Electronic – Voltage regulator for DC motor

The cheap and flexible way to deal with a combination of massive drop in voltage and current drawn for a DC motor is to make an H-bridge from discrete diodes and transistors and control them from a microcontroller. Such converters chop the voltage and ideally wouldn't dissipate any power (but they will from non-zero transition times). There are plenty of H-bridge designs on the Internet, but the basic things to keep in mind are gate saturation voltage (which you'll need to apply to the gates), saturation current, resistance when ON, max drain/source voltage.

Just chop 12V down to 7.4V with one of your transistor and a diode (see buck converter) before feeding that voltage in the motor controller. You'll need to control the transistor with a square wave of a high frequency (bear in mind the lower the frequency the more the motors will vibrate from the current harmonics), say 20kHz or more, modulated in pulse widths with a duty cycle of 7.4/12=0.61. You'll probably need to filter the voltage if the motor controller does anything other than applying it to the motor, otherwise the current is what is of interest and it is already filtered by the motors (but checking that's enough from solving the differential equation could be useful).

Eventually, you could control the converter from a 555 instead of the microcontroller should you need more computational power.

The figure above is a general example of a step-down switching DCDC converter, but you would only place the transistor (properly controlled) and the diode in between the motor controller and the 12V supply; forgetting about the inductor if the motor's is enough, the capacitor if the motors are the only target, and the resistor as you have a different load.

It is likely you can solve your problem by starting your motor slow then ramping up the speed. Tutorials are all over the web to do this. Here are three: 1, 2, 3.

To control motors the Arduino generates a fast pulsing signal that switches on and off over and over. The frequency is generally constant. However the duty cycle can vary. To make a motor go slow the on part is very small compared to the off part. This type of signal has a low duty cycle. Perhaps 0% to 25%. To make a motor go fast the on part is very large compared to the off part. This type of signal has a high duty cycle. Perhaps 75% to 100%. The following image shows duty cycles from 0% to 100%:

The Arduino function call analogWrite() is the secret to controlling the duty cycle of the Pulse Width Modulator (PWM) feature.