Rider Control Identification in Bicycling

Abstract

Following in the wake of the increased bicycle popularity, bicycle research arose in the late 19th century. Early research, regarding the dynamic behavior of an uncontrolled bicycle, resulted in the Carvallo (1899) and more general Whipple (1899) model. In the past years, extensive research has been done to validate these uncontrolled bicycle models. However, the bicycle is normally accompanied by a rider, for which the combined rider/bicycle dynamics are less understood. The goal of this research is to identify the active rider contribution during stabilization tasks in bicycling. This knowlegde may be used to develop better and more user-specific bicycles in the future. The equations governing the combined rider/bicycle system subjected to an external disturbance are derived in the first chapter. Here, the bicycle is modeled according to the linearized Whipple model, where the passive rider dynamics are already included. After a process of trial and error, a flexible rider model structure is chosen, which interacts with the bicycle through steering torque. To be more specific, the rider model allows for proportional, integral, derivative and 2nd order derivative linear feedback on both the roll and steering angle and is limited by activation dynamics and transport delays. An experimental dataset from our colleagues of the UC Davis is used to obtain a preliminairy rider model. First a non parametric FIR model is derived, which serves as a platform for subsequent parametric modeling. The parametric models are fitted by minimizing the sum of errors squared between the non parametric and parametric steering angle responses, resulting in a set of optimized parameters. The resulting parametric model, which consists of 8 parameters, acounts for 97% of the variance of the non parametric model output. The parameter may be reduced from 8 up to 4 parameters, while the variance acounted for only lowers with 3%. The following important observations are made from the parametric model results: • The steer into the fall principle is observable in the positive roll angle and rate feedback for all measurements. • The roll angle, roll rate, steering rate and integral action are the key contributers and cannot be removed without causing a major drop of the VAF. • The integrative steering action controls the heading by applying counter steering. The identification results are used to set up a future frequency domain rider identification experiment. The experiment should be performed at forward velocities of 2, 3, . . . , 7 m/s, since the dynamic behavior is velocity dependent. A disturbance input signal has also been designed, and should be applied as a generalized roll torque to the system. A randomly appearing multisine input signal is created, with a bandwidth of 0.2 to 4 Hz, and where the input power is scaled sucht that its absolute value does not exceed the 40 Nm. The measurement time is set to 163.84 s at a sampling frequency of 200 Hz. A simulation study indicates that the parameters can be estimated with an error of less than 3% relative to the true parameters. Next, a number of perturbator designs are presented. The goal of these designs is to apply a desired perturbation spectrum as a generalized roll torque to the rider/bicycle configuration. 4 perturbator designs are presented, namely; the swing, sliding mass, lateral accelerator and simple rope perturbator. The designs are evaluated by the following criteria; active system contribution, passive system contribution, rider interaction, implementability and cost. Here, the sliding mass perturbator shows the best overall score and is recommended for further development. Apart from the rider identification, some errors in bicycle literature where encountered. To be more specific, the models presented in van Lunteren and Stassen (1970) and Stassen and Lunteren (1973) where found to contain sign errors. After correcting for these sign errors, the models where implemented in Matlab, but where found to be unstable.