Martijn Wisse

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.

This paper presents the simplest walking model with an upper body. The model is a passive dynamic walker, i.e. it walks down a slope without motor input or control. The upper body is confined to the midway angle of the two legs. With this kinematic constraint, the model has only two degrees of freedom. The model achieves surprisingly successful walking results: it can handle disturbances of 8% of the initial conditions and it has a specific resistance of only 0.0725(−).

The authors have built the first three-dimensional, kneed, two-legged, passive-dynamic walking machine. Since the work of Tad McGeer in the late 1980s, the concept of passive dynamics has added insight into animal locomotion and the design of anthropomorphic robots. Various analyses and machines that demonstrate efficient human-like walking have been developed using this strategy. Human-like passive machines, however, have only operated in two dimensions (i.e., within the fore-aft or sagittal plane). Three-dimensional passive walking devices, mostly toys, have not had human-like motions but instead a stiff legged waddle. In the present three-dimensional device, the authors preserve features of McGeer’s two-dimensional models, including mechanical simplicity, human-like knee flexure, and passive gravitational power from descending a shallow slope. They then add specially curved feet, a compliant heel, and mechanically constrained arms to achieve a harmonious and stable gait. The device stands 85 cm tall. It weighs 4.8 kg, walks at about 0.51 m/s down a 3.1-degree slope, and consumes 1.3 W. This robot further implicates passive dynamics in human walking and may help point the way toward simple and efficient robots with human-like motions.

Autonomous walking bipedal machines, possibly useful for rehabilitation and entertainment purposes, need a high energy efficiency, offered by the concept of ‘Passive Dynamic Walking' (exploitation of the natural dynamics of the robot). 2D passive dynamic bipeds have been shown to be inherently stable, but in the third dimension two problematic degrees of freedom are introduced: yaw and roll.We propose a design for a 3D biped with a pelvic body as a passive dynamic compensator, which will compensate for the undesired yaw and roll motion, and allow the rest of the robot to move as if it were a 2D machine. To test our design, we perform numerical simulations on a multibody model of the robot. With limit cycle analysis we calculate the stability of the robot when walking at its natural speed.The simulation shows that the compensator, indeed, effectively compensates for both the yaw and the roll motion, and that the walker is stable.