Toy
shows bare bones of walking
By
Chhavi Sachdev,
Technology Research NewsRunning, 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 Coleman.
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,” Coleman said.
“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, he said.
“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.
Timeline: now
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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October 3, 2001
Page One
Neurons battle to a draw
Quantum crypto gear shrinks
Toy shows bare bones of walking
Tiny jaws snatch cells
Plastic mix helps shrink circuits
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