Watch a dog trotting or a horse galloping, and it is hard to see how such different gaits could all be explained by a single set of equations. But Hugh Herr's team working at MIT have modelled running animals ranging in size from a chipmunk to a large horse, with a single set of equations, and the results are very convincing (p. 959)!
Herr's `Leg Lab' is interested in anything to do with movement. Over the years they've built robots that balance, run and even hop. Ultimately, they want to understand how humans and animals walk and run. One way to learn how animals move is by mathematically simulating the physics that keeps them up and about. Greg Huang, a postdoc in the Leg Lab, was intrigued by the effect an animal's size has on the way it moves. So he set out to develop a set of equations that could simulate large and small animals' movements. But first he figured out how to model the movements of a medium sized animal, like a pony.
Instead of simulating every sinew and joint, Huang models a leg as two rigid sections joined by a spring-knee. The knee isn't like the hinged joint we all know, it behaves like a telescope, so the walking leg shortens as it swings forward. Each leg is joined to the cyberpony's body by a hinge, so the springy leg swings back and forth. Next, Huang gave the simulated animal joints in its neck and back, to model its bobbing movements, and finally he programmed in the forces on the animals hips and shoulder joints that drive the animal forwards. He set the simulations running to see how well his pony trotted through the computer chip.
The results were spectacular. Even though it isn't intuitively obvious that an animal's leg behaves like a spring, the simulation reproduced the physics of the animal's performance extremely well! His cyberpony used the same energy per stride as its flesh and blood cousin, threw its legs out at the same frequency and pushed off from the earth with the same force as an animal cantering across a field. What's more, the movies his simulations produced were startlingly realistic.
Having got the simulation to work for one animal, Huang wanted to know how unified his theory was. He had to test it on larger and smaller beasts.
Huang modified his simulation to behave like a tiny chipmunk, a goat, two breeds of dog and a large horse. Again the simulations reproduced the physics of the movements well. Just by changing the animal's weight and body plan, a single set of motor controls accurately reproduced all six animal's gaits. The simulations worked so well, that Huang believes `we've gotten a lot of the biology right!'
One thing the simulation can't do yet is switch from trotting to galloping as the animal gains speed. Huang explains that his simulation of a horse trotting at galloping speeds looks pretty funny. He hopes that in the future he will learn why high speed trotting is unphysical and what throws the gait-switch as an animal steps up the pace.