I've read through the USB functionality of CHDK, and made myself a USB connector that can be plugged in straight to my arduino, but I'm struggling to find on the wiki and the internet on how exactly to command the camera via Lua.
Alternatively, camera can also be controlled by using the 'USB remote' functionality in a script running on the camera. An example for such a script is here, or a really simple one from that script's forum thread. A collection of available script commands is here: http://chdk.wikia.com/wiki/CHDK_Scripting_Cross_Reference_Page
But if I understand the OP's question, he is looking to control the camera via USB messages. Which will be difficult with a stock Arduino as the USB i/f is not the right one for what he wants to do.
But if I could send actual data commands directly via USB, that would be even better.
Set up a wlan access point on the Pi and connect the phone with the Pi. The smartphone need a real vnc client. So you have the full control over the camera via wlan.
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