# An Efficient Trajectory Planning Method for High-Speed Interception of Invasive Drones
## 1 Introduction
High-speed flight in dynamic environments may require drones to quickly adjust and recalculate trajectories based on changes in the environment or external disturbances. Therefore, the computational efficiency of trajectories, the degree of freedom of parameters, and the degree of respect for constraints are usually important indicators for evaluating trajectory generation methods. The time consumption of the above methods in trajectory execution and constraint optimization has hindered their application in real-time flight planning in dynamic scenes. Reference [6] proposes a computationally efficient motion primitive that uses a fast recursive method to test for constraint violations instead of explicitly encoding constraints during the planning phase. This provides high flexibility in defining quadcopter terminal states and achieves advanced goals through low-cost searches on multiple primitives. The computational efficiency of this method makes it a low-level trajectory generator for other advanced tasks [3; 20], and has achieved good results. It is worth noting that such methods describe quadcopters as a rigid body with six degrees of freedom, using rigid body motion equations to describe drone motion while ignoring external disturbances such as air resistance. Under the condition of low-speed flight in unmanned aerial vehicles, this method can compensate for modeling errors by sacrificing the accuracy of single planning and continuously re-planning. However, in certain contexts where drones approach their maximum flight speed, such as pursuit and evasion [21; 22] and racing [23; 24], research indicates that the aerodynamic drag encountered by the aircraft escalates with the square of the flight speed. This nonlinear progression results in a swift increase in aerodynamic drag, eventually stabilizing at an equilibrium with the aircraft's thrust. This becomes a significant factor limiting the flight state and trajectory. Consequently, this limitation means that the efficacy of existing methods cannot be reliably ensured in medium to high-speed flight scenarios. Recent studies have demonstrated notable advancements in high-speed flight scenarios using intelligent methods, particularly reinforcement learning. These methods have achieved high-speed flight under complex external disturbances through extensive trial and error learning in virtual simulation environments. They can indeed approach the limit performance of aircraft after prolonged training in specific fixed scenarios [24]. However, these methods exhibit significant limitations during application. Firstly, their training process is time-consuming, significantly reducing their practical applicability, especially in real-time tasks within high dynamic environments. Secondly, as these methods depend on specific simulation environments and scenarios, their generalization ability and adaptability need improvement when confronted with diverse actual flight environments. In conclusion, existing research still faces substantial limitations in real-time high-speed flight tasks within high dynamic environments. Therefore, it is imperative to further explore more efficient and adaptable solutions. Taking inspiration from reference [6], this article attempts to design a computationally efficient and applicable high-speed flight trajectory planning method for multi-rotor aircraft based on a rigid body motion model that includes aerodynamics, and is applicable to any performance characteristic (mass, aerodynamics). The method mainly includes two parts: air resistance approximation and motion primitive generation and evaluation. The first part is based on the dynamics of a rigid body with six degrees of freedom, with the goal of minimizing the drag model error of quadcopters in the speed operating range. A linearized approximation method for air resistance is designed, and an approximate air resistance model is obtained for the purpose of solving the optimal trajectory in a closed form.