Which is best: "with", "by", or "using"?

Solution 1:

By doesn't have the right meaning for this situation. With could work, but it sometimes connotes along with, as in with a companion, which is not the case. Using is the best bet, since that connotes using a tool, which is what we want. Also, do exploration is clunky, and sounds wrong. Explore means the same thing, but sounds much more natural:

Explore using Mobile Robot.