A Variable Gain LQR Control for a Front Drive Motor Bicycle Model

This study addresses the self-balancing control challenges of a novel unmanned bicycle under complex operating conditions by proposing a variable-gain LQR robust control strategy. An innovative front-wheel fixed steering mechanism was designed, utilizing a universal joint for front-wheel directional control, while employing a servo steering mechanism at the rear wheel for auxiliary course adjustment. Through systematic analysis of the novel bicycle model, the variable-gain LQR control method was implemented to dynamically solve the Riccati equation for real-time updates of the feedback gain matrix K. This adaptive matrix enables continuous adjustment based on bicycle velocity and body posture variations, ensuring stable trajectory following. A linear dynamic vehicle model was established and validated through a semi-physical simulation platform. Experimental results demonstrate that the intelligent system achieves stable control within a [−30°, 30°] roll angle range, maintains self-balance under variable-speed conditions, and exhibits strong robustness against road disturbances. The findings confirm that the variable-gain LQR method provides reliable and stable control for this novel bicycle system. This research achieves breakthrough innovations in dynamic modeling and control theory for unmanned intelligent motorcycles, offering a new technical paradigm for dynamic balance control in wheeled robotics.