I have looked into http://wiki.roblox.com/index.php?title=Mobile_Controls only to get information on how to add new buttons or information about how to use the touchscreen instead of anything on the joystick that Roblox provides to move the character.
Is there any way to hook a script onto the joystick that moves your character to tell a script that the user moved it up, down, left, right, or let their finger off?
I'm not sure if there is API for joysticks, but you can probably code it yourself using C++ and Lua.