With all the thousands of possible ways to move our legs, why do people prefer only two – walking and running? After all, there are many other things we could do – hopping, skipping, Monty Python silly walks,Groucho walks or the smooth level walk of a waiter with a tray full of cups of hot coffee. Most people would say that walking and running feel easiest. Other gaits are more tiring. But testing this simple and venerable idea – that walking and running use the least energy at low and high speeds, respectively– is surprisingly difficult to do.

Rather than trying to measure energy consumption of people walking strangely, Manoj Srinivasan and Andy Ruina built a minimal mathematical model of bipedal locomotion, which they describe in Nature. Their goal was to simplify locomotion enough that, for a given speed and step length, they could choose the optimal energy-conserving gait out of the infinite space of possible periodic motions.

The model approximates each leg to something like a reverse pogo stick. Rather than absorbing energy through a spring, each leg can lengthen up to the maximum leg length, applying a force to the ground. Between steps, the body can become aerial, only being affected by gravity. Only one leg can contact the ground at a time. With these simplifications, the researchers used standard optimization techniques to find the forces each leg would have to apply to the ground to produce the most cost-efficient locomotion at a given speed and stride length.

Despite the fact that legs aren't reverse pogo sticks, the model found two optimal gaits that look a lot like walking and running – and one gait that humans don't use. At low speeds and low stride lengths, the model produces an `inverse-pendulum' walk, in which the body vaults over a stiff leg much like our own walking gait. The leg produces forces only for very short periods at the beginning and end of the step. At high speeds, the model settles into an impulsive run, in which the body flies through the air most of the time and the leg only touches down very briefly before launching the body again. In between these two caricatures of walking and running, the model found a hybrid gait: at low speeds, but long stride lengths, the reverse pogo stick uses an inverse-pendulum step, like a walk, but with an aerial phase like a run. The researchers speculated that where healthy, strong people might normally change from walking straight to running, weak or obese people might choose something like the hybrid gait because of an inability to maintain true running speeds.

Srinivasan and Ruina also found a fairly simple explanation for why walking and running are optimal gaits. They have a key similarity: they both compress all force production (and thus energy expenditure) into very short impulses– for walking, at the very beginning and end of the step, and for running, the brief foot contact period. The rest of the cycle – for walking, the inverse pendulum period, and for running, the aerial period– requires no energy. Other gaits, like a flat level walk, require energy throughout the stance phase and are thus less efficient. They really are more tiring.

Srinivasan, M. and Ruina, A. (
). Computer optimization of a minimal biped model discovers walking and running.