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 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.