Thursday, 13 October 2016

Optimal Feedback Control and Its Relation to Uncontrolled Manifold Analysis

Motor control theories must propose solutions to the degrees of freedom problem, which is the fact that the movement system has more ways to move than are ever required to perform a given task. This creates a problem for action selection (which of the many ways to do something do you choose?) and a problem for action control (how do you create stable, repeatable movements using such a high dimensional system?).

Different theories have different hypotheses about what the system explicitly controls or works to achieve, and what is left to emerge (i.e. happen reliably without explicitly being specified in the control architecture). They are typically about controlling trajectory features such as jerk. Are you working to make movements smooth, or does smoothness pop out as a side effect of controlling something else? This approach solves the degrees of freedom control problem by simply requiring the system to implement a specific trajectory that satisfies some constraint on that feature you are controlling (e.g. by minimising jerk; Flash & Hogan, 1985). They internally replace the solutions afforded by the environment with one desired trajectory

Todorov and Jordan (2002a, 2002b; thanks to Andrew Pruszynski for the tip!) propose that the system is not optimising performance, but the control architecture. This is kind of a cool way to frame the problem and it leads them to an analysis that is very similar in spirit to uncontrolled manifold analysis (UCM) and to the framework of motor abundance. In these papers, they apply the mathematics of stochastic optimal feedback control theory and propose that working to produce optimal control strategies is a general principle of motor control from which many common phenomena naturally emerge. They contrast this account (both theoretically and in simulations) to the more typical 'trajectory planning' models.

The reason this ends up in UCM territory is that it turns out, whenever it's possible, the optimal control strategy for solving motor coordination problems is a feedback control system in which control is deployed only as required. Specifically, you only work to control task-relevant variability, noise which is dragging you away from performing the task successfully. The net result is the UCM patterns; task-relevant variability (V-ORT) is clamped down by a feedback control process and task-irrelevant variability (V-UCM) is left alone. The solution to the degrees of freedom control problem is to simply deploy control strategically with respect to the task; no degrees of freedom must be 'frozen out' and the variability can be recruited at any point in the process if it suddenly becomes useful - you can be flexible.

What follows is me working through this paper and trying to figure out how exactly this relates to the conceptually similar UCM. If anyone knows the maths of these methods and can help with this, I would appreciate it!

Tuesday, 11 October 2016

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!

Thursday, 15 September 2016

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. 

Wednesday, 7 September 2016

The Bliss of Motor Abundance

The fundamental question in psychology boils down to "why did that person do that thing they just did?". Welcome to my new favourite example.
Figure 1. I am pretty sure this move totally makes sense
I saw this on Twitter the other day and I couldn't stop watching it. What the ever-loving hell is that cat doing? Then I realised I had a hypothesis, and that it was a fun example of an ecological affordance analysis. So here we are, at last, with a cat-themed blog post. I'll review this manouver, claim that it's all about effecting affordances, and then chat a little about complex actions like this.

Wednesday, 10 August 2016

The Affordances of Prehistoric Objects

I have a new paper in press at Scientific Reports (Wilson, Zhu, Barham, Stanistreet & Bingham, 2016; see also the slides from my EWEP14 talk) and I am so excited about it I can hardly cope. This project has been the most pure, good-old-fashioned science fun I've had in years and I'm very proud of the result.
Figure 1. Spheroids
The paper is an affordance analysis of some prehistoric objects (spherical rocks called 'spheroids') that were excavated from a cave in South Africa. There are several theories about what the prehistoric humans used these for, but one is that they were projectiles used for hunting. I created a simulation of projectile motion and set the parameters of the simulation using data from the literature on throwing for maximum distance. We then showed that a majority of our sample spheroids were ideally suited for throwing to inflict useful damage to a medium sized prey animal over fairly long distances. Given that we know humans have been anatomically specialising for throwing for millions of years, and given that we know modern humans can perceive the affordance for throwing to a maximum distance and select objects that best fit this affordance, we argue that these simulations provide evidence that these objects were selected to be used as projectiles.

