In recent years, Segway robots have emerged as a promising solution for urban mobility, thanks to their maneuverability and energy efficiency. However, their nonlinear and unstable dynamics require adapted control strategies. This article presents a complete modeling of the system using the Lagrangian formalism, followed by linearization around equilibrium. Classical control approaches, notably PID controllers, although commonly used, show limited performance in terms of trajectory tracking. To overcome these limitations, a state feedback LQR controller has been synthesized for improved trajectory tracking. To overcome the inaccessibility of internal states, a Kalman observer was designed for the first time ever for this type of system. An adaptive controller of the MRAC type was synthesized to manage user mass uncertainties. Based on a frequency analysis, the simulation results confirm the robustness of the synthesized controller. This opens up promising prospects for the design of self-balancing mobility systems.