Swing-free transport of suspended objects: a general treatment

It is shown that there is a family of control strategies that result in swing-free movement of objects suspended from a movable point (e.g. a bridge crane). While it is possible to control the swing with acceleration periods of arbitrary length, it is necessary in that case to know the period of the suspended object, which requires knowledge of the location of the object´s center of mass. In a practical application of this result, the best strategy is to build a sensing system into the bridge and crane hook that allows the crane to recognize when the hook is directly below its support point. The control strategy is then to accelerate for one full period, which is recognized when the hook returns to the point directly below its support point. If the bridge continues to move at this velocity, the suspended object will not swing. To stop in a swing-free state, the crane begins to decelerate at the same rate as it accelerated, starting at a distance from its goal equal to the distance traveled while accelerating