Method and device for optimized autonomous driving, wherein a trajectory for the actuation of the vehicle is determined. A profile of the trajectory is defined by a bending line of a bending band. The bending line is preferably determined by the finite element method, in particular according to the principle of virtual shifting, and achieves an optimization goal and satisfies a boundary condition. The boundary condition is defined in accordance with a profile of a roadway for the vehicle. The optimization goal is defined by a desired driving property of the vehicle.