Abstract
The motor system generates time-varying commands to move our limbs and body. Conventional descriptions of motor control and learning rely on dynamical representations of our body's state (forward and inverse models), and control policies that must be integrated forward to generate feedforward time-varying commands; thus these are representations across space, but not time. Here we examine a new approach that directly represents both time-varying commands and the resulting state trajectories with a function; a representation across space and time. Since the output of this function includes time, it necessarily requires more parameters than a typical dynamical model. To avoid the problems of local minima these extra parameters introduce, we exploit recent advances in machine learning to build our function using a stacked autoencoder, or deep network. With initial and target states as inputs, this deep network can be trained to output an accurate temporal profile of the optimal command and state trajectory for a point-to-point reach of a non-linear limb model, even when influenced by varying force fields. In a manner that mirrors motor babble, the network can also teach itself to learn through trial and error. Lastly, we demonstrate how this network can learn to optimize a cost objective. This functional approach to motor control is a sharp departure from the standard dynamical approach, and may offer new insights into the neural implementation of motor control.
Highlights
That standard framework for describing the motor system is dynamical
We examined the ability of a deep network to represent a trajectory function; that is, a function that outputs the entire state and command trajectory for a movement
A Point-to-point Optimal Trajectory Function A deep network that approximates an optimal trajectory function was trained on point-to-point reaches moving freely through space, in a clockwise curl field, or counterclockwise curl field
Summary
That standard framework for describing the motor system is dynamical. Forward and inverse models along with a control policy represent the motor system at a specific instant in time; they are representations across space, but not time. To generate feedforward commands and estimated state trajectories these representations must be integrated forward in time (Figure 1A). This dynamical approach is sensible given Newton’s Laws of motion and the standard descriptions of optimality (e.g., Euler-Lagrange or Hamilton-Jacobi-Bellman equations). The easy analogies between the motor system and robotics have long fueled synergies between these fields, further strengthening the dominance of these dynamical concepts. Informs us that there are alternatives to the dynamical description for controllers. The nervous system could rely on different representations, perhaps explicitly time-varying representations of commands and trajectories
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