Unifying Hierarchical Sliding Mode Control and Control Barrier Function for Tilt Angle Constraint of a Ball-Balancing Robot

Abstract

This paper presents a novel control methodology that combines control barrier functions (CBFs) and hierarchical sliding mode control (HSMC) for the ball-balancing robot. The motivation arises from the need to achieve stable balancing and position tracking while guaranteeing physical safety under tilt angle constraints. The proposed approach aims to achieve stability objectives, including position tracking and balancing, and ensure compliance with safety constraints defined as an invariant set. To ensure the satisfaction of these safety constraints, CBFs are employed. Based on the construction of a suitable CBF, a nonempty set of control signals satisfying the CBF-dependent inequality is given. The integration of CBFs and HSMC is facilitated through quadratic programming (QP), enabling the unification of stability objectives and safety constraints. The applied nominal control law is HSMC, an effective solution for the underactuated system. The safety constraint is considered to guarantee that the tilt angle of the body never exceeds a predetermined value. Simulation results demonstrate that the proposed controller maintains the deviation angle within safe bounds while achieving robust tracking performance. These findings confirm the potential of combining HSMC with CBFs to ensure both performance and safety, paving the way for future experimental validation on physical platforms.