This slightly out-of-left-field project was the result of some good luck, some careful management and the hard work of all my collaborators as we tied this together. The paper stands as an exemplar and proof-of-concept of how a task-dynamical affordance analysis can tell us about the behaviour of prehistoric humans.

Monday, 25 July 2016

Relational Theories of Affordances are Functional, Not Mechanistic (A Purple Peril)

Everyone and their dog has a theory about how to interpret Gibson's famously vague definition of affordances;
The affordances of the environment are what it offers the animal, what it provides or furnishes, either for good or affordance is neither an objective property nor a subjective property; or it is both if you like. An affordance cuts across the dichotomy of subjective-objective and helps us to understand its inadequacy. It is equally a fact of the environment and a fact of behavior. It is both physical and psychical, yet neither. An affordance points both ways, to the environment and to the observer.
There are two basic flavours of theories: affordances as dispositional properties of the environment (Turvey, Shaw, Reed & Mace, 1981; Turvey, 1992) and affordances as relational features of the animal-environment system. (A recent paper has just claimed they should be best understood as events, but to be honest I don't really know what's motivating this). The two most recent and popular relational accounts are Chemero's book (Chemero, 2009; see these posts on the relevant chapter) and Rietveld & Kiverstein (2014) in a paper entitled 'A Rich Landscape of Affordances'. Their goal, like most of the relational accounts, is to handle higher-order cognition by scaling up affordances to support it (our move, in contrast, has been to expand the uses of perceptual information; Golonka, 2015Golonka & Wilson, 2016 preprint).

I am firmly in the 'affordances as dispositional properties' camp (see, for example, the discussion section of my recent throwing paper for an extended analysis). Specifically, they are dynamically defined dispositional properties of objects and events in the context of tasks. The reason is that this is the only way affordances can be the kind of thing that can create information and therefore be perceivable. They have to be 'out there' and made of things that light can bounce off, for example, and relations between organism and environments are not typically such things. In addition, if they do not exist until perceived, we need a story to explain how we come to learn to perceive them, and there is no viable ecological framework that will make this happen (Wilson et al, 2016).

Reading this material with my new mechanism glasses on has given me a new, concise way to identify the problems with these relational accounts:

Affordances-as-relations theories are all functional explanations, and not mechanistic explanations

Thursday, 21 July 2016

Framing the Debate

In 2014 we published a book chapter with Eric Charles in which we argued that the most important thing psychology and neuroscience needed from people like us was a new language in which to talk about the problems we are trying to solve. Our Ecological Representations paper is part of this, and we have a much larger paper in development laying out the more complete set of conceptual tools needed to do ecological psychology across a wider range of problems.

One reason why this is important is a simple fact; we are asking psychology to change and it is up to us to clearly articulate what we want it to change into, or else nothing can happen. A related reason is that without a clear framework, we can't reformulate the questions in a useful way and we're left stuck because we can't explain something like 'theory of mind' because the actual solution is that ToM doesn't exist or need explaining. Ecological neuroscience, for example, will look very different to cognitive neuroscience.

A final reason is that the language in which psychology frames it's understanding of behaviour drives popular understanding of behaviour too. I recently came across my favourite example of this in a tweet by Alice Dreger;
Dreger, for some reason, spends most of her life only using her right eye, even though her left is perfectly functional. She blogged about it here. Every now and again, something makes her left eye kick in and she suddenly has stereo vision.

What caught my eye here is her description of her experience is grounded in the myth that you need two eyes in order to perceive in 3D (I bug my students about this in class every year too). The myth is based in the standard image-based analysis of vision which I'll lay out below; but the point I want to make here is that people still describe their experience of monocular vision as 'not being able to see 3D/depth' even though this is inarguably, demonstrably not what is happening in their visual experience. It's like blind echolocators talking about how the sound creates 'an image in their minds'; this is just not the case, but this is the language psychology has provided them for talking about the perceived experience of spatial layout. What fascinates me is that it's trivial to demonstrate that monocular vision allows for 3D perception, but everyone lets the framing override their own experience. This, to me, is a big part of why our work right now is important - we will never make progress until we can reframe the debate.