Rest to rest movement of a crane’s swinging load, at the bottom end of a cable, by moving a speed-limited gantry trolley at the top, involves resolving the apparently conflicting demands of exact load positioning and active swing damping. If system parameters are unknown beforehand, best existing strategies offer only asymptotic solutions. The proposed control strategy stops the load dead, exactly on target, in a finite time. It is robust and self-adapting. Using mechanical wave concepts, the gantry controller “learns” from the previously unknown dynamic response in the first part of the motion exactly how to terminate the motion. All results are verified numerically.