Skateboards, Bicycles, and Three-dimensional Biped Walking Machines: Velocity-dependent Stability by Means of Lean-to-yaw Coupling

One of the great challenges in the development of passive dynamic walking robots (useful for an understanding of human gait and for future applications in entertainment and the like) is the stabilization of three-dimensional motions. This is a difficult problem due to the inherent interaction between fore-aft motions and sideways motions. In this paper we propose a simple solution. Conceptually, one can avert a sideways fall by steering in that direction, similar to skateboards and bicycles. We propose to implement this concept for walking robots by the introduction of an ankle joint that kinematically couples lean to yaw. The ankle joint has an unusual orientation; its axis points forward and downward, without any left-right component. The effect of the ankle joint is investigated in a simple three-dimensional model with three internal degrees of freedom: one at the hip and two at the ankles. It has cylindric feet and an actuator at the hip joint, which quickly moves the swing leg to a preset forward position. The simulations show that it is easy to find a stable configuration, and that the resultant walking motion is highly robust to disturbances. Similar to skateboards and bicycles, there exists a critical velocity (as a function of the parameters) above which stable walking motions occur. The critical velocity can be lower for a more vertical ankle axis orientation. As an additional benefit, the ankle joint allows a straightforward implementation for steering; a simple sideways offset of the mass distribution will cause the model to gently steer in that direction. The results show great potential for the construction of a real-world prototype with the proposed ankle joint.