Internal model (motor control)

A. Francis and W. M. Wonham[1] as an explicit formulation of the Conant and Ashby good regulator theorem.

In their simplest form, forward models take the input of a motor command to the “plant” and output a predicted position of the body.

Michael I. Jordan, Emanuel Todorov and Daniel Wolpert contributed significantly to the mathematical formalization.

Sandro Mussa-Ivaldi, Mitsuo Kawato, Claude Ghez, Reza Shadmehr, Randy Flanagan and Konrad Kording contributed with numerous behavioral experiments.

Two interesting inverse internal models for the control of speech production[6] were developed by Iaroslav Blagouchine & Eric Moreau.

[7] Both models combine the optimum principles and the equilibrium-point hypothesis (motor commands λ are taken as coordinates of the internal space).

There is also a rich clinical literature on internal models including work from John Krakauer,[8] Pietro Mazzoni, Maurice A. Smith, Kurt Thoroughman, Joern Diedrichsen, and Amy Bastian.

Forward model of an arm movement. The motor command, u(t), of the arm movement is input to the plant and the predicted position of the body, x̃(t), is output.

Figure 1. The desired position of the body is the reference input to the hypothetical controller, which generates the necessary motor command. This motor command is sent to the plant to move the body and an efference copy of the motor command is sent to a forward model. The output from the forward model (predicted body position) is compared with the output from the plant (body position). Noise from the system or the environment may cause differences between the actual and predicted body positions. The error (difference) between the actual and predicted positions can provide feedback to improve the movement for the next iteration of the internal model.

Figure 2. Inverse model of a reaching task. The arm's desired trajectory, Xref(t), is input into the model, which generates the necessary motor commands, ũ(t), to control the arm.