Optimal force distribution applied to a robotic crane with flexible cables

A multiple cable robotic crane designed to provide improved cargo handling is investigated. The equations of motion are derived for the cargo and flexible cables using Lagrange´s equations and the assumed modes method. The resulting equations are kinematically redundant due to fewer degrees of freedom of the cargo than the number of cables. A nonlinear transformation is used to reduce the number of variables. An optimal force distribution method is then applied to the equations to solve for a set of necessary cable tensions which will cause the system to track a desired trajectory. These tensions are tested on the dynamic model using computer simulation. The results are compared against desired cable lengths and results gained in previous research using a rigid cable model