Control of electric actuators
An H-bridge with current detection sounds exactly right. You could also incorporate some kind of limit switch, either a mechanical switch, or a hall effect sensor, or an opto-interrupter, rather than relying on detecting the stall at the end of the travel. It's an extra part to buy, but perhaps more robust. You can avoid the mechanical stress from the maximum motor torque into the stops at the end of the travel and have less chance of false-positives leaving your doors half-open.

You could probably use an Arduino, but you could also just get a microcontroller which would be smaller, cheaper, and lighter. An H-bridge can be a simple as four discrete MOSFETs. There are also integrated H-bridges that have all four transistors in one package, which might save you some weight and assembly complexity. Unless this is a very large model, you can probably get away with a lighter, smaller, and cheaper solution than the Arduino motor shield.