A control apparatus for the longitudinal and/or lateral guidance of a vehicle, in particular of a utility vehicle, relative to at least one further vehicle in a vehicle group, comprising: - a determination unit, which is configured to determine a vehicle air resistance, FL, of the vehicle and a further vehicle air resistance, wFL, of the at least one further vehicle; - a control unit, which is configured to control a control variable of the longitudinal and/or lateral guidance of the vehicle and/or of the at least one further vehicle in the vehicle group; - a memory unit, which is configured to store the determined FL and wFL in association with the controlled control variable in a characteristic map, wherein the control unit is configured to vary the control variable, the determination unit is configured to determine the FL and the wFL in the state of the varied control variable, and the memory unit is configured to store the FL and wFL determined in the state of the varied control variable in the characteristic map in association with the varied control variable; and - a computational unit, which is configured to calculate a control variable optimizing the FL and the wFL on the basis of the stored characteristic map, wherein the control unit is further configured to control the control variable of the longitudinal and/or lateral guidance of the vehicle and/or of the at least one further vehicle in the vehicle group in accordance with the optimized control variable, and wherein the optimized control variable calculated by the computational unit is configured to orient the vehicle by means of the longitudinal and/or lateral guidance in relation to the at least one further vehicle such that an average formed from the FL and the wFL is minimal. - a determination unit, which is configured to determine a vehicle air resistance, FL, of the vehicle and a further vehicle air resistance, wFL, of the at least one further vehicle; - a control unit, which is configured to control a control variable of the longitudinal and/or lateral guidance of the vehicle and/or of the at least one further vehicle in the vehicle group; - a memory unit, which is configured to store the determined FL and wFL in association with the controlled control variable in a characteristic map, wherein the control unit is configured to vary the control variable, the determination unit is configured to determine the FL and the wFL in the state of the varied control variable, and the memory unit is configured to store the FL and wFL determined in the state of the varied control variable in the characteristic map in association with the varied control variable; and - a computational unit, which is configured to calculate a control variable optimizing the FL and the wFL on the basis of the stored characteristic map, - a computational unit, which is configured to calculate a control variable optimizing the FL and the wFL on the basis of the stored characteristic map, wherein the control unit is further configured to control the control variable of the longitudinal and/or lateral guidance of the vehicle and/or of the at least one further vehicle in the vehicle group in accordance with the optimized control variable, and wherein the optimized control variable calculated by the computational unit is configured to orient the vehicle by means of the longitudinal and/or lateral guidance in relation to the at least one further vehicle such that an average formed from the FL and the wFL is minimal.