Multi-robot cooperation is a typical application of multi-robot system, which has strong potential applications in many special occasions. However, few scholars have considered cooperative optimization transportation from the perspective of optimization. This paper investigates the cooperative transportation optimization problem for multiple mobile robots with kinematically redundant manipulators. First, a discrete-time distributed optimization algorithm with fixed step size is proposed to achieve linear convergence. Second, by introducing a rotation variable into the optimization problem, the joint angular velocity of manipulator and the velocity of moving platform change more smoothly. Third, a virtual leader-follower transport strategy is used in this paper to improve the stability of the multi-robot system. In the physical experiment, the trajectory of each end-effector matches the expected trajectory, and the center trajectory of the transport object almost coincides with the virtual leader trajectory with acceptable error. Moreover, the simulation and physical example are provided to demonstrate the effectiveness of the proposed algorithm.

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