| In recent years, robots have been widely used in many fields, such as industrial manufacturing, ocean exploration and aerospace, especially that manipulators of various functions become the focus of current research as the development of the economy and technique. In shipbuilding, aerospace, automotive and other fields, manipulators not only operate rigid objects, but also large-scale or thin metal plates. Vibration would occur inevitably during operation. The accuracy and safety requirements are high in these areas so the vibration must be controlled.According to statistics, in the automotive manufacturing it includes hundreds of metal plates in each car. In order to weld them together, the complex fixture must be designed. The error allowing is less than 1millimeter in automobile manufacturing, even if the auto body places a very small change in the shape which means that the fixture needs to be redesigned. It takes many years to modify a fixture. Therefore it is important that the manipulator is used instead of the fixture. In the aerospace field, satellite's solar panels are mostly made from flexible materials. After a long time the position or posture will change and they must be maintained with manipulators. Coincidentally, printed circuit board is composed of many small flakes. Manipulators instead of people completing tasks are more efficient and secure.Therefore, study on manipulators handling flexible payloads has importantly practical significance. Manipulators could liberate people from heavy repetitive work, moreover, these tools can continue working without tiredness, and this would bring indirect economic benefits. From the current situation of research at home and abroad for manipulators operating flexible payload it is still at the initial stage. The cooperative control and vibration suppression problems are still not formed a complete system. There are a lot of challenging works needed to be solved.Manipulators cooperative systems handling flexible payloads are complex distributed parameter systems. Flexible payloads are bound to vibrate and deform during operation, and the role of internal forces exist between manipulators and flexible payloads. Therefore, system model, trajectory planning and vibration suppression are more complex. Based on finite element method and Lagrange equation, kinematic model and dynamic model of manipulator cooperative systems handling flexible payloads are detailedly deduced. In order to have a uniform expression, the relations of three coordinates are listed. The rigid dynamic equation and vibration equation of the system are derived in the object coordinate system. The obtained dynamic model is divided into a slow subsystem describing the large rigid motion and a fast subsystem expressing the elastic vibration by singular perturbation theory. Two manipulators handling a flexible payload are studied based on adaptive backstepping control theory, and a cooperative controller is designed based on adaptive backstepping control. The slow subsystem can complete system trajectory tracking performance. The fast subsystem can suppress the elastic vibration of the system. By assuming that the ends of the manipulators can be the installed sensors, the information of points between the ends and the flexible payload and the characteristics of the flexible payload can be measured so it can derive the vibration state. The feedback control method based on observer is proposed for the fast subsystem to suppress the elastic vibration of the system. The stability of the system is proven based on Lyapunov equations,and the results of simulation demonstrate the effectiveness of the proposed method.Some based work is done for two manipulators handling a flexible payload. Because it's a very complex distributed parameter system and many problems will appear in dealing with the system. This paper mostly solved the problems of model decomposition, trajectory planning and vibration suppression, but there are many works needed to be solved. |
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