Experimental validation of a model of an uncontrolled bicycle

Abstract

In this paper, an experimental validation of some modelling aspects of an uncontrolled bicycle is presented. In numerical models, many physical aspects of the real bicycle are considered negligible, such as the flexibility of the frame and wheels, play in the bearings, and precise tire characteristics. The admissibility of these assumptions has been checked by comparing experimental results with numerical simulation results.The numerical simulations were performed on a three-degree-of-freedom benchmarked bicycle model. For the validation we considered the linearized equations of motion for small perturbations of the upright steady forward motion. The most dubious assumption that was validated in this model was the replacement of the tires by knife-edge wheels rolling without slipping (non-holonomic constraints).The experimental system consisted of an instrumented bicycle without rider. Sensors were present for measuring the roll rate, yaw rate, steering angle, and rear wheel rotation. Measurements were recorded for the case in which the bicycle coasted freely on a level surface. From these measured data, eigenvalues were extracted by means of curve fitting. These eigenvalues were then compared with the results from the linearized equations of motion of the model. As a result, the model appeared to be fairly accurate for the low-speed low-frequency behaviour.

Comparison of Two Experiments Based on a Physical and a Torsion Pendulum to Determine the Mass Moment of Inertia Including Measurement Uncertainties

“…Both disadvantages may be overcome with more advanced set-ups which cancel out the above-mentioned advantages to some extent due to the higher complexity [5]. Torsion pendulum set-ups are typically used for DUTs with smaller mass moments of inertia [6].…”

Design and Implementation of Model Predictive Control for a Gyroscopic Inverted Pendulum

“…The history and state-of-the-art discussions on topic of bicycle dynamics and control were reviewed comprehensively by Schwab and Meijaard [6]. In a study of bicycle stability, Meijaard et al [7] analysed the eigenvalues of a linearized bicycle model that was experimentally validated by Kooijman [8]. Results of these works showed the relationship of the bicycle's stability with its longitudinal speed.…”

Estabilización Automática de una Bicicleta sin Conductor mediante el Enfoque de Control por Rechazo Activo de Perturbaciones

“…En este modelo asumen que la bicicleta sólo está constituida por cuatro cuerpos rígidos y obtienen un modelo en espacio de estado con parámetros variantes (LPV), a partir de unas ecuaciones diferenciales de movimiento que provienen del principio de D'Alembert (Whipple, 1899). La validación del anterior modelo se desarrolló en (Kooijman et al, 2008) mediante la adquisición de datos en tiempo real de una bicicleta en movimiento. Este modelo es base del diseño utilizado en la estrategia propuesta del presente trabajo.…”