Walking crowds on a shaky surface: stable walkers discover Millennium Bridge oscillations with and without pedestrian synchrony

Why did the London Millennium Bridge shake when there was a big enough crowd walking on it? What features of human walking dynamics when coupled to a shaky surface produce such shaking? Here, we use a simple biped model capable of walking stably in 3D to examine these questions. We simulate multiple such stable bipeds walking simultaneously on a bridge, showing that they naturally synchronize under certain conditions, but that synchronization is not required to shake the bridge. Under such shaking conditions, the simulated walkers increase their step-widths and expend more metabolic energy than when the bridge does not shake. We also find that such bipeds can walk stably on externally shaken treadmills, synchronizing with the treadmill motion for a range of oscillation amplitudes and frequencies, sometimes performing net positive work on the treadmill. Our simulations illustrate how interactions between (idealized) bipeds through the walking surface can produce emergent collective behavior that may not be exhibited by just a single biped.

当足够多的人群在伦敦千禧桥（London Millennium Bridge）上行走时，该桥为何会发生晃动？人类行走动力学的哪些特征，在与晃动的桥面耦合后会引发这类晃动？本文中，我们采用一种可在三维空间中稳定行走的简化双足模型，对上述问题展开探究。我们模拟多台该类稳定双足模型同时在桥面上行走的场景，结果显示，在特定条件下它们会自然形成同步，但同步并非引发桥面晃动的必要条件。在桥面发生晃动的工况下，模拟行走者的步幅会增大，且相较于桥面静止时，其代谢能耗更高。此外我们还发现，这类双足模型可在外部驱动晃动的跑步机上稳定行走，并在一系列振荡振幅与频率范围内与跑步机运动同步，有时还会对跑步机输出净正功。我们的模拟结果展示了（理想化的）双足个体通过行走表面产生的交互，如何催生仅单个双足个体无法展现的涌现集体行为。