When Newton has first devised his mathematical formula for gravitational force between any two objects in space, he related it as a force transmitted by unknown means. Later many scientists studied ways to defy gravitational energy to create anti-gravity situations.
Although an anti-gravity situation requires that the object be free from the gravitation force of any other object nobody was able to achieve this situation practically. The practicality of achieving anti-gravity is still considered as impossible. Whatever some scientists tried to do was to oppose gravity by means of either electromagnetic or some other forces.
Typical example is a balloon which contains hot air or some special gas enabling it to float in space defying gravity. Here the balloon is not free from gravitational attraction but rather countering it with an opposing force arising out of differences in its density and density of surrounding gases.
If an external repulsive force is some how developed for an object in the presence of another object to counter the attractive force due to gravitation, the net effect will that first object will tend to move away from the other while the other will move towards the first. This situation completely consumes the energy supplied through external means without accomplishing anti-gravity situation.
Presently no theory could be implemented practically which allows for anti-gravity situation. The general scientific community does not even think its possible to create one.