Adaptive-based hierarchical sliding mode control for ball-balancing robots moving on an inclined plane

In contrast to managing a robot on a flat surface, controlling a balanced robot on a spherical wheel on an inclined surface is more challenging since the robot travelling up and down a slope has a higher chance of falling over. In this paper, the kinematic equation of the ball balancing robot (ballbot) is built as the learning method according to a 2D mathematical model. The authors use an adaptive-based hierarchical sliding mode control (AHSMC) based on Lyapunov theory to handle the target of a system whose parameters are undefined or change over time. The proposed sliding surfaces are demonstrated to be asymptotically stable and are validated through a simulation model implemented in Simscape software. The simulation results of the closed control design work correctly to control the motion of a ballbot when moving up the inclined surface.