Exponential Convergent Second‐Order Sliding Mode Control Based on Barrier Lyapunov Function of State Constraint Robotic Manipulators

ABSTRACT This study presents the development of a robust second‐order sliding mode controller (SOSMC) that incorporates position error constraints into the control design. To achieve this, a barrier Lyapunov function (BLF) is employed, enabling the enforcement of predefined bounds on tracking errors throughout the system's evolution. This approach ensures that errors remain within previously known limits, thereby improving safety and reliability in practical applications, particularly robotic systems. The proposed control scheme guarantees the existence of a sliding mode and achieves exponential convergence of the tracking errors, even in the presence of bounded disturbances and model uncertainties. Hence, the main contribution of this study is the integration of the BLF into the SOSMC framework, which not only maintains robustness but also addresses the critical issue of constraint satisfaction. This is often overlooked in traditional sliding mode designs. The effectiveness and improved performance of the proposed controller are validated through simulation studies conducted on a three‐degree‐of‐freedom robotic manipulator and through experiments on a six‐degree‐of‐freedom robotic manipulator. Comparative results demonstrate that, unlike a conventional SOSMC without error constraints, the proposed controller successfully maintains position errors within the specified limits while preserving fast convergence and robustness. These findings highlight the significant benefits of incorporating barrier Lyapunov functions in sliding mode control strategies for systems with strict performance and safety requirements.