Motor Abundance & the Affordances for Reaching-to-Grasp

Movements are never the same twice, even when you are trying to do that same thing over and over. Variability is an inescapable fact of trying to organise and run a complex system such as a human body. But there is more than one source of variability in movement; there's noise, and then there's redundancy, and these are not the same thing. 

Our movement systems are redundant; specifically, they always have more degrees of freedom available than are ever required to perform a given task. This means that there is always more than one way to perform any given task, and this can range from slight variations to complete reorganisations. 

Redundancy is a feature, not a bug. It means that we can reliably achieve a task goal in the face of perturbations that range from trial-to-trial fluctuations in execution up to surprises like tripping or the sudden appearance of an obstacle. However, it poses two related control problems. First, a problem of action selection: given that there are many functional organisations of degrees of freedom that could solve that task, which do we choose, and why? Second, a problem of action control: once we have our degrees of freedom organised, we still have some left over that need to be actively controlled; how do we do this, and why do we control them the way we do?

Trip Report from the Uncontrolled Manifold

I've spent the past few months getting a new paper to the 'complete first draft' stage (you can find a copy here in the meantime; it's still got some work to do though). It's about affordances, using targeted long-distance throwing as the task, and it's my first dip into the world of the uncontrolled manifold. I collected this data over five years ago, and it's been deeply satisfying to actually use it after all this time.

Part of what's taken so long is that I've had to learn the details of the uncontrolled manifold analysis. I blogged some about it here and here but this was the year I finally had the time and data to actually get into the maths. I still really like it as an approach to analysing human movement, but learning the details and trying to figure out how to get affordances into it has raised a lot of interesting questions about how it gets used right now and what this all implies for how we think movement is controlled. I'm raising a bunch of these issues in the paper but I wanted to sketch some out here for comment.

Broadly (and this shouldn't be a surprise to anyone really) I've realised that UCM is only a method, not a theory, and it's therefore not able to serve as a 'guide to discovery' about movement control. However, it's being used as if it can, and to be honest I was quite shocked at how carelessly it's being used in the literature. 

What Limits the Accuracy of Human Throwing?

Throwing a projectile in order to hit a target requires you to produce one lot of the set of release parameters that result in a hit; release angle, velocity (speed and direction) and height (relative to the target). My paper last year on the affordances of targets quantified these sets using a task dynamical analysis.

There is one additional constraint; these release parameters have to occur during a very short launch window. This window is the part of the hand's trajectory during which the ball must be released in order to intercept the target. It is very easy to release slightly too late (for example) and drill the projectile into the ground.

How large is this launch window? It is surprisingly, terrifyingly small; Calvin (1983) and Chowdhary & Challis (1999) have suggested it is on the order of 1ms. Those papers used a sensitivity analysis on simulated trajectories to show that accuracy is extremely sensitive to timing errors and this millisecond level precision is required to produce an accurate throw.

Smeets, Frens & Brenner (2002) tested this hypothesis with dart throwing. If this intense pressure on timing the launch window determines accuracy, then throwers should organise their behaviour and throw in a way that makes their launch window as tolerant of errors as possible. They replicated the sensitivity analyses on human data to see if people try to give themselves the maximum error tolerance in the launch, or whether they were trying to accommodate errors in other variables.

What they found is that the launch window timing is not the limiting factor. Their throwers (who were not especially expert) did not throw so as to minimise the sensitivity of the launch window timing to errors. Quite the contrary; they lived in a fairly sensitive region of the space, and then didn't make timing errors. They did throw so as to reduce the sensitivity to speed errors, however, and errors in the targeting came from errors in the spatial path of the hand that the system did not adequately compensate for, rather than the timing of the hand's release. (The authors saw some evidence that the position, speed and direction of the hand trajectory were organised into a synergy, which aligns nicely with the motor abundance hypothesis).

I would like to replicate and extend this analysis process using more detailed simulations and data from better throwers. I've become convinced it's a very useful way to think of what is happening during the throw. I also think these results point to some interesting things about throwing. Specifically, while timing and speed must both be produced with great accuracy, the system has developed two distinct solutions to coping with errors. Timing errors are reduced by evolving neural systems that can reliably produce the required precision. Speed errors have been left to an online perception-action control process which adapts the throw to suit local demands. The latter is the more robust solution; so why was timing solved with brain power?

