I don't know about this particular project, but the standard approach is to use a PID controller, which uses the derivative term to control overshooting and oscilations.

(Jonny the author here)

At the moment the control is proportional - the microcontroller works out the difference between the desired angle (set by the pilot on the ground) and the actual angle (as reported by the IMU algorithm fed by the gyro/accelometer). This error signal is then scaled and sent to the aileron servos.

The USB flight-controller I am using has a spare knob on it so I can adjust the scaling coefficient in flight. It still isn't perfect (as the video at the bottom demonstrates) - it veers to the right, probably because the IMU isn't held down very well!