The collective dynamics and structure of animal groups has attracted the attention of scientists across a broad range of fields. A variety of agent-based models have been developed to help understand the emergence of coordinated collective behavior from simple interaction rules. A common, simplifying assumption of such collective movement models, is that individual agents move with a constant speed. In this work we critically re-asses this assumption. First, we discuss experimental data showcasing the omnipresent speed variability observed in different species of live fish and artificial agents (RoboFish). Based on theoretical considerations accounting for inertia and rotational friction, we derive a functional dependence of the turning response of individuals on their instantaneous speed, which is confirmed by experimental data. We then investigate the interplay of variable speed and speed-dependent turning on self-organized collective behavior by implementing an agent-based model which accounts for both these effects. We show that, besides the average speed of individuals, the variability in individual speed can have a dramatic impact on the emergent collective dynamics: a group which differs to another only in a lower speed variability of its individuals (groups being identical in all other behavioral parameters), can be in the polarized state while the other group is disordered. We find that the local coupling between group polarization and individual speed is strongest at the order-disorder transition, and that, in contrast to fixed speed models, the group’s spatial extent does not have a maximum at the transition. Furthermore, we demonstrate a decrease in polarization with group size for groups of individuals with variable speed, and a sudden decrease in mean individual speed at a critical group size (N = 4 for Voronoi interactions) linked to a topological transition from an all-to-all to a distributed spatial interaction network. Overall, our work highlights the importance to account for fundamental kinematic constraints in general, and variable speed in particular, when modeling self-organized collective dynamics.

动物群体的集体动力学和结构引起了广泛领域科学家的关注。已经开发了各种基于代理的模型来帮助理解从简单交互规则中出现的协调集体行为。这种集体运动模型的一个常见的简化假设是，个体代理以恒定速度运动。在这项工作中，我们批判性地重新评估了这一假设。首先，我们讨论了实验数据，展示了在不同种类的活鱼和人工代理 (RoboFish) 中观察到的无处不在的速度变化。基于考虑惯性和旋转摩擦的理论考虑，我们推导出个人的转动响应对其瞬时速度的函数依赖性，这由实验数据证实。然后，我们通过实施一个基于代理的模型来研究变速和依赖速度的转向对自组织集体行为的相互作用，该模型解释了这两种影响。我们表明，除了个体的平均速度之外，个体速度的变异性会对涌现的集体动力产生巨大影响：一个群体与另一个群体的不同仅在于其个体的较低速度变异性（群体在所有其他行为方面都相同）参数），可以处于极化状态，而另一组是无序的。我们发现群体极化和个体速度之间的局部耦合在有序-无序转变时最强，并且与固定速度模型相比，群体的空间范围在转变时没有最大值。此外，N= 4 用于 Voronoi 交互）与从多对多到分布式空间交互网络的拓扑转换相关联。总的来说，我们的工作强调了在对自组织集体动力学建模时考虑一般基本运动学约束的重要性，特别是可变速度。