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.

Opposition

Hands provide us with the usual problem: a huge number of degrees of freedom, so what constrains how we use these so the control problem is manageable? Iberall et al (1986) take a task analysis approach; examining what is required to achieve various goals and using that to constrain the analysis. It's an early version of the affordance analysis Bingham does in the 2011 paper (Bingham was doing a lot of this sort of thing in the 80s: basically doing affordances without using the word as a way to get the stuff published). 

Reaching to grasp and manipulate objects imposes a variety of constraints on hand posture. Iberall et al detail how these constraints are mostly about forces, and specifically the need to balance and cancel out a variety of force vectors. Lifting an object means overcoming gravity, for example; maintaining a grip means generating enough friction, and so on. A stable grip is one where all the forces are in equilibrium; this is generally achieved by opposition. If you place two surfaces parallel to one another (within the tolerances afforded by friction), these can each exert a force of equal magnitude in opposite directions along an opposition axis. What forces remain to be wrangled then depends on where that opposition axis is relative to the object centre of mass. 

In reach-to-grasp movements, this opposition axis lives in the space between the finger and thumb (the two roughly parallel and opposable surfaces). This axis has a length (the grip aperture) and an orientation, and the goal of a reach-to-grasp movement is to place this axis across an object in a way that enables the various forces to be balanced out. 

This analysis is a functional (affordance) analysis of the key constraint on hand degrees of freedom and their resulting kinematics, specifically force balance. This task dynamical affordance analysis then implies an effectivity, the opposition axis. van Bergen et al (2007) adapted the opposition axis idea to an opposition vector, to emphasise that this axis has both a magnitude and an orientation, but this doesn't fundamentally alter the concept. 

Mon-Williams & Bingham (2011) explicitly analysed the spatial behaviour of this axis as a function of target affordance properties, because of this functional task analysis of reaching-to-grasp. Fingers get placed so as to place the axis somewhere appropriate to the object, and here the axis is the unit of analysis and the proposed unit being controlled.

Finger Control

There is another way to create the necessary opposition axis, and that is to independently control the fingers and thumb and land them separately. This was proposed by Smeets & Brenner (1999). 

As you can tell by the dates, Smeets & Brenner weren't targeting the affordance analysis. Their problem was with the more standard analysis of reaching coming from the classic work of Jeannerod. This work identified the two major components of reach-to-grasp actions (transport and grasp), identified that they were distinct components (transport is about the wrist/hand system, grasping is about the fingers), and identified that each depended on different properties of the object to be grasped (transport depends on extrinsic properties such as object location in space, grasp depends on intrinsic properties such as object size). This comes with another element for Jeannerod, specifically that intrinsic and extrinsic properties are processed via separate neural channels.

Smeets & Brenner first note that because objects are typically not symmetrical, it can readily be shown that this extrinsic/intrinsic transport/grasp distinction does not hold up; intrinsic property changes affect transport and so on. Second, the anatomical distinction between transport (of the hand) and grasp (using the fingers) also isn't clean, either in terms of the neuroanatomy or even behaviourally (for example, Alan Wing famously proposed that what is being transported is primarily the thumb, not the wrist). So these two components aren't cleanly separable in terms of perception or action distinctions (defined very internally, I'll note). Finally, they note that (at the time they wrote) there was only one model of grasping, and it was was designed to reproduce the empirically observed kinematics, rather than explain how these might emerge. Essentially it had done the standard motor control thing, which was to take the observed kinematics and simply credit all of them to custom built controllers. These worries are, I think, all broadly warranted.

They then make their move. Wing thinks the thumb is what is being transported and targeted because thumb variability decreases on approach while the wrist variability remains the same. Based on one paper and a personal communication with Wing, Smeets and Brenner propose the same could be true of the finger. So, to quote them, they 'abandon the grip as a variable in our model of grasping'. They take the Iberall functional analysis, and decide that the key to grasping is finding the right positions to grasp the objects, and landing the fingers there. They then argue that all that's required to land on these positions is to control the fingers so as to end up perpendicular to the surfaces. 

This is where it all falls apart:

To plan how to grasp an object, the nervous system begins by determining suitable positions on the object's surfaces. How these positions are determined is a problem beyond the scope of this paper. Our approach is to leave out any other information processing (determining the object's size, etc) and regard grasping as nothing more than moving the thumb and fingers to these positions

This is, frankly, an insane thing to say. First, it does exactly what they accuse the earlier model of doing: simply giving the model a solution to a key part of the problem. As Mon-Williams & Bingham identify, key structure in the behaviour emerges from the system figuring out where to land, so simply presenting the model with a solution is a terrible modelling strategy. Second, to say that grasping is about placing the finger and thumb in good positions for the object, and to then say figuring out how those positions are identified is beyond the scope of this work, is astonishing and frankly I'm amazed it got published. 

So Which Is It?

Smeets & Brenner review a couple of papers that suggest the finger and thumb do get controlled separately sometimes and that their kinematics do separately look like pointing movements. But they never ask the key question, which is do the finger and thumb look like they are working as a synergy? Mon-Williams & Bingham test exactly this, by looking at the variability of the thumb and finger positions at the terminal grip aperture. If Smeets & Brenner are right, these variabilities should be independent of each other; if they are instead working as a synergy, the variability should be negatively correlated (as variation in one is compensated for by variability in the other). The result was clear: the finger and the thumb variability show the clear signature of a synergy (or coordinative structure, to use the term Mon-Williams & Bingham use). Another study perturbed the thumb target and found effects on both the thumb and finger trajectories, more evidence they are coupled to each other (Van de Kamp & Zaal, 2007). This data clearly favours the opposition axis analysis.

Summary

Any affordance hypothesis implies an effectivity hypothesis too, because these are complementary dispositions. The affordance analysis of reaching-to-grasp came with an effectivity analysis of the hand acting to create an opposition axis for the nervous system to control. The data strongly support both the affordance and the effectivity analysis over the alternative independent targeting hypothesis. 

The Smeets & Brenner hypothesis suffers from several fairly serious conceptual flaws. The most important is to simply present the target positions to the model as a given, without engaging with the process of perceiving where to land given the task dynamics. This analytically separates perception from action and treats perception as the easy bit. Ecologically, this is the conceptual error; empirically, this analysis missed the fact that the process of perceiving where to land affects reach kinematics (this is the Mon-Williams & Bingham data). All this points to the problem of subtracting out part of a nonlinear process and expecting linear consequences. It's genuinely wild to me that this analysis gets any time at all, frankly (cited nearly 600 times!!)