Advances and Future Directions in Flocking Control Models for Multi-Agent Systems

Collective behavior, a significant manifestation of self-organization phenomena, is widely observed in both natural and human societies, encompassing living systems (e.g., bird flocks, fish schools, insect swarms) and non-living systems (e.g., crystal arrangements, mechanically driven discrete objects). This paper systematically reviews the core mechanisms and theoretical models of collective behavior, with a focus on the mathematical frameworks and clustering conditions of the Vicsek model, Cucker-Smale (CS) model, and their derivatives (e.g., the Motsch-Tadmor model, improved models incorporating free will and time delays). Research indicates that local alignment, velocity matching, and group cohesion among individuals are key principles for the emergence of macroscopic order. Theoretical achievements have been applied to biomimetic robotics, UAV cooperative navigation, financial market volatility synchronization, and military formation control. Future studies should address time-delay effects, dynamic interactions between free will and hierarchical structures, and the integration of multiple constraints in practical scenarios to advance the depth and applicability of collective behavior theory in complex systems.