Robust Sliding Mode Control for Two-Wheel Robot Without Kinematic Equations

This article proposes solutions to control the balance of a two-wheel robotic system in the presence of uncertainties in the dynamic equations and without the need for kinematic equations. To do this, the dynamic equations of this system are first transferred to the error area and then these equations are divided into two completely independent subsystems, under excitation, and full excitation. In the following, two completely different sliding mode controllers are presented to control the under-excitation subsystem, which can make this subsystem asymptotically stable in the presence of structural and non-structural uncertainties. After that, a sliding mode control is proposed to control the entire excitation subsystem, making this subsystem asymptotically stable in the presence of existing uncertainties. Since these two subsystems are completely independent of each other, proving their global asymptotic stability provides proof of the global asymptotic stability of the closed-loop system. The isolation of two-wheel balancing robot subsystems eliminates the need to use kinematic equations, resulting in structural uncertainties not affecting the tracking accuracy of closed-loop system state variables. Finally, to verify the performance of the proposed controllers and compare their performance results, three-stage simulations are implemented on the two-wheel Balance robotic system. Mathematical proofs and simulation results show the optimal performance of the proposed solutions.