The demand for fast, economic and high load capacity intralogistics transport is a growing trend. One of the recent solution is a logistic train, which consists of a tractor and a certain number of towed trailers. It is essential that the trailer follows the track of the preceding unit as it allows reduction of shopfloor area dedicated for transport. A perfectly suited steering system for this application is the double Ackermann system. In this study, the kinematic model of the tractor with n trailers was developed based on the Jacobian matrix. The tractor model was adapted to drive along a given trajectory using a PD controller. The simulation studies confirmed that the PD controller is sufficient to control the trajectory for developed kinematic model. The obtained results showed that the trailers with the double Ackermann steering system follow a similar path, which is the most convenient for narrow turn ride. The developed kinematic model can be used for the fast path planning and the design of transportation routes in manufacturing areas. The expanded model with an advanced control system can be used to control a real logistic train.