Human Balancing on Rolling Balance Board in the Sagittal Plane: Balancing Success and Stabilizability

A two-degree-of-freedom mechanical model of human balancing on rolling balance board in the sagittal plane is investigated with rolling radius and board elevation as two adjustable parameters. The balancing process is modeled as a closed-loop state feedback mechanism with reaction delay, hence the underlying mathematical model is a delay-differential equation. Connection is established between the stabilizability criteria by means of critical delay and the success of balancing trials by human subjects. While the mathematical model shows that the rolling radius and the board elevation equally contribute to the difficulty of the balancing task, experiments suggest that a change of rolling radius has a more significant effect on difficulty than a change of board elevation. Furthermore, it is found that experimental balancing success overlaps with plausible stabilizability of the model if the intrinsic ankle stiffness of the human subject is negligible.