Cooperative Path Planning for Heterogeneous UAV Swarms: A Stackelberg Game Approach

The coordinated operations of Stealth Unmanned Aerial Vehicle (SUAV) and Swarming Drones (SD) have demonstrated formidable power in the military domain. Efficient path planning is a critical technology that enhances combat effectiveness. This paper proposes a game-theoretic optimization approach to achieve cooperative penetration and target search path planning for swarm UAVs. Multi-task and multi-objective optimization models are developed for complex scenarios whose optimal solutions are NP-hard. Consequently, SUAV and SD are defined as leader and followers, respectively. The formulated Stackelberg game model enables distributed intelligent decision-making for SUAV and SD. We theoretically prove that by selecting an appropriate potential function, subgames within the leader-level and followers-level become an Ordinal Potential Game (OPG) with a Nash equilibrium, thereby ensuring the existence of a Stackelberg Equilibrium (SE) through leader-follower interactions. We propose a Gradient-based Hierarchical Learning and Optimization Algorithm (GHLOA) to achieve SE. At the leader-level, a Stochastic Gradient Ascent (SGA) algorithm optimizes the penetration path for SUAV, while in the followers-level, we demonstrate that the designed Hybrid Learning-based Multimodal Adaptive Pigeon-Inspired Optimization (HLMAPIO) algorithm converges with probability one to the suboptimal solution for each SD. Numerical results indicate that our approach is suboptimal, scalable, and fast adaptable to dynamical scenarios, and it outperforms the state-of-the-art techniques. Note to Practitioners—With the rapid advancement of artificial intelligence technologies, the coordinated operations of stealth unmanned aerial vehicle (SUAV) and swarming drones (SD) have demonstrated immense potential in modern high-tech warfare. This paper investigates a heterogeneous UAV swarm system comprising a single SUAV and several, or even dozens of, SDs deployed in complex, dynamic scenarios with moving threats during the execution of diverse tasks. Our core concept is to propose a game-theoretic swarm intelligence decision-making framework that optimizes the rewards and costs of swarm members. This approach effectively mitigates potential conflicts, ensures suboptimal and collision-free paths, and enhances the scalability, adaptability, and robustness of the swarm system in dynamic environments. Notably, our method theoretically guarantees system stability and solution suboptimality. Numerical results show that the proposed approach significantly improves the swarm system’s overall utility while ensuring the safety of individual UAVs. Even when the number of UAVs and targets increase by a factor of five, the computational time remains within an acceptable range. Future work will focus on integrating game theory with reinforcement learning to explore decision-making and autonomous planning technologies for multi-objective and multi-task scenarios across larger-scale scenarios.