Have you ever heard of gyroscopic inertial thrust propulsion units?
The theory behind it is that a set of balls travel inside a circular "track" just like the balls in a ball bearing work, but unlike a ball bearing, the width of the track varies so that the contact area moves and the balls spin faster but travel through the arc slower than the balls on the opposite side. This means that the mass of the balls has more velocity in one direction than on the "slow" side of the arc. As a result, the faster balls decelerate as the track widens and some amount of that deceleration consistently "pushes harder" on the section of track on the fast side, creating thrust from a differential of inertia between the two halves of the circle, bisected perpendicular to the apexes and apogee/perigee of track width.
An important thing to note is that the energy of the balls is translated from kinetic velocity to kinetic rotation, what isn't "lost" to friction, especially on the "fast" side where the balls push on the track harder, and the transfer of energy that propels, goes into spinning up the balls and slowing down their speed along the track. After the apex the ball's spin is used to accelerate the ball, and transferring spin back into velocity. Basically it's a system that uses the translation to and from angular velocity to cause a centrifugal imbalance that affects one portion of the arc to a greater degree, thereby creating inertial thrust.
Years ago i saw a video of some homebuilt units made from cut up cooking pots and billiard balls propelling themselves slowly "forward" while floating on water.
But as for true antigravity, that would mean negating the force of gravity iteslf. But what is gravity anyways? I don't think anyone has actually proved or disproved gravitons and the Higgs-Boson particle that's supposed to "activate" it or something, so true antigravity may be possible when we actually understand what gravity is in the quantum and particle physics sense. Maybe when the Unified Field Theory is put together and validated some garage genius will figure out antigravity, it'll be as simple as following the instructions on youtube on how to combine the plastic bag, aluminum foil, coathanger, and moldy avocado into a DIY localized field gravity disruptor. It'll be use by bored kids to shoot neighbors' cats off into space.