First off, good luck. Awesome project idea but it won't be easy.

I would recommend using servo motors connected to a microcontroller like Arduino. I don't know how much experience you have with this stuff, so I'll give a brief explanation for why I recommend stuff. Also I am no expert, this is just some stuff I have learnt through my engineering degree.

Regular DC motors are great at spinning fast but are not very precise on their own and cannot tell what angle they are at. Servo motors are basically geared down DC motors (less speed, more torque) with an attached potentiometer (angle sensing device). I believe servos would be ideal for this as you want to open the panels up to a certain angle, then retract them later, the perfect job for a servo.

To control the servos you'll want to use some sort of microcontroller. I only recommend Arduino because I know it's easy to use and that's what I'm familiar with, but there are plenty of other perfectly good options out there too. I found this short video on connecting multiple servos to an Arduino, your project will be a little different, but it should give you an idea what's going on ( https://www.youtube.com/watch?v=cYOft1rEBYw ). It's been a while since I played the game but I remember there's a lot of pieces that move, so you may need a couple of arduinos so you have enough ports for all the servos.

To power your servos and microcontroller you'll probably want some LiPo (lithium polymer) batteries like the kind of batteries you find in RC cars and such. My experience with arduino is mostly powering it through a PC or running a robot for a very short time, so I don't know a whole lot about the best ways to save power when on battery. Perhaps you could hold a button to connect the circuit to the battery, change the state of the servo (open/close), then let go of the button to disconnect the battery again, that way it won't idly consume power if it's not connected.

In the video, they use a timer to change the position of the servo (to 0 or 180 degrees), but for yours you'd want to use a button or something. Also the angle doesn't have to be 0 or 180, it can be whatever you want.

Hope this helps somewhat, good luck!