From other hobbies involving tires, I would guess that you want to go as low as possible while avoiding
pinch flats (where the wheel rim contacts the ground, pinching the inner tube and putting two nice little holes in it). Low psi gives better cushion, but too low and you'll pop tubes. This will vary depending on your robot weight/geometry/driver aggressiveness.
We were close to 15psi in all of our tires during
this test, and came close to pinching the tubes. I would guess that ~20-30psi would be more desirable if you intend to ram the defenses.