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Next: Conclusion Up: Optimal Walking Experiments Previous: Forward Velocities and Collisions

Walking with and without Liftoff Forces

Figures 7 and 8 display the optimal applied torques for the model with and without impulsive liftoff forces from the same set of experiments as the previous section. Including an impulsive liftoff force is an easy way of modeling the same effects as having a foot. The solid and dashed lines indicate the torques for the optimal walking motion for the model with and without ankle actuation respectively. There is a notable difference between the 12 m/min (globally optimal) and the 50 m/min walk. It is evident that the torques for the faster walk reach the magnitude constraints placed upon them several times. The torque saturations can be greatly reduced with the introduction of an impulsive liftoff force. These torques (and their rates) are of much smaller magnitude showing the beneficial effect this additional control parameter has.

For a given velocity, it is difficult to distinguish the difference between including and not including ankle actuation. The difference only becomes visible at the higher forward velocity when during the second phase a slightly smoother and smaller torque actuation is required for the hip and knee. An interesting effect witnessed in our experiments is that the knee comes more into use with ankle actuation. As a result, the torque inputs and associated cost in injected energy will be more equally distributed through the different joints of the biped.

Michael W. Hardt
Mon Oct 11 17:19:43 MET DST 1999