Mobile App Controlled Drone

A few friends and I plan on making a drone that can be controlled through a mobile app. Of course we will be making the mobile app. I was just wondering if this project is feasible with arduino. I'm not sure what board we would be using. I'm looking at the arduino wifi shield for connectivity between the phone and the drone. So, before I start buying the materials, I'd like to know if an arduino is capable of this

i predict that while you are fiddling with your mobile device, the drone will fly away or crash. How about a slower moving ground vehicle?

That would be the case if we programmed it to fly ahead of time. I'm thinking of taking it step by step. before actually building the drone, we have to make sure that it's getting the correct instructions. Initial flight testings would have to be done in an enclosed environment so it does not "fly away." The flight patterns have to be observed to checked with the program to check for bugs.

You are going to endanger others with this foolish plan.

Take a look at http://ardupilot.com, It doesn't have anything on a mobile as far as I can see, but it might help you get started.