shows bare bones of walking
Technology Research News
Running, jogging, tiptoeing, and skipping
are the motions that set us apart from most of the animal kingdom. We
learn to do them on a predetermined schedule and we do them without thinking.
We also don’t know exactly how we do them.
Researchers at Cornell University have taken a step towards figuring out
the mathematics behind the mechanics of human motion by explaining the
movement of a Tinkertoy that walks like we do.
The researchers developed the walking toy in 1998, inspired by the passive
dynamic walker designed over a decade ago by Tad McGeer, then a researcher
at Simon Fraser University in Canada. Passive dynamic walkers are powered
and directed only by gravity. The Cornell model is more like a human skeleton
than the McGeer model because it moves in all three dimensions and cannot
stand up unless it is moving.
After proving empirically that the toy could walk in a stable manner,
the researchers set out to find how it worked mathematically. “Our goal
with the mathematical model and associated computer simulations was to
find stable periodic walking solutions that could explain the observed
behavior of the walking toy,” said Michael Coleman, a researcher and lecturer
in Cornell’s Department of Theoretical and Applied Mathematics.
Most theories of walking rely on neuromuscular explanations. Cornell’s
approach literally strips the issue to its bare bones. Because the toy
walks without muscles, its motion must by controlled by something more
basic. The research differs from most biological approaches to understanding
locomotion because it “emphasizes the role of pure mechanics in explaining
the coordination of animal locomotion,” Coleman said.
This appeal to pure mechanics differentiates the work from other engineering
approaches that use actuators and computer control to “coax mathematical
and physical models to imitate mostly the geometry of walking motions
rather than the full dynamics,” Coleman said. The tinkertoy’s motion is
propelled only by gravity, he said.
Models of rigid bodies, whose parts don’t change shape, can explain motions
at the joints independent of friction between the feet and the ground
and between surfaces, he said. Bypassing neuromuscular theories and those
of friction, the researchers’ math showed that motion is sufficient to
keep a body upright.
The tinkertoy’s two straight legs are hinged to an axle; each leg has
a balancing weight on the side. Its feet are vertical disks. Its steady
walk down the ramp is a balance between the kinetic energy gained as the
toy falls before its feet collide with the floor, and the energy that
is lost in the collisions, said Coleman. Part of the balance comes from
automatic steering, or the way the toy moves from side to side as it places
each foot. Moving the support point from left to right is also the way
people stay balanced when riding a bicycle, walking, or running, said
Walking is essentially a smooth, repeated, inverted-pendulum-like three-dimensional
motion interrupted by joint and foot collisions, said Coleman. While a
bicycle needs both mechanical energy and friction to move, the walking
toy needs neither.
Though the Cornell toy can toddle downhill endlessly, it cannot stand
if it is not in motion. The same is true of a human skeleton stripped
of muscle support. If the muscles and central nervous system were omitted,
leaving only enough connective tissue to hold the skeleton at the joints,
the resulting collection of bones would collapse while standing still,
Coleman said. “So, we imagine that this simple model of the body cannot
stand still in any configuration.” Walking, however, is a very stable
action; small disturbances do not disrupt the gait very much, he said.
The original McGeer walker was less human-like because it had four legs
and could only move in a vertical plane. The walker could also stand still
with its legs splayed in the fore-aft position, said Coleman. Since McGeer’s
walkers moved only in a vertical plane with all the motions visible from
one side, it is referred to as a two-dimensional model, he said.
Although the Cornell model is closer to a human, there are still several
differences. The distribution of mass in the Cornell walkers is not very
human-like, Coleman said. The models also do not have an upper body or
knees. However, they tie in with human locomotion because they walk in
a stable, steady way.
Like a human, the toy moves in three dimension, but because understanding
three-dimensional motions can be more complicated than the two-dimensional
ones McGeer designed, the researchers chose to use straight legs, point
feet, no hip spacing, and no knees in their first attempts. The latest
mathematical models have curved feet and spaced hips, but the researchers
have not yet added knees, Coleman said.
The work shows how passive dynamics affect stability, said Coleman. This
could help in designing stable and efficient legged robots
as well as cures and prosthetics for walking ailments. “We expect that
our biggest impact will be nearly invisible -- as a change in the point
of view of people who study human motions and try to correct problems,”
“It's a good complement to the more traditional controls approach of trying
to make a system do what we want it to, regardless of what it wants to
do,” said Ben Brown, a project scientist at the Robotics Institute at
Carnegie Mellon University. Developing and analyzing simple passive, stable
walkers will lead to a better understanding of the fundamental principles
of walking and is a step toward finding simple and efficient locomotion
methods, he said.
The researchers next plan to build a model that has a gait even more like
that of humans, said Coleman. They also plan to see how much locomotion
and coordination passive strategies can accomplish and measure the tradeoffs
between the key features of correct motions, energetic efficiency, and
stability, he said. They will see if an upper body or a head can be added,
“It is possible that adding more human-like anatomical features to our
models will result in their having more human-like walking characteristics.
But it is likely that these additions will make the walkers unstable and
thus needing control like humans have,” Coleman said.
Coleman’s research colleagues were Andy Ruina and Mariano Garcia at Cornell,
and Katja Mombaur from the University of Heidelberg in Germany. They published
the research in the journal Physical Review E. Andy Ruina received a grant
from the National Science Foundation (NSF) and Katja Mombaur received
a grant from the University of Heidelberg.
Funding: Government; University
TRN Categories: Robotics
Story Type: News
Related Elements: Technical papers, "Prediction Of Stable
Walking For A Toy That Cannot Stand," Physical Review E, vol. 64, 2001;
“An Uncontrolled Walking Toy That Cannot Stand Still,” Physical Review
Letters, vol. 80, 1998.
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