Speed, Efficiency and Stability of Small-Slope 2-D Passive Dynamic Bipedal Walking

This paper addresses some performance limits of the kneed and non-kneed passive-dynamic walking machines discovered by McGeer [10, 11]. Energetic inefficiency is measured by the slope γ needed to sustain gait, with γ = 0 being perfectly efficient. We show some necessary conditions on the walker mass distribution to achieve perfectly efficient walking. From our experience and study of a simpler model, only two gaits exist; the longer-step gait is stable at small enough slopes. Speed is regulated by energy dissipation. Dissipation can be dominated by a term proportional to speed or a term proportional to speed from normal foot collisions, depending on the gait, slope, and walker design. For special mass distributions of kneeless walkers, the long-step gaits are especially fast at small slopes. A period doubling route to chaos is numerically demonstrated for the kneed walker.