Does anti-lock braking system (ABS) perform reverse rotation sometimes? In cartoons we can see, how vehicles brake by rotating wheels reverse.
Will this be helpful sometimes in real situations? I know that the main tactics of ABS is to maintain tractive contact. But may be it will be better sometimes, at some speeds, friction and so on -- to rotate back?
Does current ABS systems do something like that? Were any experiments on this performed?
 A: No, for normal context of a car and a road.  The point of ABS is to prevent slipping so that tire traction is governed by the static coefficient of friction instead of the dynmamic one.  It also helps with control of the car.  Once a wheel is slipping, you no longer have any directional control with that wheel.  ABS systems also just don't have the ability to drive a wheel backwards.  All they do is essentially lessen the brake pressure when they detect a wheel slipping or locking up.
However, for some unusual cases it is possible that actively driving a wheel backwards provides more decelleration force that optimal breaking.  If the tires have rough treads and the road surface is sufficiently loose, then spinning a wheel can make road material fly in the opposite direction from what the wheel is driving.  For example, in the case of trying to slow down forward motion, the spinning wheel would have to actively propel road matrial forwards.  If enough material is propelled forwards fast enough, the force required to impart that momentum can exceed the friction force from optimum braking, especially with loose road material where the friction force is low to begin with.
This sounds far fetched, and it is for any normal context of "car" and "road", but this principle is actually exploited in something called a "tractor pull" contest.  That's sortof a tug of war between two tractor.  They aren't trying to decellerate but are still trying to produce the maximum force of wheel against road possible.  Spinning at high speed and ejecting lots of material wins over trying to anchor yourself on the ground with a stationary wheel.
A: No it would not. Both from a purely physical point of view, and from a practical one.
From a physical perspective, the wheels have a lot of inertia going forward. To make them spin back you would have to exert enormous, and almost instantaneous, power in the reverse direction.
In practice, even if you would manage to do that, the backwards motion of the wheels would take a long time to compensate the inertia of the whole vehicle. The wheels would just spin backwards and slide and no braking would take place. The only net result would probably be a nice set of skid marks on the ground, and a crashed car.
What ABS really does is to ease the braking on a wheel that starts to lock up, simply because a locked wheel, much like a backwards-rotating wheel, will have little friction with the ground and will not contribute towards stopping the car. ABS reduces the brake power applied to that wheel until it starts spinning correctly, then it applies normal braking again.
