Estimation of Reaction Time During Human Balancing on Rolling Balance Board Based on Mechanical Models

Human balancing on rolling balance board in the sagittal plane is analyzed such that the geometry of the balance board can be adjusted: the radius R of the wheels and the elevation h between the top of the wheels and the board can be changed. These two parameters have a significant influence on the stability of standing on the board as shown by preliminary experiments. The human body was modeled by a single inverted pendulum, while the balance board was considered by the geometry of the mechanical model. Based on literature, it was assumed that the central nervous system (CNS) controls by signals proportional to the angle and angular velocity of the human body and the balance board and is able to tune the feedback gains with 40% accuracy during the balancing process. To take the reaction time into consideration, operation of the CNS was modeled as a delayed proportional-derivative feedback. The critical time delay for the stabilization process is defined such that if the delay is larger than the critical one then no control gains could stabilize the system. Four balance board configurations were chosen with different wheel radius and the corresponding critical time delays were computed based on the mechanical model. Eight young healthy individuals participated in the experiments. Their task was to perform 60 s long balancing trials on each balance board. The reaction time of the participants was estimated by comparing the numerical results obtained for the critical time delay and their successful and unsuccessful balancing trials. The reaction times were found to be in the range of 0.10–0.15 s which are in good agreement with the literature.