Yes. It is called a star-ground: Common ground and why you need one - #2 by Ballscrewbob
I'm not sure if the black wire from the servo battery pack should go first to the star-ground point or first to the servo motors. I assume that the servo motor is close to the Arduino board ? Then just add a GND wire from the servo motors to that star-ground point.
It works best if the red and black wires for the power are together in a single cable.
Sorry, I made a mistake with resistor. I gave it a quick glance and thought that R2 was in the GND wire 
A single power supply is preferred. For example a 12V battery with a DC/DC-converter for 5V and power everything from the 5V.
Or a 5V USB power bank, and power everything from 5V.