## Dynamic Walking

Gait from mechanical design

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1. Computer simulation of a "compass gait walker". This is an idealized mathematical model of two rods joined by a hinge and with a mass at the joint. The computer solves the equation of motion for this mechanical linkage, including footfall impacts as it steps down a shallow slope. There is no friction in the model. A natural biped walking gait emerges in which the energy dissipated when a foot hits the ground exactly equals the energy gained from gravity during the previous step. This gait is self-stabilizing - if you bump the walker it will automatically correct itself and return to the steady gait. The compass gait walker shows how stable gait can emerge from mechanical design, with no need for muscles or a brain (or, if you are a robot, motors and computers). The concept of "passive dynamic locomotion" is causing biologists to re-think ideas about animal and human agility, and engineers to re-think the design of walking robots.

2. Student Kim McKelvey gained an MSc in Computational Modeling. He used computer simulations to study the stability of passive dynamic walkers with realistic mass distributions. These are walkers that you could actually build and test, unlike the compass gait walker, which is a mathematical idealization with "massless legs" and "point masses" at the hip and feet. Then he built and tested one, called "Kimbot". Kimbot walks on cork tiles laid out on the slope. This is so that the swing leg(s) don't scuff the slope on the way through. In the computer simulation we just leave out that bit of the physics, by simply not including an "event detector" for foot scuffing. The computer model tells us how steep to make the slope and how far apart to put the tiles on a given slope. Kim went on to become a computer game engine developer - his code drives some walking and falling behaviours of characters in "GTA 4", one of the world's top-selling games.

3. PhD student Te Yuan Chyou has been looking at how to make passive dynamic walking more efficient by passively eliminating the footfall impacts. In this model there are springs around the hip, connecting the torso and the legs. These springs capture kinetic energy from the swing leg and bring the foot to a stop just as it contacts the ground. The result is a passive dynamic mechanism that can walk on a horizontal plane using no energy! This mathematically ideal linkage is like a mathematically ideal wheel in this sense. This walker can also walk downhill, and it is stable like the compass gait walker. But on level ground it is inherently unstable because any perturbation must cause a loss of energy, and there is no source of energy to replace it. Te Yuan is now studying active and passive mechanisms for stabilizing gait on horizontal and uneven terrain. This work has interesting implications for understanding human gait (with medical and sports applications) and for designing agile legged robots.