Supplementary material from "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 three dimensions 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 behaviour that may not be exhibited by just a single biped.