Study on Bicycle Self-Stabilization Mechanism by Dynamic-and-Data-Driven Surrogate Modelling

Bicycle self-stabilization is an intriguing phenomenon that remains not fully understood. While it is known that the inherent self-stabilization mechanism arises from the spontaneous behavior of turning towards a fall (TTF), the driving force behind the spontaneous TTF remains unclear. To enable a comprehensive quantitative analysis, we develop a dynamic-and-data-driven bicycle surrogate model based on the structure derived from bicycle symmetries and model reduction. The coefficients of the surrogate dynamic equations reveal how the gravity-induced overturning torque can be balanced by a stabilizing torque caused by the TTF behavior and why the TTF occurs spontaneously. Our analysis shows that the nonholonomic constraints on bicycle motion play a critical role in generating the stabilizing and driving torques of the TTF. Additionally, we reveal that the nonholonomic-constraint-related gyroscopic moment induces stiffness and damping effects in the surrogate model. Consequently, the TTF behavior autonomously performs feedback control to generate the balancing torque, while stiffness and damping enhance the bicycle system's stability. Finally, we explore the influence of bicycle geometric parameters on self-stabilization, discovering limit-cycle motions for specific configurations. Results indicate that while straight-line motion is unstable for negative fork angles, stability is achieved in a limited positive range. Furthermore, for certain positive fork angles, the system exhibits stable limit-cycle motions rather than stable straight-line motion. This novel phenomenon highlights how system nonlinearities improve resilience by enabling stable oscillatory behaviors before instability arises. These findings provide valuable insights into the mechanisms of self-stabilization and lay a foundation for future studies on bicycle dynamics and design.