One solution would be to add gyroscope(s) to stabilise the gun. This might work well, although I’m guessing that the weight/size of the battery and motor(s) would detract from the benefits.

A more compact solution would be a computer controlled stabilizer which finely adjusts the angle of the barrel relative to the body of the gun. So the barrel is kind of ‘floating’ on the gun body.

The chamber and barrel by are hingedly connected to the gun stock, so the chamber and barrel have a small degree of freedom to pivot in azimuth and elevation relative to the rest of the gun. The muzzle end of the barrel is coupled to the gun body by a fine-adjustment mechanism e.g. several solenoids or piezoelectric elements.

An onboard computer tracks the movement of the gun by means of accelerometers. Alternatively the gun’s movement is tracked by its position relative to a fixed object e.g. by using reflected light or sound etc.

When a gun is being aimed it is held fairly steady, but there is lots of small distance vibrations (caused by breathing, pulse and constant re-adjustment by the shooter). If you fix a laser onto the barrel of the gun the path the laser resembles a ‘random walk’. The desired target is approximately in the middle of this random walk.

As the computer detects the gun is being aimed (lots of small shaking, no big shaking), it calculates the desired target. Alternatively, pressure on the trigger could be sensed to indicate the gun is being aimed.

The barrel orientation is adjusted by the fine-adjustment mechanism to be aimed at the target and could either be constantly re-adjusted, or adjusted at the moment the trigger is pulled.