I would like to try the attached circuit (minus the inductor) with a mosfet to drive two relatively small motors (about 5 amps each).
I am ordering parts and would like to build a circuit like the one shown on Grumpy Mike’s decoupling page at the bottom.
The Arduino will be reading PIR sensors and Sonic Sensors.
If a single battery supply provides enough power (such as a 35Ah deep cycle), can I get away with one power supply? Or is it standard practice to have the Arduino power supply separate from the motor power supply?
A separate power supply is an easy way to keep the power to the microcontroller clean and I see a lot smart people recommend separate power supplies.
That said, I have a lot of different types of robots and none of the have separate power supplies for the microcontroller.
From reading a previous thread (here), I think you are being influenced too much by the statement on Grumpy Mike's decoupling page "The inductance value is not too critical, but generally as big as you can manage, a few tens of mill Henrys is normal".
For a rating of 5 amps, reasonable size inductors of about 220µH are readily available as this example. Such inductors can have valuable reactance (in ohms) at frequencies such as 100kHz. I therefore suggest you consider placing such an inductor in series with each motor (with the decoupling capacitors as shown in your circuit diagram).
You could also place an inductor in series with the power from your battery going to your Arduino and its associated sensors, breakout boards etc. As there will be much lower current, you could have a higher value of inductance and/or a smaller component. Again, include decoupling capacitors. If you are planning to use a 12 volt battery, a voltage regulator could provide some valuable protection against electrical noise from the motors.
It may be a mistake to choose as large an inductance as you can manage because components with larger values of inductance tend to have lower self-resonant frequency (SRF).