Modelling human balancing tasks

Human balancing tasks are modelled by differential equations and are compared to experimental observations. First, the classical inverted pendulum model is revisited with respect to stabilizability. Namely, the relation between the reaction time delay and the shortest pendulum length (critical length) of the stick is derived and is demonstrated experimentally. Conclusions are drawn related to human tests, such as stick balancing on the fingertip, balancing a linearly driven inverted pendulum and virtual stick balancing. Second, the ball and beam balancing is considered, where the task is to stabilize a rolling ball at the mid-point of a beam by manipulating the angular position of the beam. Assuming a delayed proportional-derivative feedback mechanism, the governing equation is delay-differential equation. Performance of the control system is analyzed in terms of overshoot and settling time. Experiments over 5-days trials shows that control parameters are tuned to the optimal point associated with minimal overshoot and the shortest settling time. Finally, some further balancing tasks are briefly demonstrated and discussed.