A system is comprised of a floor processing device, an object located in the environment of the floor processing device, which has a partial object area and a displacement device for automatically displacing the partial object area, a detection device, which is suitable for detecting a presence of the floor processing device in a detection area of the detection device, and a control device for generating a control command for the displacement device as a function of the detection result of the detection device. In order to prevent a collision with the floor processing device given automatic displacement devices of objects, the control command is suitable for deactivating the displacement device, thereby preventing a displacement of the partial object area even if the floor processing device is present in the detection area.