The Stability of a Bicycle-Rider System

Abstract

Part of the goal of Europe’s Strategy Vision Zero is to eliminate all severe cycling accidents in Europe by 2030. The majority of cycling accidents are single vehicle accidents; this term indicates the absence of collisions with other road participants and implies a fall of the cyclist. Research has shown that mainly elderly cyclists are victim to those accidents. An untested hypothesis is that their slowed motor responses are one of the main reasons behind this. This study aims to address this hypothesis by studying the influence of neural time delay on the lateral stability of bicycle-rider systems. In this study, the slowed motor responses are represented by single neural time delay values. The influence is quantified by the sizes of the identified basins of attraction of stability (BoA). The BoA contains the set of finite lateral disturbances for which stability is
retained and is acquired via numerical integration. Binary threshold criteria are used to determine the stability of the solution. The bicycle-rider system consists of two components: a bicycle model and a rider model. The bicycle is modelled using the Whipple(-Carvallo) bicycle model with the set of non-linear equations derived by Basu-Mandal [2]. The rider is modelled using an implicit experimentally validated model from literature [31]. This model consists of a PID controller with full state feedback, neuro-muscular dynamics and, in this study, is extended to include nonzero time delay. The neural time delay value of a young cyclist has been based on literature [4]. The value is doubled to model an older cyclist. The control strategy of the young cyclist is identified using system identification techniques. The basins of the young and old cyclist are compared to study the detrimental effect of time delay on lateral stability in cycling. It declined over 80% when the time delay was doubled. The human’s ability to adapt its control to circumstances has been considered by repeating the control identification process for the rider which suffers from double the time delay. With respect to the young cyclist, a decline of over 50% was observed. Therefore, the results strongly support the hypothesis. Further research should focus on increasing complexity of the rider model to include preview and prediction. In this way, the influence of slowed motor responses can be mapped more clearly.
A secondary objective of this thesis is the preliminary development of a steer assist control model to aid the elderly cyclist balance during cycling. This development builds further on a simple control model from literature [29] which uses roll angle feedback. As a result, a nonlinear velocity dependent roll rate feedback control law was developed. This control law yields a constant basin height over the commonly used velocity range of cyclists. This height indicates the maximum allowable steer rate perturbations the bicycle-steer assist system could handle and is approximately the same height as what was identified for
a young cyclist. Future research is required for improving the steer assist. This means adding maximum allowable control torque, sensorial time delays and trajectory tracking