If you use a servo controlled by a conventional pwm signal as used by most hobby R/C systems, the Arduino can control them directly. However, you would need a fairly hefty servo to give fast, accurate positioning of something as heavy as a gun and I don't think an ordionary small hobby servo would be up to the job. Bigger servos are available, however. I expect you already know this if you're studying mechatronics.
If you choose to use a conventional DC motor/gearbox and have the Arduino do position sensing and feedback control, that's when you would need an H-bridge drive circuit to control the motor.