A numerical controller of a processing machine determines corresponding setpoint axis values based on setpoint position values for position-regulated axes operating on machine elements. Before controlling the position-regulated axes, volumes to be occupied by protection bodies associated with the machine elements, a workpiece and a tool are defined and it is checked whether the protection bodies remain disjoint while controlling the position-regulated axes. Depending on the result of the checks, the controller either controls the position-regulated axes in accordance with the setpoint position values or merely executes an error response without control. The controller contains a position error field which specifies for any given setpoint axis value an actual position the tool relative to the workpiece. The position error field is taken into consideration, at least for a subset of the protection bodies, when defining the volumes to be occupied by the protection bodies upon activation of the position-regulated axes.