This paper proposes a new cooperative transportation control algorithm in consideration of not only the internal force but the external force applied to 'Mobile Robot for a Wheel (MRWheel)'. First, we describe the merits and demerits of the model-based external force compensation method proposed in our previous study and explain the necessity of this new control algorithm. Secondly, we explain this new control algorithm mathematically. In this new algorithm, each follower receives the motion errors estimated by the other followers with TCP/IP, which enables each follower to estimate its motion error by using the force applied to it. Moreover, this new algorithm also enables 'intelligent Cooperative Autonomous Robot Transporters-type II (iCART II)' to transport many types of cars at a variety of places without the preliminary car transportation needed for identifying the model parameters of the external force. Finally, we conduct the transportation experiments of two types of cars for the comparison between this new algorithm and the conventional algorithm with the modelbased external force compensation method. These experimental results illustrate the validity of this new control algorithm.