No physics are being violated here -- the authors themselves point out: > Notably, the robot’s ability to move does not violate the usual rule against movement

No physics are being violated here -- the authors themselves point out: > Notably, the robot’s ability to move does not violate the usual rule against movement without forces in three-dimensional space because the full three- dimensional dynamics in fact include normal forces on the robot supplied by the boom arm that confines it to the sphere. (And I'm sure they would agree that you can even eliminate forces from the table itself from the equation, if you attach an identical robot on an opposite arm to supply that normal force from within the system.) What I don't understand is -- given that the Euclidean physics are known, why was an experimental setup involved in this paper, as opposed to simply mathematical proof? Or is the experimental demonstration the purpose in and of itself?