The RTI system I've designed and built has full control over turning lights on and off inside the dome. It can also turn the camera on and off in sequence with the lights, and do both in an automated, sequential fashion ... but only if there's a way to fire the camera automatically using the Arduino-based controller. There is a manual option, where you can turn a light on, press the shutter manually, then go on to the next light, but that requires you to sit at the system and push buttons for a few minutes at a time; automatic is much better. The following camera remote modes are currently supported by the control system:

1. The control software uses Sebastian Setz's Multi Camera IR Control library, which currently supports cameras with IR remote capability from Canon, Nikon, Olympus, Pentax, Sony, and Minolta. Double-check that your camera has IR capability; for example, Canon DSLRs do but most Canon point-and-shoots don't.
2. I've also built hardwired remote cables that work with Canon/Nikon cameras, using the pin out specs at this page. Basically, you use an optoisolator as an electronic relay to close a circuit and fire the camera. If your camera supports a hardwired remote, there should be a way to hack it to work this way as well.
3. Most Canon point-and-shoots do not support a remote by default. But the Canon Hack Development Kit (CHDK) allows many Canon point-and-shoot cameras to be fired remotely through the USB connector, and this is the system I normally use for most of my RTI photography. Not all Canon point-and-shoots are supported, though; in particular, support for the most recently-released Canon point-and-shoots is spotty to non-existent. Check the list of supported cameras on the main CHDK page to make sure your camera is supported. I use the Canon S110 Powershot (not the Elph); not only does it support CHDK, it also has support for the RAW format. It's also very small and lightweight, perfect for a portable system.
4. If your camera can be fired via computer software, the control code supports firing the shutter using the Adafruit Bluetooth HID module. I use this for automated control of microscopic RTI using USB microscope imagers, but it should work fine with Canon/Nikon PC software for controlling cameras, or any other computer-based camera controller.

After I've finished fully documenting dome construction, I may look at designing/building a simple mechanical system to fire a pushbutton shutter on any camera using a servo. No promises, though. And if you've seen plans for such a shutter servo online, please send me the link - I'd rather not re-invent the wheel.