Optimal force distribution applied to a robotic crane with flexible cables

Abstract

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.