MATHEMATICAL MODEL AND ANALYSIS OF A TWO-LOOP STEERING CONTROL SYSTEM FOR A MOBILE ROBOT WITH ACKERMANN GEOMETRY

This paper presents the development and investigation of a mathematical model of a two-loop steering control system for a mobile robot with Ackermann geometry, aimed at improving trajectory tracking accuracy under external disturbances and measurement noise. The inner control loop implements the classical Ackermann geometry, ensuring coordinated steering angles of the front wheels and minimizing lateral slip. The outer loop represents a corrective control system based on a proportional-derivative (PD) controller, which compensates for position and orientation errors caused by mechanical backlash, inertial effects, model inaccuracies, and sensor measurement errors. An analytical stability analysis of the closed-loop system was conducted using the Lyapunov function method. It is proven that for positive values of the PD controller gains, asymptotic stability is guaranteed, and the position and orientation errors converge to zero.
To numerically validate the proposed model, simulations were performed in the MATLAB R2023b environment using parameters of real autonomous platforms such as Clearpath Husky, Jackal, and Scout Mini. Various motion scenarios were considered, including S-shaped and curved trajectories, IMU and odometry noise, as well as steering angle constraints.
Simulation results demonstrate that the proposed two-loop control architecture reduces the root mean square trajectory tracking error by 38-52%, decreases the maximum tracking error by 44%, and improves robustness to noise and disturbances. The developed system ensures smooth and stable motion and shows strong potential for application in autonomous vehicles, robotic platforms, and intelligent navigation systems.

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