The configurable and multi-articulated urban bus is a new type of urban vehicle with the advantages of road vehicles and urban rail trains. However, its articulated and long body structure will bring about difficulties in steering control and trajectory following. Moreover, the following carriages easily deviate from their expected path, leading to the fishtailing and folding of the compartment. In this paper, we propose a generic framework that allows the rapid building of kinematic models for the new train. By introducing the MPC theory, we design a trajectory tracking controller for a multi-articulated vehicle with an arbitrary number of carriages. To verify our models, we establish kinematic models and a trajectory tracking controller for a multi-articulated train with different number of compositions in MATLAB. Under the double-lane-change track and serpentine road conditions, the trajectory tracking of the train is simulated. The influence of the number of carriages, velocity, and length of carriage on the trajectory tracking are further analyzed. The experimental results show the feasibility of our method. Our findings thus provide significant guidance for the design, actual configuration, and trajectory tracking control of the new multi-articulated urban bus.