Modeling and Flatness of Rigid and Flexible Cable Suspended Underactuated Robots

A modeling framework is proposed for the control of rigid and flexible cable-like systems such as cranes, together with a systematic algorithm for computing flat outputs of mechanical systems for which the flat output is a linear combination of the free coordinates. Key Lagrange multipliers are shown (i) to impose the condition of cable looseness, and (ii) to act as the extended states in the classical state-space representation. Some examples of cranes and suspended cable robots are given with their corresponding dynamics summarized as a set of well-defined vectors and matrices of real numbers.