Symmetry and Asymmetry in Dynamic Modeling and Nonlinear Control of a Mobile Robot

Abstract

This paper examines the impact of symmetry and asymmetry on the dynamic modeling and nonlinear control of a mobile robot with Ackermann steering geometry. A neural network-based residual model is incorporated as a novel control enhancement. This study presents a control-oriented formulation that addresses both idealized symmetric dynamics and real-world asymmetric behaviors caused by actuator imperfections, tire slip, and environmental variability. Using the Euler–Lagrange formalism, the robot’s dynamic equations are derived, and a modular simulation framework is implemented in MATLAB/Simulink R2022a, that incorporates distinct steering and propulsion subsystems. Symmetric elements, such as the structure of the inertia matrix and kinematic constraints, are contrasted with asymmetries introduced through actuator lag, unequal tire stiffness, and nonlinear friction. A residual neural network term is introduced to capture unmodeled dynamics and improve the robustness. The simulation results show that the control strategy, originally developed under symmetric assumptions, remains effective when adapted to systems exhibiting asymmetry, such as actuator delays and tire slip. Explicitly modeling these asymmetries enhances the precision of trajectory tracking and the overall system robustness, particularly in scenarios involving varied terrain and obstacle-rich environments.