Cloud Type Interpretation of Statistical Properties of Human Response Delay in Pendulum Balancing

Abstract

We present the results of our experiments on studying the probabilistic properties of human response delay in balancing virtual pendulum (stick) with over-damped dynamics. The overdamping eliminates the effects of inertia and, thereby, reduces the dimensionality of the system under control. Two types simulators were employed for studying human response in the stick balancing. One of them hides the stick when it is located in some neighborhood of the upward position, the other just makes the stick unaccessible for subject's control. It enabled us to measure directly the delay time as the time lag between the moment when the pendulum becomes visible or accessible and the moment when a subject starts to move the mouse. It is demonstrated that the response delay time is characterized by a wide distribution sensitive to the particular details of stick balancing process and its possible correlations in the sequence of actions are ignorable. Besides, in experiments with the second simulator the subject's anticipation is shown to play a significant role in human control. In particular, the formal delay time can take negative values. It poses a question about the applicability of standard formalism of delayed differential equations to describing human intermittent control.