Humans can simultaneously exert force and maintain motion states on both arms with synchronous attributes to accomplish interactive cooperation tasks. To endow dual robots with the same remarkable capability, a multi-objective synchronization control scheme is investigated in this article. The feedback laws for each robot are twofold. Specifically, the integral of the past synchronization force errors is adopted to design an impedance-based force feedback law. Moreover, the integral of the future predicted synchronization motion errors is used to establish a motion feedback law based on the nonlinear model predictive policy. The stability of the closed-loop system is theoretically proven. The practical performance of the proposed method is verified by a dual-robot mirror grinding experiment, where each robot exhibits high-accuracy motion capability and force compliance behavior. The experiment results show that the synchronization accuracy of position, velocity, and force is within 1 mm, 0.1 mm/s, and 1 N, respectively.