# Cooperative Guidance Law for the Mother-Cabin of the Anti-UAV Cluster Mother-Son Missile
###### Abstract  
This article investigates a novel operational pattern for intercepting UAV clusters over the range of middle and far distances using mother-son missiles. To address the guidance issue of the mother-cabin in the operational pattern, a special cooperative guidance law, which takes into account acceleration constraint and satisfies the constraints of impact time, speed, and zero line of sight angle (LOS), is proposed. Based on consistency theory and sliding mode control theory, the proposed cooperative guidance law is specifically designed for the mother-cabin of the mother-son missile. This approach offers several advantages, including a simple structure and smooth controller output, and smooth flight trajectory. Finally, numerical simulations are presented to demonstrate the effectiveness and applicability of the cooperative guidance law. cooperative guidance; mother-son missile; consistency theory; sliding mode control; acceleration constraint +
Footnote †: journal: Medical  
guidance structure [6] or the two-layer cooperative guidance structure [7] is used as a framework for most cooperative approaches. Both homogeneous and heterogeneous missiles can theoretically cooperate based on the two architectures, but in practice, the \"leader-follower\" structure is more appropriate for heterogeneous missiles and has the advantages of good real-time information, easy expansion of missile groups, and high economic benefits [8; 9; 10; 11]. The two-layer structure is suitable for both homogeneous and heterogeneous missiles with its flexible cooperative mode and strong robustness [12; 13; 14]. Cooperative design based on sliding mode control theory has become a popular research area, in addition to the cooperative guidance method design based on optimal control theory and the proportional navigation method. In recent years, consistency theory has been introduced into the development of cooperative methods [15; 16; 17; 18]. This theory has been combined with the theory of sliding mode control, using a non-singular terminal sliding mode [19; 20; 21] or a super-twisting sliding mode control [22; 23] which can achieve fast convergence of missile states with reduced output chattering. Reference [24] proposed a prescribed performance-based approach for the cooperative control of missile flight angles. For practical problems such as the fragility of the prescribed performance approach and the high-complexity of neural prescribed performance control, [PERSON] et al. proposed non-fragile and low-complexity prescribed performance approaches [25; 26; 27; 28; 29], which provide advanced approaches to the design of prescribed performance-based cooperative control laws. While controlling multiple missiles for tactical cooperation, reference [30; 31] furthered design of collision avoidance between multiple missiles. While most of the solutions to the controller are based on quadratic Lyapunov functions, reference [32; 33] considered a non-quadratic Lyapunov function with one degree of freedom denoted as \(\alpha\) and showed that they had a much faster response. Among them, most of the cooperative guidance laws have been designed for specific application scenarios, and the guidance effect cannot be guaranteed after changing the application scenario. These laws also take less account of acceleration constraints and the feasibility of flight trajectories. As a result, it is necessary to design a special cooperative guidance law that is tailored to specific operational contexts and can meet specific constraints while taking into account practical constraints such as acceleration limits and flight trajectories. Numerous academic and research organizations have conducted studies on UAV countermeasures in response to the growing threat posed by them.