Abstract
Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with alternating aerial and stance phases. Stance is modelled as a passive, impulsive collision followed by an active, impulsive push-off that compensates for collisional losses. Such a runner has infinitely many strategies to maintain periodic gaits on flat ground. However, these strategies differ in how perturbations due to terrain unevenness are propagated. Instabilities manifest as tumbling (orientational instability) or failing to maintain a steady speed (translational instability). We find that open-loop strategies that avoid sensory feedback are sufficient to maintain stability on step-like terrains with piecewise flat surfaces that randomly vary in height. However, these open-loop runners lose orientational stability on rough terrains whose slope also varies randomly. The orientational instability is significantly mitigated by minimizing the tangential collision, which typically requires sensory information and anticipatory strategies such as leg retraction. By analysing the propagation of perturbations, we derive a single dimensionless parameter that governs stability. This parameter provides guidelines for the design and control of both biological and robotic runners.
Highlights
Legged terrestrial animals run stably on rough terrains, despite potential difficulties such as sensory latencies and the highly dynamic nature of running
Open-loop runners always fail through an orientational instability on rough terrains regardless of the energy dissipated per step
This is because forward and vertical dynamics are decoupled on piecewise flat terrains, and the open-loop runner does not fall as long as the step height is smaller than the apex height of the aerial phase
Summary
Legged terrestrial animals run stably on rough terrains, despite potential difficulties such as sensory latencies and the highly dynamic nature of running. Evidence for the importance of feed-forward strategies for running come from computational studies of SLIP-like running dynamics [16] that show how swing-leg retraction automatically modulates the landing angle in response to unexpected variations in the terrain height. These studies on running have not yet considered the effect of slope variations in the terrain. SLIP-like models are an unfolding of these point-mass instantaneous-stance models to have finite stance duration They have helped us understand the kinetics of stance [15], the energetics of producing forces on flat terrains [21], and the role of swing-leg retraction on piecewise flat terrains [6].
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