Cascade Control for Trajectory-Tracking Mobile Robots Based on Synergetic Control Theory and Lyapunov Functions

This paper aims to synthesize a synergetic control law using a cascade approach for trajectory-tracking robots. A nonlinear model was established for a differential two-wheeled mobile robot. The robot’s operation can either stabilize along a desired trajectory or deviate due to model uncertainty and external disturbances. The cascade approach is utilized to reduce system complexity while maintaining the robustness of the control law. The kinematic control law in the outer loop is designed using Lyapunov functions, while the dynamic control law is derived using synergetic control theory. This law ensures system control quality under model uncertainties and external disturbances. Finally, simulation results demonstrate that the proposed controller provides robust stability for the mobile robot, along with excellent disturbance rejection and robustness against model uncertainties.