Effectivities for Reach-to-Grasp Actions

I just reviewed the affordance properties that produce the spatial structure in reach-to-grasp actions, and there's an unquestioned assumption lurking in that analysis. Luckily, Mon-Williams & Bingham (2011) actually did question it, so I wanted to cover that part of the paper here.

The assumption in the analyses I described last time is that the unit of action is the aperture between the finger and thumb, and not the fingers themselves. Bingham refers to this as an opposition vector (Iberall, Bingham, & Arbib, 1986; van Bergen et al, 2007). In some ways, this is a weird idea; the action system working to control a space between limbs, and not the limbs! Smeets & Brenner (1999) proposed that grasping is actually about the two limbs. Mon-Williams & Bingham tested these hypotheses and found evidence in favour of the opposition vector.

I want to walk through this in a little detail, though, as of course identifying the relevant elemental variables is part of an UCM analysis, and affordance research helps here too. The task analysis that reveals affordance property options also points to effectivity property options (at least it should - these are complementary after all!). But another part of the UCM approach is that it can, in principle, test hypotheses about elemental and performance variables, so I want to lay this out as well.

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.