An Uncontrolled Walking Toy That Cannot Stand Still

Abstract

We built a simple two-leg toy that can walk stably with no control system. It walks downhill powered only by gravity. It seems to be the first McGeer-like passive-dynamic walker that is statically unstable in all standing positions, yet is stable in motion. It is one of few known mechanical devices that are stable near a statically unstable configuration but do not depend on spinning parts. Its design is loosely based on simulations which do not predict its observed stability. Its motion highlights the possible role of uncontrolled nonholonomic mechanics in balance.

Dynamic stability differences in fall-prone and healthy adults

“…the dynamic state is attracted to an orbit that never intersects a static balance configuration at the origin. Therefore, the system can be dynamically stable but is unstable in most static postures (Coleman and Riuna, 1998). Similar behavior is observed in human locomotion but has more degrees-of-freedom than can be graphically illustrated.…”

Stabilization of Lateral Motion in Passive Dynamic Walking

“…Unless there is an unforeseen passive means to delay ground contact when a perturbation increases the roll velocity (see Figure 3), active stabilization should be a necessity. Empirical results by Coleman and Ruina (1998) suggest that a passively stable 3-D walking machine may be feasible, and other 3-D systems can indeed exhibit passive stability (Coleman, Chatterjee, and Ruina 1997), but we do not expect those results to apply to the present mechanism. Step length increases with slope, as do stance and swing velocities.…”

Delay effects in the human sensory system during balancing

“…Note that the control force F is clearly external in the case of stick balancing. In the case of balancing ourselves on the tips of skates, this control force F is provided by the friction force that is controlled by us in an intricate way of walking strategies based on small internal torques at the hip and ankle joints (for more details see Coleman & Ruina (1998) and Piiroinen & Dankowicz (2005)). If the mass of the slider is negligible relative to the mass m of the bar of length l, the Lagrangian equations assume the form 1 3 ml 2 1 2 ml cos 4…”