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

Abstract

ResearchCite this article: Joshi V, Srinivasan M. 2018 Walking crowds on a shaky surface: stable walkers discover Millennium Bridge oscillations with and without pedestrian synchrony. Biol. Lett. 14: 20180564. http://dx.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. 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.

A controller for walking derived from how humans recover from perturbations

“…To be clear, there is an infinity of possible controllers that would stabilize the inverted pendulum gait (e.g. [25][26][27][28]30]).…”

“…The heel strike is modelled as a passive plastic collision with a nominally rigid leg. By changing the push-off impulse and where the foot is placed (X foot , Y foot ), the inverted pendulum walker can achieve complex walking trajectories and also recover from perturbations [2,28]. See electronic supplementary material, S1 for mathematical details and the equations of motion.…”

“…Other authors have considered natural step-to-step variability in unperturbed steady-state locomotion [10,[20][21][22][23][24] to obtain information about stability and control of walking and running, but again, we do not know of a complete synthesis of a walking controller from such measurements. Similarly, there have been many stable bipedal walking simulations [25][26][27][28], stable two-legged walking robots [29,30], and robotic prostheses and exoskeletons [31,32], but none of these simulations, robots or assistive devices have controllers that are quantitatively derived from human walking response to perturbations. Our study could be considered a partial analogue of [33] in which a running controller was obtained for a simple biped model by fitting model responses to human responses to natural step-to-step variability.…”

Emergence of the London Millennium Bridge instability without synchronisation

“…Until now, it has been hard to quantify this negative damping effect in a model-independent way. A number of theories have been proposed for its physical origin 17 , 18 , 28 , 31 ; however, it is not clear whether negative damping can be a consequence of synchronisation 34 or vice versa.…”

Walking on a Vertically Oscillating Platform with Simulated Gait Asymmetry

“…Recently, we developed a vertically oscillating platform and treadmill that results in a greater coupling strength when healthy individuals walk and the platform oscillates at a frequency that is close to their preferred stepping frequency [34,35]. This approach is based upon the Symmetry 2021, 13, 555 2 of 13 "wobbly bridge" phenomenon, which suggests that humans will subconsciously entrain their gait to sinusoidal movement of the walking surface if the frequency of motion is near their normal step frequency [36][37][38]. Unintentional synchronization with the motion of this platform may affect gait asymmetry in a manner similar to that of side by side treadmill walking, but this has not been evaluated.…”