A Minimal Model for Emergent Collective Behaviors in Autonomous Robotic Multi-Agent Systems

Collective behaviors such as swarming and flocking emerge from simple, decentralized interactions in biological systems. Existing models, such as Vicsek and Cucker-Smale, lack collision avoidance, whereas the Olfati-Saber model imposes rigid formations, limiting their applicability in swarm robotics. To address these limitations, this paper proposes a minimal yet expressive model that governs agent dynamics using relative positions, velocities, and local density, modulated by two tunable parameters: the spatial offset and kinetic offset. The model achieves spatially flexible, collision-free behaviors that reflect naturalistic group dynamics. Furthermore, we extend the framework to cognitive autonomous systems, enabling energy-aware phase transitions between swarming and flocking through adaptive control parameter tuning. This cognitively inspired approach offers a robust foundation for real-world applications in multi-robot systems, particularly autonomous aerial swarms.