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Our investigation into the generation of minimum energy symmetric, periodic
gaits gathers together several different research areas in the modeling
and control of complex, nonlinear systems.
Our ability to solve this problem has relied upon the use of recursive,
symbolic multibody algorithms coupled with powerful numerical optimal
Some of the more interesting conclusions that can be made from our
- Minimum energy walk for biped model
(without explicit modeling of the feet) has a much slower
walk than optimal human walk.
The optimal model walk has shorter steps than optimal human walk,
however the notion of step length is problematical since
the model has no feet.
- Impulsive liftoff forces help prevent
torque saturation, smooth the walking motion, and reduce the
- Ankle actuation smooths the walking step and
distributes the input torques more equally among the hip, the knee,
and the ankle.
Using polar coordinates as in Section
to convert leg vs hip geometric constraints to
was critical to numerical success.
Michael W. Hardt
Mon Oct 11 17:19:43 MET DST 1999