Steering control and stability analysis for an autonomous bicycle. Part II. Experiments and a modified linear control law

Abstract

This paper presents experimental results to verify the reduced dynamics modeling and stability analysis of an autonomous bicycle, following the theoretical framework presented in Part I. A self-fabricated autonomous bicycle is introduced, and experiments are conducted to verify its stability in uniform straight motion (USM) and uniform circular motion (UCM). While the experimental results are qualitatively consistent with the theoretical findings, they also reveal that the stability of the bicycle is affected by uncertainties in the real system, primarily stemming from the drift error of the gyroscope sensor used to measure the bicycle's lean angle. Parameter uncertainty analysis confirms the gyroscope drift as the main source of uncertainty. To compensate for this drift error, a modified linear control law with a time-varying intercept term is proposed. This results in a three-dimensional reduced dynamic system governing the bicycle's controlled motion. Theoretical analysis and experiments demonstrate that the bicycle under the modified linear control law achieves stable USM and UCM with a desired steer angle, and exhibits an interesting phenomenon of a limit cycle motion when the control parameters are set such that the trivial relative equilibrium becomes unstable through a supercritical Hopf bifurcation.