Robust control for uncertain and space confined robotic systems: Udwadia–Kalaba theory and diffeomorphism approach

ABSTRACT Robotic systems in practical applications are subject to various uncertainties, including sensor measurement errors, parameter variations, and external disturbances, which can compromise system performance and stability. Additionally, ensuring operational safety is crucial to prevent harm to both personnel and the surrounding environment. To address these challenges, this paper proposes a novel robust constraint‐following control method incorporating inequality constraints, based on the Udwadia–Kalaba (U‐K) equation, to enhance the reliability and safety of complex mechanical systems. First, the dynamic equation of selective compliance assembly robot arm (SCARA) robots is derived using the U‐K equation. Then, employing a diffeomorphism approach, the finite state variables are mapped to infinite state variables via a tangent function, ensuring that the joint displacement of the SCARA robot remains within a bounded range. Based on this transformed mathematical model, a robust constraint‐following controller is designed. The Lyapunov method is then utilized to establish the uniform boundedness and uniform ultimate boundedness of the controlled system. Finally, the proposed control algorithm is validated through numerical simulations and experimental testing on a SCARA robot platform.