The AGVs or mobile robots are well used in today's manufacturing supply technologies and also can be used in engineering's education. The motion controlling and simulation of such vehicles are a crucial question. This paper introduces the steps of motion planning for a driverless carrier vehicle from the positions initially available to the speed of the wheels. The vehicle is located in the High-Tech Logistics Systems Laboratory of the Logistics Institute of the University of Miskolc. For motion controlling and simulation between two points the further modules are necessary: 1. path planner, 2. trajectory planner, 3. velocity-voltage converter using velocities gained from trajectory planner, 4. motion controlling and simulation of a motor dynamical model using voltages from the converter, 5. simulation of the path and 6. data processing. In this paper the first two modules are detailed, i.e. the path planning and then the trajectory planning. Path planning is based on a new approach, using Bezier-curves and Hermite curves. The trajectory planning tends to the mininum energy, which can be carried out by the examining the current consumption created in the other modules. The smaller consumption originated from the two curves determines the final path and trajectory.