Fast-Convergent Stabilization and Trajectory Tracking of a Two-Wheel Self-Balancing Robot on Sloped Terrain

Abstract

The Two-wheeled Balancing Robot system is increasingly demonstrating its importance in both research and
practical applications. Ensuring stability and flexible mobility on complex terrains, particularly sloped surfaces,
remains a significant challenge. To address this issue, the research presented in this paper first establishes
a precise mathematical model for the robot system operating on a slope. Building upon this model, the paper
proposes a novel control strategy based on an improved Hierarchical Sliding Mode Control (HSMC) technique
incorporating a Terminal Sliding Surface. The primary objective of this controller is to achieve extremely fast
convergence speed, thereby simultaneously solving two key problems: maintaining stability at a fixed position
on the slope and safely navigating the robot across the sloped area to reach a target destination in a 2D model.
The research also provides an in-depth analysis of the system’s operating point on the sloped terrain and offers
a rigorous mathematical proof of the overall system’s stability using Lyapunov stability theory. To validate the
effectiveness, simulation results on the MATLAB/Simulink platform were conducted and directly compared with
those of a conventional HSMC. The obtained results demonstrate that the proposed controller not only ensures
higher stability but also exhibits superior responsiveness and performance in both assigned tasks.