Flocking Dynamics of Multi-Agent Systems Based on an Extended Cucker–Smale Model with Nonlinear Coupling and Binding Forces

This paper develops an extended Cucker–Smale model that integrates nonlinear velocity alignment with state-dependent binding forces to achieve stable, collision-free flocking in multi-agent systems. Our framework introduces two dedicated control mechanisms: a velocity-dissipative term (K1) for accelerated convergence, and a distance-regulating term (K2) for formation cohesion and collision avoidance, which collectively ensure stable flocking. Rigorous Lyapunov analysis establishes provable guarantees for asymptotic velocity alignment and collision safety under verifiable initial energy conditions. Numerical simulations validate the theoretical predictions for a 20-agent swarm; scalability analysis demonstrates effective coordination in systems of up to 100 agents and reveals that velocity synchronization improves substantially—with errors decreasing by nearly two orders of magnitude—as K2 increases from 0.05 to 0.50. A Pareto-optimal parameter region (K2∈[0.15,0.30]) is identified, which achieves sub-centimeter-per-second alignment accuracy while maintaining energy consumption below 35% of the baseline. The proposed framework provides a theoretically rigorous yet practically viable solution for applications demanding guaranteed safety and precise coordination, such as UAV formations, robotic swarms, and autonomous vehicle platoons.