Dynamics and control of rotary cranes executing a load prescribed motion

Manipulating payloads with rotary cranes is challenging due to the underactuated nature of a system in which the number of control inputs/outputs is smaller than the number of degrees-of-freedom. In this paper, the outputs (specified in time load coordinates) lead to servo-constraints on the system. A specific methodology is then developed to solve the arising inverse dynamics problem. Governing equations are derived as a set of index three differential-algebraic equations in state variables and control inputs. An effective numerical code for solving the equations, based on the backward Euler method, is proposed. A feedforward control law obtained this way is then enhanced by a closed-loop control strategy with feedback of actual errors in the load position to provide stable tracking of the required reference load trajectory in presence of perturbations. Some results of numerical simulations are provided.