An Integral Maneuvering Control of Autonomous Bicycle Using a Linear Quadratic Regulator with Luenberger Observer

In this work, we present a Linear Quadratic Regulator (LQR) controller with integral action to maintain straight-line motion in an autonomous bicycle. We derive the transfer function between steering torque and path deviation, resulting in a fourth-order linear system. A state-space representation of the maneuvering control system is then developed, and the LQR controller is designed within an output-feedback framework. Additionally, a Luenberger observer is employed to estimate the full state vector, enabling precise computation of the steering torque. Our computational study indicates that the proposed LQR controller with integral augmentation effectively maintains trajectory accuracy, with path deviation converging to zero at steady state time under both disturbance-free and disturbed conditions. In contrast, while the conventional LQR controller performs adequately in disturbance-free conditions, it fails to eliminate steady-state error in the presence of disturbances, thereby underscoring the superior robustness of the proposed method.