By introducing an attractive–repulsive force in Cucker–Smale model, the dynamic behaviour of multi-agent system is studied. The Cucker–Smale-type model considered in this paper has three properties: collision-avoidance, aggregation and velocity-matching, which are significant rules in dynamic behaviour of multi–agent systems. Results of collision-avoidance, flocking and swarming are given respectively. Different from previous work, the Cucker–Smale-type model shows unconditional and conditional swarming respectively when weight function $f={(r-d_0)}^{-\theta }$ of the attractive–repulsive force satisfies $\theta \in [1,3]$ and $\theta >3$. Moreover, for the case $f=r^{-\theta },\theta \ge 2$, results of collision–avoidance tell us that there exists a positive lower bound of relative distance, which improve previous work of collision-avoidance.

通过在 Cucker-Smale 模型中引入吸引力-排斥力，研究了多智能体系统的动态行为。本文考虑的 Cucker-Smale 型模型具有三个特性：避免碰撞、聚合和速度匹配，这是多智能体系统动态行为的重要规则。分别给出了避免碰撞、聚集和蜂拥的结果。与之前的工作不同，Cucker-Smale 型模型分别在权重函数$F={(r-d_0)}^{-\theta }$ 吸引力-排斥力满足 $\theta \in [1,3]$ 和 $\theta >3$. 此外，对于这种情况$F=r^{-\theta },\theta \ge 2$，避免碰撞的结果告诉我们存在相对距离的正下限，这改进了先前的碰撞避免工作。