Abstract: A method for determining optimized basis functions for describing trajectories. The method includes receiving reference data which describes possible trajectories; preprocessing the reference data, wherein the reference data is aggregated in a matrix Y; carrying out a singular value decomposition Y=USVT, wherein the matrices U and V each comprise singular vectors and S is a diagonal singular value matrix with singular values ?i; identifying at least one of the singular values ?i as a dominant singular value ?d,i and at least one other of the singular values ?i as a non-dominant singular value ?nd,i; and determining a matrix Ud which comprises dominant singular vectors assigned to the dominant singular values ?d,i, wherein the optimized basis functions are described by the dominant singular vectors.

Abstract: A method for controlling an automated or autonomous locomotive device, including automatically ascertaining a deviation from a predefined trajectory, the deviation requiring a return of the locomotive device to the predefined trajectory; automatically calculating a jerk as an input variable, as a function of the deviation from the predefined trajectory; automatically calculating an unconstrained correcting variable for the return to the predefined trajectory, as a function of a weighted sum that includes a weighted summand of the input variable and a weighted summand of the state for the return path; automatically calculating a constrained correcting variable regarding the jerk; the unconstrained correcting variable being manipulated via a cascade that includes multiple stages having one saturation function per stage; integrating the constrained correcting variable, to obtain a constrained return trajectory to the predefined trajectory; automatically steering the locomotive device to the predefined trajectory

Abstract: A method for controlling an automated or autonomous locomotive device, including automatically ascertaining a deviation from a predefined trajectory, the deviation requiring a return of the locomotive device to the predefined trajectory; automatically calculating a jerk as an input variable, as a function of the deviation from the predefined trajectory; automatically calculating an unconstrained correcting variable for the return to the predefined trajectory, as a function of a weighted sum that includes a weighted summand of the input variable and a weighted summand of the state for the return path; automatically calculating a constrained correcting variable regarding the jerk; the unconstrained correcting variable being manipulated via a cascade that includes multiple stages having one saturation function per stage; integrating the constrained correcting variable, to obtain a constrained return trajectory to the predefined trajectory; automatically steering the locomotive device to the predefined trajectory