Nonlinear Covariation Analysis (Müller & Sternad, 2003)

I have been working my way through some analyses that fall under the idea of the motor abundance hypothesis (Latash, 2012) - the idea that motor control does not work to produce a single, optimal movement trajectory, but rather works to produce a particular task goal, or outcome. Motor control preserves function, and not structure; it exhibits degeneracy. So far I have looked at uncontrolled manifold analysis here and here, and stochastic optimal control theory here. 

This post will review nonlinear covariation analysis developed by Müller & Sternad (2003). This purports to address several issues with UCM.

What Can You Do With Uncontrolled Manifold Analysis?

There is generally more than one way to perform a task (the ‘bliss of motor abundance’) and so it’s possible for a movement to incur a little noise that doesn’t actually affect performance that much.
Uncontrolled manifold analysis (UCM) is a technique for analysing a high-dimensional movement data set with respect to the outcome or outcomes that count as successful behaviour in a task. It measures the variability in the data with respect to the outcome and decomposes it into variability that, if unchecked, would lead to an error and variability that still allows a successful movement.

In the analysis, variability that doesn’t stop successful behaviour lives on a manifold. This is the subspace of the values of the performance variable(s) that lead to success. When variability in one movement variables (e.g. a joint angle, or a force output) is offset by a compensation in one or more other variables that keeps you in that subspace, these variables are in a synergy and this means the variability does not have to be actively controlled. This subspace therefore becomes the uncontrolled manifold. Variability that takes you off the manifold takes you into a region of the parameter space that leads to failure, so it needs to be fixed. This is noise that needs control.

With practice, both kinds of variability tend to decrease. You produce particular versions of the movement more reliably (decreasing manifold variance, or V-UCM) and you get better at staying on the manifold (decreasing variance living in the subspace orthogonal to the UCM, or V-ORT). V-UCM decreases less, however (motor abundance) so the ratio between the two changes. Practice therefore makes you better at the movement, and better at allocating your control of the movement to the problematic variability. This helps address the degrees of freedom control problem.

My current interest is figuring out the details of this and related analyses in order to apply it to throwing. For this post, I will therefore review a paper using UCM on throwing and pull out the things I want to be able to do. All and any advice welcome!

Uncontrolled Manifold Analysis

Human movement is hard to study, because there are many ways to perform even simple tasks and given the opportunity, different people will take different routes. It becomes hard to talk sensibly about average performance, or typical performance, or even best performance. 

This fact - that the action system contains more elements than are needed to solve a given task - was first formalised by Bernstein as the degrees of freedom problem. Anything that can change state is a degree of freedom that can contribute to movement stability and if you have more than you need then there is immediately more than one way to perform a task. This means you have to select the best action, and even then there are always variations in the details of how you perform that action (Bernstein called this 'repetition without repetition'). From this perspective, selecting the right action means freezing out redundant degrees of freedom and working with just the ones you need.

A more recent way to think about the problem is as the bliss of motor abundance (Gelfand & Latash, 1998; Latash, 2012; see this recent post too). From this perspective, selecting the right action is about balancing the contributions of all the degrees of freedom so that the overall behaviour of the system produces the required outcome. Nothing is frozen out, but errors incurred by one degree of freedom are compensated for by changes in other degrees of freedom. If (and only if) this compensation happens, then you have a synergy in action. 

This analysis leads to a prediction and an analysis. It predicts that there are two kinds of movement variability - variability that pulls you away from your target state and variability that doesn't. The former is a problem that must be corrected by another element in the synergy compensating. Successful movement requires clamping down on this variability. The latter requires no correction, no control, and successful movements can still happen even if this variability is high. An analysis of movement then follows. You can decompose the variability of movement in the total state space of that movement into that which pulls you away from the target, and that which does not. Successful movement lives on a subspace of the total space of possible values of your degrees of freedom. If the ratio of the 'good' variability to the 'bad' variability is high, you are hanging out close to that subsapce and working to keep yourself there, although not working to keep yourself doing anything in particular. You have a system that is working to compensate for 'bad' variability while ignoring the rest; a synergy defined with respect to the task demands. 

This subspace is referred to as the uncontrolled manifold. It is uncontrolled because when the system is in this subspace of it's total state space, it does not work to correct any variability because that variability is not affecting the outcome. Control only kicks in when you come off the manifold.