# Advanced Cooperative Formation Control in Variable-Sweep Wing UAVs via the MADDPG-VSC Algorithm
## 1 Introduction  
As unmanned aerial vehicle (UAV) technology continues to advance rapidly, the value of variable-sweep wing UAVs has become increasingly evident, particularly due to their ability to adapt to a wide range of flight states, which significantly enhances overall performance and efficiency [1]. Traditional trajectory planning algorithms, such as A*, rapidly-exploring random trees (RRT), and probabilistic roadmaps (PRM), have been widely employed in UAV systems due to their effectiveness in structured environments with known dynamics and constraints. However, these classical methods often face challenges when applied to high-dimensional spaces, dynamic obstacles, and real-time applications, where their computational complexity and adaptability are limited [2; 3; 4]. This growing recognition highlights the critical importance of advancing research in variable-sweep wing technology through more adaptive control mechanisms, such as deep reinforcement learning (DRL). However, despite their potential, current research has not fully optimized these systems, particularly in the implementation of advanced control mechanisms such as the proximal policy optimization (PPO) algorithm [5]. With the expanding application of multi-UAV systems across commercial, environmental, and defense sectors, where coordinated operation is crucial, optimizing variable-sweep wing UAVs has become imperative [6]. This study seeks to integrate variable-sweep wing technology with advanced control algorithms,aiming to enhance multi-UAV system capabilities by providing more flexible and efficient solutions, especially for formation and cooperative control tasks. In the area of formation control, variable-sweep wing UAVs face significant challenges, particularly in achieving precise control and maintaining formation. Early studies, such as those by [PERSON] et al. [7] and [PERSON] et al. [8; 9], employed Q-learning to optimize formation control for morphing UAVs based on aerodynamic characteristics. While these methods showed some effectiveness, their application was limited by the discrete nature of state and action spaces. [PERSON] et al. [10] applied deep reinforcement learning to simplified morphing aircraft models, achieving some progress in formation control; however, the simplifications in the models constrained the precise definition and execution of control actions. [PERSON] et al. [11] advanced the field by using the deep deterministic policy gradient (DDPG) algorithm to control multiple biomimetic morphing UAVs, but this approach still lacks flight validation to support the optimization of formation control. [PERSON] et al. [12] explored the adaptive control of UAV wing configurations using Q-learning, but these studies have yet to establish a direct link between formation control strategies and actual improvements in flight performance. In the domain of cooperative control, existing methods such as Q-learning and deep Q-network (DQN) algorithms [13; 14] have been widely applied in UAV systems, but they exhibit significant limitations when dealing with continuous action spaces and dynamic environments. Specifically, the discrete nature of state and action spaces in Q-learning restricts its adaptability, making it incapable of addressing the complexities of dynamic cooperative control tasks. While DQN is more effective in handling high-dimensional control tasks, it still faces challenges in complex dynamic environments, particularly in regards to multi-UAV cooperative formation control [15; 16]. These methods often struggle to maintain stability and efficiency in scenarios requiring real-time responsiveness and robust decision making [17]. Therefore, there is an urgent need for advanced algorithms capable of overcoming these challenges, particularly in the context of variable-sweep wing UAVs, which demand precise and adaptive control mechanisms. To tackle these challenges, this study presents the following key innovations:  
1. Optimization of the multi-rigid-body dynamic model for an adaptive morphing wing.