Accurate tracking control of autonomous cooperative transportation systems (CTS) remains challenging owing to the complexity of the mechanisms and the high requirements of coordination between carriers. In this paper, the trajectory tracking control of a CTS with a pair of autonomous vehicles serving as carriers is investigated. A novel constraint-oriented hierarchical modeling method is proposed to describe the dynamics of the system. By dividing the system dynamics into two portions: the lower-level individual modeling and the upper-level constraints abstraction, the modeling process is significantly simplified. Then an innovative constraint-following control law is designed to address the tracking control problem under the special system topology, based on the internal and external constraints designed in the modeling process. The asymptotic convergence of the tracking error is theoretically guaranteed. To reduce potential damage of the payload during transportation, a payload force optimization method is creatively proposed. It relies on the closed-form relationship between the control input and payload forces established by the constraint-oriented modeling. The normal and shear stress on the payload is successfully limited, without affecting the trajectory tracking performance. Simulation results show that the proposed control method and the payload force optimization strategy can help achieve accurate and safe autonomous cooperative transportation simultaneously.