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This article proposes a synthetic robust model predictive control method (RMPC) with input mapping for the image-based visual servoing (IBVS) problem with constraints, where the novel control law is constructed by the robust control law designed offline and the online linear compensation of the past data. This proposed method can overcome the conservatism of RMPC and reduce the online computational burden. The input mapping method is suitable for the IBVS with no requirement of the slow time-varying model or time-invariant model as most adaptive control methods need. Its linear combination coefficients can be online optimized by solving a quadratic programming problem. The stability of the visual servoing system under our proposed method is proven, and its convergence speed is demonstrated to be faster than the traditional RMPC. A real-time experiment on a six-degree-of-freedom manipulator with eye-in-hand construction is designed to evaluate the proposed method. The results indicate that besides the ability to handle the constraint and the singularity problem, our proposed method provides a faster convergence rate than several classic robust control methods, and improves the computational efficiency by an order of magnitude compared with the online RMPC.