@Doubtful,
Either way, this is an odd use of "directed." "Directed to" implies that one person or thing is instructing another person or thing, such as, "I was directed to the restaurant by John." "Directed at" suggests something is aiming in the direction of something else, as in "The gun was directed at me!"
I supposed you could say "an instrument dedicated to," but why not just simply say, "The group created an instrument for the treatment of obesity." ??