Controlling Variability

ABSTRACT

In human motor control, there is uncertainty in both estimation of initial sensory state and prediction of the outcome of motor commands. With practice, increasing precision can often be achieved, but such precision incurs costs in time, effort, and neural resources. Therefore, motor planning must account for variability, uncertainty, and noise, not just at the endpoint of movement but throughout the movement. The author presents a mathematical basis for understanding the time course of uncertainty during movement. He shows that it is possible to achieve accurate control of the endpoint of a movement even with highly inaccurate and variable controllers. The results provide a first step toward a theory of optimal control for variable, uncertain, and noisy systems that must nevertheless accomplish real-world tasks reliably.

Keywords:

• Bayes' rule
• Fokker–Planck equation
• Markov process
• Stochastic control
• uncertain control

Notes

1. For example, if

• (which means that = 1 if x > 0 and = -1 if x ≤ 0), then for all initial conditions, x moves away from 0 (in both directions) and the probability of x = 0 will be zero. This behavior is not well described by second-order equations in the form of Equation 6, which would predict a Gaussian distribution centered at 0.