Sliding Mode Control Applied in Two-wheeled Self-Balancing Robot System in Presence of Structured and Un- Structured Uncertainties in Dynamical Equations and Without the Need for Kinematic Equations

In this paper, we proposed solutions for controlling the two-wheel self-balancing robot system in the presence of uncertainties in dynamical equation and without the need for kinematic equations. For this purpose, the dynamical equations of this system are initially transmitted to the domain of error, then these equations are divided into two independent subsystems, one of which is an under-actuated system and the other is fully actuated system. In order to control the under-actuated subsystem, two completely different sliding mode controllers are proposed that are able to provide this subsystem in the presence of structured and un-structured uncertainties with global asymptotic stability. Subsequently, in order to control the fully under-actuated subsystem, a sliding mode control is proposed to provide this subsystem in the presence of existing uncertainties with global asymptotic stability. Since these two subsystems are completely independent of each other, their global asymptotic stability proofs prove the global asymptotic stability of the closed-loop system. The separation of two-wheeled self-balancing robot sub-systems eliminates the need to use the kinematic equations, and this causes the presence of structured uncertainties to have no effect on the accuracy of tracing the closed-loop system state variables. Finally, to evaluate the performance of the proposed controllers and compare their performance results, three-stage simulations are implemented on the two-wheeled self-balancing robot system. Mathematical proofs and simulation results show the desired performance of the proposed solutions.