Formation control for multi-UAV (Unmanned Aerial Vehicles) systems presents practical challenges, including communication range limitations and constrained working space. Various distributed control methods have been proposed to address these issues and to facilitate formation tasks for multiple UAVs. Optimization-based control strategies are commonly preferred for their ability to take into account system constraints [3]. Communication limitations among agents can be integrated using graph description. However, existing literature often assumes a fixed communication graph, which is different from real-world implementations where formations dynamically vary. Game theory emerged recently as a useful tool for designing control systems for UAVs, providing flexibility for both model-based and data-driven methods [4]. It helps to represent the interactions between agents functioning as decision makers. Moreover, evolutionary game theory or population games more specifically have found applications in distributed control for solving constrained optimization problems with stability properties [2].

This study builds upon the concept of distributed population dynamics proposed in [1] to control a groups of indoor nanodrones, employing a leader-follower architecture. First, a connected graph representing the communication links among multiple drones is considered. As the distance from one drone to another changes during the scenario, this network representation will evolve accordingly. Subsequently, the trajectories of the nanodrones are thoroughly planned, taking into account operational constraints, particularly for the leader. These planned trajectories are then communicated to the followers with certain relative coordination ensuring constraint satisfaction while avoiding collision. Next, a population game framework is introduced, leveraging an interpretation of the desired formation shape and the constraints of the UAV system. Within this framework, drones autonomously make decisions to track the reference trajectories. This decision-making stage is governed by distributed dynamics derived from evolutionary game theory, ensuring convergence to a stable equilibrium point known as the Nash equilibrium. The approach is provable to be applicable for time-varying communication network as denoted in [1]. Experimental validation under various scenarios for a groups of indoor nanodrones validate the approach and paves the way for future research directions.