With a conventional RC vehicle, I would probably suggest getting your own receiver-transmitter set (something like XBEE transceivers or similar) and completely gutting the original system, but with a small quadcopter like you have, I think trying to replace the receiver would be very difficult to do while maintaining the aerodynamics of the vehicle.
You could try to monitor the control signals and re-create them, but a third option you might consider would be to spoof the input devices on the transmitter. That is, as I see it, you could:
- Replace the transmitter-receiver pair (not recommended due to receiver form factor).
- Spoof the transmitter output (requires purchasing another transmitter-receiver pair of the same frequency with which to line monitor and spoof).
- Spoof the transmitter input.
The last option is what I would recommend. Get a multimeter and check the joystick outputs. I would imagine they're just potentiometers; I would expect a battery V+, a battery ground, and an analog voltage output. Then all you would need to do is to duplicate that functionality. Best case scenario would be that analog voltage falls within the same band as an Arduino analog output, in which case you could just wire ground to Arduino ground and the analog output direct to the joystick analog output line (after you remove the joystick).
Failing that, you could buy digital potentiometers and duplicate the functionality. Depending on how clever you wanted to be (and how much space is available) you could install a USB port and a switch to jump between joystick and Arduino control and have a modified computer-capable transmitter that can also be controller by people.