‘Dynamic primitives of motor behavior’ is a recent paper (2012) out by Neville Hogan and Dagmar Sternad.
This paper starts out professing the need for a theory of motor control that extends beyond a single task and situation, something near and dear to my heart. As they state, one of the problems with developing an encompassing theory is that most proposed theories are all seen as competing by the authors, slowing assimilation of ideas and development of an overarching structure. Laid out here, two of the most important features for any encompassing theory is that it accounts for broad classes of actions and addresses the major limitations of the human neuromuscular system, the highlighted limitation being the slow speed of efferent and afferent signals.
Synergies and dynamic primitives
The authors propose that human motor control is encoded solely in terms of primitive dynamic actions. This, as they point out, is definitely not a novel proposal, but they suggest that it and its implications haven’t been fully investigated. When people think of combining primitive actions, the idea of a synergy most often comes to mind, which refers to ‘steretyped patterns of simulataneous motion of multiple joints or simultaneous activation of multiple muscles that may simplify control’. The driving idea being that synergies could provide a means of dimensionality reduction for the controller, instead of having to fret over issuing every muscle activation signal, the controller modulates a set of larger actions, stitching them together simultaneously or sequentially. This making performing complex actions significantly simpler.
Taking this definition of a synergy, the authors say, is however insufficient for generating the complexity of behavior seen in humans: ‘this account of synergies constitutes an algebraic constraint, not a dynamic object. Even time-varying synergies are not dynamic objects, but constitute a kinematic constraint with time included as one of the variables related by the constraint’. That is to say, I believe, that this definition of a synergy is a strictly feedforward (open-loop), simplistic thing. It’s just a set of muscle activations that execute in a given order, without accounting for starting point, perturbations, or environment. In this sense they’re static, non-adapting to dynamic environments.
So, something more is needed. ‘Reducing the dimension of commands alone is not sufficient to account for how humans control complex dynamic objects. For that, the primitives of control should themselves be dynamic objects.’ At this point they bring in the discussion of dynamic primitives presented by the Schaal lab way back in the early 2000s, also known as the pre-Katy Perry era. The basic idea behind dynamic primitives is that there is a target point in state space that the system is drawn to (according to spring dynamics), and there is a time driven function that activates a forcing function which can move the system in interesting ways along its path to the target. Dynamic primitives can generate both discrete and rhythmic movements, ie they can act as point attractors or limit cycles. In the discrete case, the time driven function goes to zero, reducing the effect of the forcing function to zero, letting the default spring dynamics take over and pull the system to the target, guaranteeing convergence. In the rhythmic case, the time driven function goes to infinity and the cosine is taken to activate the forcing function in a rhythmic manner, where its movements are centered around the target in state space. There is a ton of really interesting and awesome things you can do with dynamic primitives, but that should be sufficient information for the discussion of this paper.
Taking dynamic primitives are used as our definition of synergies, we can generate significantly more robust behavior than with the alternate definition, because dynamic primitives are more than a sequence of muscle activations, they are attractors with dynamics that can guide the system in the face of perturbations and other noise. The authors term this property ‘”temporary permanence” (permanence due to robustness to perturbation; temporary because dynamic primitives, like phonemes of verbal communication, may have limited duration)’. Discrete and rhythmic dynamic primitives are then rewritten and termed ‘submovements’ and ‘oscillators’, respectively, that have an explicit mathematical summation and a speed profile with a single peak.
Virtual trajectories and mechanical impedance
The idea is then for the system to create a virtual trajectory to follow by combining these submovements and oscillators, creating a ‘trajectory attractor’. Although combinations of submovements and oscillators can account for a vast repertoire of movements in unconstrained environments, they’re not sufficient for describing any involving interactions with the environment. To do this, another aspect, mechanical impedance, is introduced as a feature to be accounted for in the construction of virtual trajectories. Mechanical impedance determines the force evoked by a displacement of a part of the system throughout the movement. In humans, mechanical impedance can be controlled by modulating the co-contraction of antagonist groups of muscles, holding a limb rigidly in place or letting it sway freely in response to applied outside force. The mechanical impedance for a given task then is a function that describes how to respond to outside forces throughout the time-course of a movement. Just like submovements and oscillations, mechanical impedances for different tasks can be combined through linear superposition to generate a novel function.
The incorporation of mechanical impedance into the specification of a movement has some really neat effects. The authors present several cases. One is the case of locomotion, instead of having two different primitive movements for different types of locomotion (such as walking normally and walking on balls of your feet, for example), these can both arise from the same composition of submovements and oscillators by varying the joint stiffness (mechanical impedance) profile throughout the movement. Another case is in reaching out to manipulate a door handle, one way to go about this is to have a precise model detailing the path to follow for the hand to appropriately close around the round object, and to adapt this over time to appropriately apply torque and open the door, but a simpler means is to have a crude model of the location of the door handle and its shape, and perform the movement with a low mechanical impedance, letting the hand form around the object appropriately as contact is made (this effectiveness of the latter method is also shown in simulation in the paper). Another point is that controlling mechanical impedance allows for feedforward specification, allowing appropriate reactions in situations where object contact is too fast for feedback based control to respond appropriately.
So, assuming we have a sets of our three classes of primitives, submovements, oscillators, and mechanical impedances, a virtual trajectory can be generated using the available primitives as basis functions which cann be combined through weighted summation. And the authors propose ‘that what is learned, encoded, and retrieved are the parameters of dynamic primitives, rather than any details of behavior’.
There were a number of interesting ideas in this paper, being already familiar with dynamical primitives and compositionality of movement (and already using both in my own work), the part I found most interesting was the incorporation of mechanical impedance as a movement feature for modulation. The door handle example being a particularly compelling example of the robustness and power this incorporation adds to movements. And a great bonus to using dynamical primitives as a basis for a motor control system is that some great work has been done incorporating learning into dynamical primitives (albeit not designed with any intent of neural plausibility), specifically the path integral policy improvement work done by Evangelous Theordorou during his time in the Schaal lab.
The terms ‘virtual trajectories’ and ‘trajectory attractor’ occur to me as a bit dangerous in their easy misintepretability, where they could seem more like a kinematic path specification method than the result of combining a number of dynamical attractor systems.
I assume that the reduced bandwidth required for the modulation of a set of primitives rather than the specification of a full control signal and the ability of these modulatory terms to specify appropriate responses to any encountered external force is the means of addressing to the transmission speed problem mentioned at the beginning of the paper. Learning the modulatory signals of a given set of primitives is another feature that appeals to me, as opposed to specifying the explicit muscle activations, because the former has the potential to take advantage of whatever built in circuitry is going on in the spinal cord, that very often ignored crazy complex structure that motor signals are routed through.
Finally, a recurring theme of the paper is also making the case for a overarching falsifiable theory that can be built up and revised incrementally, and isn’t thrown away when some experiment provides contradicting data. This is another call in the field lately, and the plan of attack I’ve been following myself. Maybe I could try directing them towards the Neural Optimal Control Hierarchy framework I’ve been building…
Hogan N, & Sternad D (2012). Dynamic primitives of motor behavior. Biological cybernetics, 106 (11-12), 727-39 PMID: 23124919