Practical Adaptive Backstepping Control for Performance and State Constrained Systems of Cable-Driven Manipulators

This article proposes a practical adaptive fuzzy backstepping control (FBC) scheme for the constrained locus tracking problem of a nonlinear cable-driven manipulator. Specifically, fuzzy logic systems aim to approximate unknown nonlinear terms, and the adaptive backstepping control achieves tracking of the desired motion state by recursively designing the virtual references and control laws. Compared with the existing FBC, the practicality is enhanced in the sense that: 1) simultaneous compliance with prescribed performance and state constraints; 2) no need for the tricky process of finding feasibility conditions for virtual references under strict constraints; and 3) insensitive to system initial conditions for the tracking error convergence of the constrained system. These advanced features lie in the improvement of backstepping protocols through the novel coordinate transformation mechanism, the designed asymmetric barrier Lyapunov functions, and adaptive fixed-time control laws. Application and comparison studies based on a laboratory-developed cable-driven manipulator not only confirm the effectiveness but also show the advantages of the proposed scheme.