Is it legal to use Duct Tape to fix a piece of wood on our robot?
Duct tape is not a structural element.
I would assume it would be legal, as long as your robot is safe to operate and passes inspection again. (I wouldn’t advise using duct tape unless it was absolutely your only option).
I would wood glue it, then use duct tape to support it.
VHB on the other hand is a structural element when used properly. It’s the same kind of tape they use to stick skyscraper windows on permanently.
Listed as Outdoor Mounting Tape