this kind of optimization problem. This method is extended to continuous-time polynomial trajectory in reference [15]. Because the time parameterization is continuous, the differential error in the numerical calculation method is avoided, and the quadrotor motion can be represented more accurately. However, the computational complexity of the above methods is large, and the success rate is low. To solve these problems, reference [16] proposed a trajectory representation method based on B-spline, which ensures trajectory safety by pushing B-spline control points away from obstacles. Reference [17] proposed a path-planning method considering the dynamic feasibility and a security assurance method based on B-spline convex hull property, which realized the safe and reliable trajectory generation. To further improve the safety of UAVs and the efficiency of trajectory planning, reference [18] considers the observation perspective of UAVs on obstacles in the trajectory generation process to avoid the collision between UAVs and new obstacles.