The discovery of antigravity has been claimed by various individuals.
In 1920, George S. Piggott was able to suspend heavy silver beads (112 inch in diameter) and other materials in the air between a charged sphere and a concave ground plate when his generator was fully charged at 500,000 electrostatic volts. The levitational feat was only observed when the charged sphere was electropositive.
In the 1921, Thomas Townsend Brown discovered that if he charged a capacitor with high voltage direct current, the capacitor would exhibit thrust in the direction of the + positive electrode. This electrical effect, termed the Biefeld-Brown Effect, was thought to deal with ionic wind that transfers its momentum to surrounding neutral particles.
The observed effects of most of these experiments appears to be the result of ion winds or electromagnetic forces. The underlying forces will be understood with experimentation.
Anti-gravity, that is creating an environment where an object is completely free from the force of gravity, has not been discovered.
From time to time someone claims have made an anti-gravity device. Usually they are fooled by things such as the Biefeld–Brown effect, which can provide some lift. In the case of the Biefeld-Brown effect, this is done through an ionic wind. This is not a new force.
The floor cancels out the effect of gravity by applying an upward force to objects thereby preventing them from continuing to accelerate towards the center of the earth. This is not antigravity. It is also not a new force.
Rockets cancel out the effect of gravity by providing enough force to lift themselves all the way into space. This is not antigravity. It is not a new force.