Generally you will require dedicated hardware to drive the motors.
- For example Pololu Dual MC33926 Motor Driver Shield for Arduino there are many others out there. These driver "boards" are driven by the Arduino and generally need to be "deterministic" or "near real-time" to operate safely.
- In the Edison these tasks are handled by the MCU see Creating applications with the MCU SDK for the Intel® Edison board: Overview | Intel® Developer Zone for how you do this.
So you will need
- acquire suitable motor drivers for your motor type and its power levels.
- connect the drivers to suitable power (usually separate from the controller)
- connect the drivers to suitable pins on the Arduino expansion board
- Program the MCU to drive the pins appropriately
- Develop I/O interfaces for any sensors you need
- Develop a UI to send commands to the MCU, set speed, forward, adjust yaw ... etc etc.
The Linux portion of the Edison is not ideal as a sole environment for things like drones, it is generally non-deterministic and the operations it directs can be interrupted. Not something you want during a critical manoeuver.