Kawato, M. (1999). Internal models for motor control and trajectory planning. Current Opinions In Neurobiology, 9(6), 718–727. doi:10.1016/S0959-4388(99)00028-8

Summary

In this review article, Kawato discusses the role of internal models in motor control. He argues that both forward and inverse internal models are used in motor control. In particular:

Fast and coordinated arm movements cannot be executed solely under feedback control, since biological feedback loops are slow and have small gains. Thus, the internal model hypothesis proposes that the brain needs to acquire an inverse dynamics model of the object to be controlled through motor learning, after which motor control can be executed in a pure feedforward manner.

First, Kawato gives an overview of the existence of internal models. One piece of evidence comes from perturbing the dynamics of participants’ motions. Initially, people make the wrong movements under these novel dynamics. However, they eventually adapt and can make the correct motion. If the new dynamics are removed, then they again make errors because they are now using an incorrect model of the inverse dynamics. Another piece of evidence comes from grip-force—load-force coupling, which is the coupling of a grip force (e.g. thumb and index finger) and load force (e.g. weight of the object that is being held). When gripping an object like this, and moving one’s arm to a new location, the motor system must both determing the appropriate trajectory for the arm as well as the grip force needed to hold the object. The way this works is:

The inverse model of the combined dynamics of the arm, hand, and object calculates the necessary motor commands from the desired trajectory of the arm. These commands are sent to the arm muscles as well as to the forward dynamics model as the efference copy. Then, the forward model can predict an arm trajectory that is slightly in the future. Given the predicted arm trajectory, the load force is calculated; then, by multiplying a friction coefficient and a safety factor, the necessary minimum level of grip force can be calculated.

Next, Kawato discusses neurological evidence for internal models in the cerebellum. I’m not going to go into detail on this.

Next, Kawato discusses the structure of internal models. Specifically, is it that internal models are just implemented as mappings between states and actions, or are they implemented using some sort of generalizable parameterization? To test this, the “generalization” paradigm is used, in which participants are trained to do a specific task under novel dynamics. They are then instructed to do another task, still under the novel dynamics, to see whether the dynamics have been fully generalized to new situations or not. The results are somewhere in the middle: some generalization occurs, but not perfect generalization.

Finally, Kawato discusses how the motor system computes trajectories. There are apparently two competing models: kinematic models (e.g. the minimum jerk model) and dynamics models (e.g. the minimum torque-change mdoel). Kawato proposes the minimum variance model as middle ground between these two models. In the minimum variance model, the objective function minimizes a kinematic value (the variance of the end pose); however, the variance is determined by motor commands, which are part of the dynamics. If this model is correct, then it gives another motivation for there being both be a kinematic internal model (i.e. a forward model) as well as a dynamics internal model (i.e. a inverse dynamics model)

Takeaways

Based on this article, there is very strong evidence for internal models in the motor system. Moreover, there is evidence for both forward kinematic models and inverse dynamics models which seem to work in tandem.

I wonder how these models are learned. In particular, when people’s motions are perturbed in some of the studies that Kawato describes, is it that people are updating their forward models, or their dynamics models, or both? Does learning in one affect the other, or are they independent?