Yep definitely try this first.I was reminded in another "brake shudder" thread that brake pad material transfer can be a cause.
You can try a few high energy stops to clean the rotors of any residue. It's the cheapest fix if it works.
Don't come to a complete stop and hold the brakes on. Just a high energy 'slow down' and then continue moving to let the brakes cool. Try 3 or 4 cycles.
Otherwise, the other posts have identified the likely causes/fixes.
Also check the tie rods. If they are worn they can contribute to the amount of shudder.