A four-wheel drive system for a hybrid vehicle includes at least two motor-generators and a single engine connected to a differential having multiple degrees of freedom. In some embodiments, by adjusting the outputs of the motor-generators, a controller allocates power from the engine, to or from each of the motor-generators, to the front wheels and to the rear wheels, each of which is connected to an element of the differential. The relationship between the elements of the differential is represented by an alignment chart of the differential.