Gedanken Experiment: Control Your Motor

Yesterday I raced at Granogue. I finished 68th. End of race report. (Also I took off my pants in public. You're welcome).

Being in full-on hard-core thesis mode, I found myself caring much less about the racing and much more about the experience. The beautiful view from the top of the course, the kegs of Victory in the beer tent, and of course the spectating.

By luck, or more likely by my own subconscious design, there is a strong connection between my research and my sport. If you know what you're looking for, you can see principles of motor control playing out in real life... and it turns out, there's nowhere better to observe motor control than at a cyclocross race (except a rally car race, but people die watching that nonsense!).

So, motor control. The way we coordinate the body's movements. It has been studied (and is studied, and will be studied) at the level of muscle activation, at the level of force production, at the level of joint rotations, and it even applies to whole-body movements through space... as on a bicycle.

One lens through which to view motor control is the Uncontrolled Manifold hypothesis, the very mention of which is generally enough to make the eyes glaze over.

The long and short of the Uncontrolled Manifold hypothesis is that there exists a subspace (Manifold) within the space of all possible actions, and that in this subspace, the motor control system allows for variability (Uncontrolled, y'see). The body is inevitably going to experience variability (try to draw two identical circles, as a quick demonstration), so we try to structure that variability so that the end result is always what we want it to be. And that's why the eyes tend to glaze over at the mention of the Uncontrolled Manifold hypothesis.

It's best for me to explain by means of a simple example. Let's say I put two pressure sensors in front of you, showed you what the total pressure was, and said "try to keep the total pressure at a value of 20".

So, here's the space of all possible activities. Any combination of pressures exists somewhere in this space.
And here's the subspace that holds the end result - the sum of the pressures - steady. In this case, the subspace is just a line.
You're going to allow the pressures to wander anywhere along the red line, because as long as the sum is 20, everybody's happy. After a while, you'll find that you've produced a cloud of data that looks like this:
Notice how along the red line, the variability is huge, but the perpendicular direction sees very little variability. Your motor control system leaves the manifold uncontrolled, but it restricts activity that reduces accuracy.

A variability profile for this one simple task would look like this:
The variability along the trajectory is called "good", because it lets you do what you're trying to do. "Bad" variability, being perpendicular to the trajectory, impedes you (mostly... more on that later).

How does this apply to bike racing? I'm glad you asked. You're so smart and curious and attractive.

Consider a turn. Let's say the turn is pretty grippy, and somewhat tight, so that there's pretty much one way to take it: enter wide, apex inside, and exit wide. Like this:

Now, more usefully, let's portray it like this:

What actually happens over the course of a race, as hundreds of competitors take this turn a half-dozen times each, is that you get thousands of repetitions of that corner... I'll show you a few dozen for clarity's sake.

The trajectories are mostly consistent, but there is variability. See?


Let's say that we take slices of these trajectories, and treat each slice as a cloud of data, so that the corner becomes a collection of the simple variability analyses we've already dealt with. At each of these slices, we look at how much variability there is parallel to (Good) and perpendicular to (Bad) the trajectory. Lo and behold, it looks something like this:

Some technical notes, for those who are looking for slip-ups with which to question my credibility (you know who you are, Will).

• I skipped the time-normalization step that contributes to variability parallel to the trajectory
• I've made no mention of the linearization of the trajectory that is key to this analysis, but I'll be happy to walk you through it off-line
• The trajectories I've shown you are rear-wheel only, because the front wheel takes a different and less interesting trajectory
• All data presented in this post are completely and entirely made up out of thin air and may very well have no bearing on reality

Back to the story.

Let's look at a different corner. maybe one of the corners after the barriers at Granogue, the sweeping downhill turns that put you at the limit of grip. Here's Todd, on just such a corner.

By virtue of being at that ragged edge of control, the course designers are forcing you to change the shape of the Uncontrolled Manifold. While the easier turn was more forgiving of various lines - entering too narrow, apexing too wide, etc - this tough turn forces you into the good line. Now your variability profile looks something like this:

You're forced into that optimal line, and so your variability is significantly lower than in a more forgiving corner.

For my road-racing colleagues, this is comparable to the rainy, twisty courses that let breakaways reach deep into their suitcases of courage and stay away from the pack. The pack can't take the optimal line at full speed, because it's too wide to allow for the optimal line.

Oh, and for my motorsport-enthusiast friends, this is why a thrilling duel between two risk-taking drivers actually slows the duelers down.

My favorite part of this analysis, which is also my favorite part of spectating 'cross (except for heckling, of course), happens at the eXtreme corners. For example, the descent from the tower at Granogue, or the "Granogue-like" turn at Rutgers 'Cross Practice. Turns so sharp, on such slippery terrain, that likely s not, the rear wheel is going to slide out. The fun turns, ya dig?

Let's throw out the incidents where the rear wheel slides and never recovers; that is, let's ignore the thoroughly unsuccessful attempts at cornering that result in a complete stop, a bruised hip, and a curse-word or two. Our trajectories look like this:

So in some cases, riders roll cleanly through the turn, but in other cases, the rear wheel slides towards the outside before the rider recovers control.

This video is a great demonstration. The first rider locks his rear wheel and slides a bit, but the following four roll through smoothly. It's subtle, watch closely...


The variability here is quite different than what we've seen so far. The slide after entry forces you outside the Uncontrolled Manifold, and the variability profile reflects this loss of control. If you look at all successful turns, the fact that some repetitions include a slide will increase variability, especially the Bad kind.

And yet, we can see that "bad" variability isn't necessarily bad. You still get through the corner (if you don't crash), and nowhere here have I mentioned the speed of the rider (remember, this is all time-normalized). We're looking at two different Uncontrolled Manifolds (UCMs) simultaneously, which is why there is a spike in variability.

In fact, if we separated the two trajectories into two groups - Rolling, where the racer rolls as usual through a corner, and Drifting, where the rear wheel slides out - both groups would probably have variability profiles similar to what we saw in the first two corners. Each group has adopted its own control strategy, its own UCM.

Charlie and Jay are masters of the brief rear-wheel lockout. They use the temporary abandonment of control as a control scheme itself, employing "bad variability" for functional gain. It's the exception that proves the UCM rule. And it's damn fun to watch... but even more fun to ride.