Fuzzy adaptive control for unknown multiple robot manipulators with time-varying output constraints

A fuzzy adaptive control algorithm featuring a non-zero time-varying parameter is devised to tackle the issue of anticipated trajectory tracking for uncertain dynamic systems of multiple robot manipulators transporting a shared object. To counteract the influence of uncertain nonlinear terms, a property of universal approximation incorporating parameters and Lipschitz conditions is employed, enabling the online adjustment of approximation accuracies. To circumvent the challenge of selecting an excessively large finite domain for the fuzzy logic system (FLS), a sliding surface with open control is introduced. This guarantees that the input states of the FLSs can be steered back to the sliding surface and subsequently enter the finite universal approximation domain, even if they deviate from it, by utilizing the devised update laws. Once the states enter this finite domain, the proposed fuzzy adaptive control, irrespective of the number of fuzzy rules, leveraging the stability theory of the integral barrier Lyapunov function (IBLF) to ensure not only a reduction in computational burden but also guarantee that the coordinated multiple manipulators transport a shared object along a predefined trajectory without violating any constraints. Simulation results are presented, comparing the proposed approach with other methods and showcasing its effectiveness across diverse environmental conditions.