The problem of redundancy in movement control: the adaptive model theory approach.

The problem of redundancy in movement control is encountered when one attempts to answer the question: How does the central nervous system (CNS) determine the pattern of neural activity required in some 5,000,000 descending motor fibres to control only 100-150 biomechanical degrees of freedom of movement? Mathematically this is equivalent to solving a set of simultaneous equations with many more unknowns than equations. This system of equations is redundant because it has an infinite number of possible solutions. The problem is solved by the neuronal circuitry hypothesized in Adaptive Model Theory (AMT). According to AMT, the CNS includes neuronal circuitry able to compute and maintain adaptively the accuracy of internal models of the reciprocal multivariable relationships between outgoing motor commands and their resulting sensory consequences. To identify these input-output relationships by means of regression analysis, correlations between the input signals have to be taken into account. For example, if the inputs are perfectly correlated, the model reduces to a virtual one-input system. In general, the number of inputs modelled equals the number of degrees of freedom encoded by the signals; that is, the number of independently varying (orthogonal) signals. The adaptive modelling circuitry proposed in AMT automatically tunes itself to extract independently varying sensory and motor signals before computing the dynamic relationships between them. Inverse models are employed during response execution to translate movements pre-planned as desired trajectories of these high-level sensory-feature signals into appropriately co-ordinated motor commands to send to the muscles. Since movement is pre-planned in terms of a number of orthogonalized sensory-feature signals equal to the number of degrees of freedom in the desired response, the problem of redundancy is solved and the correlation or co-ordination between motor-command signals is automatically introduced by the adaptive models.