The need to optimize the trajectory of vehicles is still highly topical, regardless weather the means of transport are robots, forklifts or road vehicles. It is not only important the safety by passing obstacles, but also the energy balance, i.e. the energy expended on the movement of the vehicle and on the change of its direction. This paper presents a mathematical approach to solving this problem through interpolation and approximation curves. This is a very important scope of knowledge for the education of future engineers.