Method for determining a trajectory , along which a mobile device , in particular a robot, a drone or a vehicle moving in an at least partially automated manner, is intended to move in an environment , comprising: providing a destination , to which the mobile device is intended to move, and/or a reference path , along which the mobile device is intended to move, a current position and/or orientation of the mobile device, and environmental information that includes in particular distances between the mobile device and boundaries of the environment and/or obstacles in the environment; determining , based on the environmental information, a movement range within the environment, which extends from the current position of the mobile device in the direction of the destination and/or the reference path and in which in particular there are no obstacles for the mobile device; and determining , within the movement range and based on the current position and/or orientation of the mobile device, the trajectory that extends from the current position of the mobile device in the direction of the destination and/or the reference path, characterized in that the movement range is determined based on a Voronoi diagram of at least one part of the environment, wherein determining the movement range comprises: projecting the current position of the mobile device onto the Voronoi diagram; determining a path from the current position of the mobile device in the direction of the destination and/or the reference path in the Voronoi diagram; extending the path in the Voronoi diagram at its beginning and/or end, taking into account dimensions of the mobile device; and determining the movement range based on the path in the Voronoi diagram. providing a destination , to which the mobile device is intended to move, and/or a reference path , along which the mobile device is intended to move, a current position and/or orientation of the mobile device, and environmental information that includes in particular distances between the mobile device and boundaries of the environment and/or obstacles in the environment; determining , based on the environmental information, a movement range within the environment, which extends from the current position of the mobile device in the direction of the destination and/or the reference path and in which in particular there are no obstacles for the mobile device; and determining , within the movement range and based on the current position and/or orientation of the mobile device, the trajectory that extends from the current position of the mobile device in the direction of the destination and/or the reference path, characterized in that the movement range is determined based on a Voronoi diagram of at least one part of the environment, wherein determining the movement range comprises: projecting the current position of the mobile device onto the Voronoi diagram; determining a path from the current position of the mobile device in the direction of the destination and/or the reference path in the Voronoi diagram; extending the path in the Voronoi diagram at its beginning and/or end, taking into account dimensions of the mobile device; and determining the movement range based on the path in the Voronoi diagram. <EOS>