|Volume 24 Issue 6 - Publication Date: 1 June 2005
|Skateboards, Bicycles, and Three-dimensional
BipedWalking Machines: Velocity-dependent Stability by Means of Lean-to-yaw
|M. Wisse and A.L.
Schwab Department of Mechanical Engineering, Delft University of
Technology, Mekelweg 2, 2628 CD, Delft, the Netherlands
|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.