Simple Degree-of-Freedom Modeling of the Random Fluctuation Arising in Human–Bicycle Balance

Abstract

In this study, we propose a new simple degree-of-freedom fluctuation model that accurately reproduces the probability density functions (PDFs) of human−bicycle balance motions as simply as possible. First, we measure the time series of the roll angular displacement and velocity of human−bicycle balance motions and construct their PDFs. Next, using these PDFs as training data, we identify the model parameters by means of particle swarm optimization; in particular, we minimize the Kolmogorov−Smirnov distance between the human PDFs from the participants and the PDFs simulated by our model. The resulting PDF fitnesses were over 98.7 % for all participants, indicating that our simulated PDFs were in close agreement with human PDFs. Furthermore, the Kolmogorov−Smirnov statistical hypothesis testing was applied to the resulting human−bicycle fluctuation model, showing that the measured time responses were much better supported by our model than the Gaussian distribution.

Keywords

• human–bicycle balance
• stochastic model
• identification
• probability density function
• particle swarm optimization