Internal model (motor control)

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

The motor command input to the forward model can be an efference copy, as seen in Figure 1. The output from that forward model, the predicted position of the body, is then compared with the actual position of the body. The actual and predicted position of the body may differ due to noise introduced into the system by either internal (e.g. body sensors are not perfect, sensory noise) or external (e.g. unpredictable forces from outside the body) sources. If the actual and predicted body positions differ, the difference can be fed back as an input into the entire system again so that an adjusted set of motor commands can be formed to create a more accurate movement.

Inverse models use the desired and actual position of the body as inputs to estimate the necessary motor commands which would transform the current position into the desired one. For example, in an arm reaching task, the desired position (or a trajectory of consecutive positions) of the arm is input into the postulated inverse model, and the inverse model generates the motor commands needed to control the arm and bring it into this desired configuration (Figure 2). Inverse internal models are also in close connection with the uncontrolled manifold hypothesis (UCM), see also here.

Theoretical work has shown that in models of motor control, when inverse models are used in combination with a forward model, the efference copy of the motor command output from the inverse model can be used as an input to a forward model for further predictions. For example, if, in addition to reaching with the arm, the hand must be controlled to grab an object, an efference copy of the arm motor command can be input into a forward model to estimate the arm's predicted trajectory. With this information, the controller can then generate the appropriate motor command telling the hand to grab the object. It has been proposed that if they exist, this combination of inverse and forward models would allow the CNS to take a desired action (reach with the arm), accurately control the reach and then accurately control the hand to grip an object.^[5]

With the assumption that new models can be acquired and pre-existing models can be updated, the efference copy is important for the adaptive control of a movement task. Throughout the duration of a motor task, an efference copy is fed into a forward model known as a dynamics predictor whose output allows prediction of the motor output. When applying adaptive control theory techniques to motor control, efference copy is used in indirect control schemes as the input to the reference model.

A wide range of scientists contribute to progress on the internal model hypothesis. 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. The DIVA model of speech production developed by Frank H. Guenther and colleagues uses combined forward and inverse models to produce auditory trajectories with simulated speech articulators. 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). The input motor command λ is found by minimizing the length of the path traveled in the internal space, either under the acoustical constraint (the first model), or under the both acoustical and mechanical constraints (the second model). The acoustical constraint is related to the quality of the produced speech (measured in terms of formants), while the mechanical one is related to the stiffness of the tongue's body. The first model, in which the stiffness remains uncontrolled, is in agreement with the standard UCM hypothesis. In contrast, the second optimum internal model, in which the stiffness is prescribed, displays the good variability of speech (at least, in the reasonable range of stiffness) and is in agreement with the more recent versions of the uncontrolled manifold hypothesis (UCM). 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.

• Repetitive control
• Efference copy