Collaboration between serial robots in industrial environments has gained increasing importance due to enhanced operational capabilities and flexibility. This paper addresses the mathematical modeling and coordinated control of two serial robots—FANUC Arc Mate 50iC/5i and PUMA 560—performing a single task. Using the Denavit–Hartenberg method, the forward and inverse kinematic models of each robot are derived, and the homogeneous transformation matrices are computed. In the dynamics section, the Euler–Lagrange equations for the cooperative system are developed, and the inertia, Coriolis, and gravity matrices are obtained. Subsequently, a fuzzy inference–based controller is designed and implemented to enable coordinated operation of the two robots. The accuracy of all mathematical models is validated in the Simscape environment of MATLAB. The simulations demonstrate that the proposed algorithm can synchronize the motion of the two robots with suitable positional accuracy, indicating that this research offers a novel solution for complex operations such as heavy object manipulation and precision assembly.