Command shaping for residual vibration free crane maneuvers

Cranes used in the construction and transportation industries are generally devices with multiple degrees of freedom including variable load-line length, variable jib length (usually via a trolley), and variable boom angles. Point-to-point payload maneuvers using cranes are performed so as not to excite the spherical pendulum modes of their cable and payload assemblies. Typically, these pendulum modes, although time-varying, exhibit low frequencies. Current crane maneuvers are therefore performed slowly contributing to high construction and transportation costs. This investigation details a general method for applying command shaping to various multiple degree of freedom cranes such that the payload moves to a specified point without residual oscillation. A dynamic programming method is used for general command shaping for optimal maneuvers. Computationally, the dynamic programming approach requires order M calculations to arrive at a solution, where M is the number of discretizations of the input commands. This feature is exploited for the crane command shaping problem allowing for rapid calculation of command histories. Fast generation of commands is a necessity for practical use of command shaping for the applications described in this work. These results are compared to near-optimal solutions where the commands are linear combinations of acceleration pulse basis functions. The pulse shape is required due to hardware requirements. The weights on the basis functions are chosen as the solution to a parameter optimization problem solved using a recursive quadratic programming technique. Simulation results and experimental verification for a variable load-line length rotary crane are presented using both design procedures.