# An Efficient Trajectory Planning Method for High-Speed Interception of Invasive Drones
## 1 Introduction
The second part, based on the designed linearized resistance model and optimal control theory, aims to minimize the input jerk of unmanned aerial vehicles. By utilizing the differential flatness characteristics of multi-rotor aircraft, the position, velocity, and acceleration state trajectories, as well as corresponding thrust and body rate input trajectories, are planned, and a fast determination method for trajectory feasibility is provided. This paper confronts the security challenges posed by malicious drones, offering a series of novel research findings designed to bolster countermeasures against these threats in high-speed dynamic environments. The primary contributions and innovations of this study are as follows:  
(1) This paper introduces an innovative linearization approximation method for the air resistance model. Existing research often neglects or oversimplifies the impact of air resistance on high-speed flight, leading to inaccuracies in trajectory planning. Our proposed method accurately restores the drone's flight conditions, thereby significantly enhancing the accuracy of trajectory planning. This not only addresses the limitations of previous studies but also provides crucial assurances for the safety and reliability of drones in high-speed flight scenarios. (2) This paper presents a set of motion primitives tailored for drones with varying performance parameters. These primitives are based on the linearized approximation of the air resistance model, enabling efficient solutions for high-speed flight trajectories. This innovation not only enhances the computational efficiency of trajectory planning but also improves the adaptability and universality of the method across different drone models. This development opens up possibilities for real-time flight planning in complex task scenarios. (3) A physical simulation environment was utilized to demonstrate the rapid arrival task of multiple moving targets. This paper substantiates the efficacy of the proposed method through tangible demonstrations, thereby illustrating its superior performance in dynamic scenarios. This accomplishment not only validates the practicality and advancement of the method but also underscores the significant importance of this research in augmenting the efficiency of drone countermeasure systems. The remaining parts of this article are organized as follows: Section 2 provides a basic description of the quadrotor maneuvering mechanics model and problems, and Section 3 provides the linearization approximation principle of the air resistance model and the method of generating motion primitives. Section 4 analyzes the impact of the two drag coefficients designed in this article on the optimal trajectory. Section 5 provides a fast method for determining the feasibility of trajectories. In Section 6, the performance of the proposed method was compared with the method in reference [6], and the error variation of the linearization approximation method in this paper within the performance limit range of unmanned aerial vehicles was analyzed. A high-speed flight mission demonstration was presented in the Gazebo [25] physical simulation environment. Section 7 presents the conclusion.