Modeling and control of robotic manipulators with rigid and flexible cables

Robotic manipulators equipped with cable-pulley based gravity compensation mechanism (GCM) have been noticed for about a decade. These robotic arms not only have the advantages of series and parallel robots but also overcome some of their static and dynamic problems. As flexibility in cables is much more than in rigid links, the use of cables in GCMs poses additional challenges in the control of the robotic manipulators for researchers. Therefore, the effects of cable flexibility should be considered not only in the modeling of the robotic arms but also in designing the control algorithms. This paper presents a novel approach of simplifying the complexity of total dynamic equations of cable in a way that the design of effective control algorithms for the robot will be simpler. Therefore, the dominant dynamics of the cable are specified, and subsequently, the robot is modeled based on it. Initially, a robust inverse dynamic controller is designed based on the rigid cable model. Then, a corrective term is added to the designed controller to dampen the effects of cable flexibility. The developed algorithm is robust to cope with unstructured and structured uncertainties. The simulations results show that the proposed control algorithm will be able to not only stabilize the closed-loop system in finite time, but also to effectively suppress the resulted vibration from the inherent axial flexibility of the cables and uncertainties.