This paper proposes transport control systems of multi-rotor unmanned aerial vehicles(UAVs) with a suspended payload. The objective of this work is exact tracking of the payload position and attitude to desired trajectories, and thus the present methods are based on exact linearization techniques. Transport control problems by a single UAV are first investigated, and it is shown that undesired UAV behavior appears in this case. Then, by taking the degree of freedom of the target system into account, a cooperative transport control system with multiple UAVs is proposed. Numerical simulations including obstacle avoidance application are conducted to show the effectiveness of the present approach.