Actually that's a very good question, how can one read how much current a motor is drawing while under program control. There are a couple of ways I can think of. The most non-invasive way it to use a hall-effect current sensor. This has a wire carrying motor current routed through the chip but otherwise no direct electrical connection to it, and output a DC measurement voltage proportional to the current. Advantages are no power loss consumed across a series resistance. Disadvantage might be cost of module, as I haven't seriously looked into their prices, current ranges, and interface voltage requirements. For battery operation on larger applications like robots, etc, efficiency is all important for maximum battery life between recharging.
The more traditional solution is to use a 'shunt' resistor like you have described and just measure the voltage drop across the resistor. It's easiest to interface with a arduino if it's a ground based measurement, so the resistor should be wired from the motor voltage sources negative voltage terminal to the entry for ground of the H-driver chips or low side driver transistors for discrete H-drive designs. As the arduino and H-drive power source should already be sharing a common ground wire, all that is required is to run a wire from the 'hot' side of the shunt resistor to a Arduino analog input pin.
One likes to have as small a resistance as possible as any voltage drop represents power loss to the motor as in watts lost = amps X amps X ohms. However as you stated your .05 ohm resistor will only present .15vdc at expected normal load current and that is a small number for decent resolution measurement on a normal arduino 0-5vdc analog input pin, only reading at 3% of measurement range. However you can enable the internal 1.1vdc A/D reference and your measurement range will shift down to 0-1,1vdc so your .15v current measurement will fill about 14% of the range and that might be usable.
Finally I think some of the H-drive IC modules include current measurement outputs, but I don't recall which ones. As most of these modules have some form of over-current shutdown/protection, they already have an internal means to measure current flow and as I said some give that measurement available on a analog output pin as I recall. I think I recall that anyway.
Any of that make sense?