illuminating science

Why do you run when you want to move fast? Or, conversely, why do you walk instead of run if you’re only going slowly?

These are just two of the questions that are being considered by a group of robotics researchers at Cornell.
Rather than trying to make detailed models of real people, these guys have gone the other way and are trying to determine the simplest possible models of a person that can be used to understand movement. Some of the questions they wanted to answer were:

• Are walking and running the most energy efficient ways of moving at their respective speeds?
• What (if any) other possible motions are there?
• Why do people not walk or run smoothly? (Like if you were carrying a cup of coffee!)

This is work that was recently published in Nature, which describes their analysis of a minimal model for movement. I’ll try and summarise their paper and results here, although the actual paper is quite readable.

In their model, the person’s body is treated as a just a point, with all their mass concentrated at the top of their legs. The legs themselves are massless, and so it requires no energy to start or stop them. And instead of bending knees, the legs are able to expand or contract just like a telescope.

This might sounds pretty extreme, but it does have a realistic basis - legs are light when compared to our body, and I suspect that a key purpose of knees is to enable us to effectively retract or expand our leg. Also, they still allow for the leg to push off at an angle, which is of course essential. Finally, they put constraints on how long the leg can extend to, and how small a step you can take, which grounds the theory in reality. If you’re still skeptical, you’re probably right to be! When designing minimal models you try use intelligent guesses to strip your system down to the bare bones (so to speak). It’s possible,though, to go too far, and the only way you’ll know for sure that your model is right is if it gives you useful and believable results at the end of the day.

What this group did was to they consider the two functions which will determine how this strange creature walks: the length of its leg, and the force that its leg is exerting (through the ability to change length), as a function of time. They’ve then used numerical techniques to explore “all” (see paper for details) the possible functions you could choose, and to see which results in the least energy cost per metre of travel.

From this, they’ve found quite a few really neat things. Firstly, and very importantly, they re-discovered walking and running (e.g., running being where you push off the ground and are airborne for a few moments). They found that these are the most efficient forms of movement at low and high speeds respectively, and that the cross-over point in their simulations occurs at roughly the same speed as in real life! They also found that walking smoothly, where your head always stays the same height, always takes more energy regardless of what speed you’re moving at. Which explains why I always spill my drink unless I’m concentrating!

Even cooler, they discovered a new type of motion, which they’ve called a “pendular run”, which you can see demonstrated (along with walking, running and level walking) in a video on their site. Apparently, even though it’s the most efficient motiorarely used by humans. The next step, then, is to slowly add features to the model to explain human behaviour.

The upshot of all this is that we now know that the basics of motion don’t depend on anything more than what’s included in this model. Sure, knees, heavy legs, ankles and so forth are going to modify things, such as the pendular-running motion, but they’re not the key details. Hopefully, this study can be used to not just design better robots, but to better understand human physiology.