Research On The Distributed Parameter Modelling And Control Method Of Manipulators Handling A Flexible Payload

In recent years, robot technology has been widely used in the fields such as industry, agriculture, military affairs, medical Science and service. In the aeronautics astronautics automobile shipbuilding and printed wiring board, when a large number of elastic sheets and flexible slightness beams need to be moved and assembled, the accuracy and safety must be considered. Thus more and more researchers have attracted to study on the manipulation of flexible objectsA typical automotive body has hundreds of different pieces of sheet flexible metal that must be held while robots spot weld them together. The complex fixture is needed. The error allowing is no more than one mm in automobile manufacturing, even if the auto body places a very small change in the shape, the fixture means to be redesigned. The design of complex fixture takes tremendous capital. A large number of flying objects have been send into space orbit, with the deep development in space. After a long time the position or posture will change and they must be maintained. It is unable to complete these tasks depending on human and must rely on space robotics. In addition some parts are made of flexible small and thin flakes by forging and stamping in the other industry, so efficiency and safety could be greatly improved while the manipulators are used. Thus it can be seen that these operations all involve the issue of manipulator operating flexible payload. Especially the precise tasks of numerous large structure payloads require double or more cooperative manipulator arms.From the current situation of research at domestic and abroad for it is only at the initial stage that manipulator handle a flexible payload. The dynamic model trajectory tracking and vibration suppression are still not formed a complete system. Compared with manipulator handling a rigid payload. flexible payload will cause elastic vibration which brings a lot of technical problems on stability and control of system. Flexible payload can produce deformation and vibration when it is operated. Moreover these uncertainties and internal forces lead to the interaction between manipulator and flexible payload. so they increase complexity of system dynamics analysis and modelling to certain extent. The flexible payload system is a typical nonlinear system with distributed parameters. Because the flexible payload has a randomicity. the sensor can not be mounted to the flexible body arbitrarily. The vibration will bring influence about stability of the system. It has difficulty in suppressing vibration of flexible payload system.Additionally internal forces must be controlled as manipulators handling a flexible payload. Otherwise, the operation is likely to be destructive for the payload. and it make the control of the system complex. In this paper, the cooperative system of manipulator handling a flexible payload is studied. Taking a flexible beam as an illustration, the system dynamic model is given by distributed parameter. Based on singular perturbation theory the finite element model and distributed parameter model which are two time-scale systems are decomposed. When the system has some uncertainties, the problem of trajectory tracking is introduced. And then control methods are improved using backstepping design. Also the issue on feedback control of system is discussed to suppress the elastic vibration based on observer. The distributed parameter model which must be expressed by partial differential equation (PDE) includes infinite mode. Thus the stability of closed-loop system is proved by operator semigroup theory, and system simulation model is given to simulate through theoretical analvsis. Main content and innovation are as follows.After discussing some assumptions on constraint situation of beam and pole in the flexible multibody dynamic system, select the constraint that one end of flexible payload is clamped, and the other is free, and then the motions of two three-link manipulators and a flexible payload are determined. When manipulators and payload are regard as a whole, the kinetic potential energy and virtual work of cooperative system are given in the reference coordinate. According to Hamilton's principle, the distributed parameter model is obtained. Several features of dynamics model are explained. The simple distributed parameter model is given to simulate through analyzing the character about solution of the Partial Differential EquationsThe dual manipulators cooperating flexible payload is a complicated two-time scale dynamic system via deep analysis of the system kinetic equation characteristics. The models of the system which are derived by the finite element method and the distributed parameter method respectively are both separated by the singular perturbation method for model order reduction. The separation obtains a slow subsystem representing the large-scale movement and a fast subsystem representing the elastic vibration. Compared to the finite element model, the distributed parameter one keeps the partial differential equation (PDE) expression of the fast subsystem and this description is more close to the system nature.When the manipulator with flexible payload exist parameter uncertainties and the operation is influenced by the external disturbance, the parameter uncertainties and the external disturbance are combined into a nonlinear function. According to two aspects that whether the uncertainties have an upper bound and the upper bound is known or not. then an adaptive sliding mode slow subsystem controller and a robust optimal fast subsystem controller are designed for the finite element model. The objective is tracking the desired trajectory and suppressing the elastic vibration of the flexible payload. Using the backstepping design theory and the quality that neural network method can approximate and gain nonlinear function, the control method is improved. Meanwhile in the case that the upper bound of the uncertainties is unknown, the system robustness is enhanced. The same design strategy is then extended to the distributed parameter slow subsystem.Since particularity conventional control methods of Euclidean space can not be used in the distributed parameter fast subsystem which shows infinite dimensional a sliding mode control is devised to suppress the elastic vibration in the infinite dimensional space effectively. The characteristic of the main operator and C0 semigroup of the fast subsystem is analyzed via changing the closed-loop distributed parameter development equation into an abstract Cauchy problem, therefore both solution of closed-loop equation and the distributed parameter closed-loop subsystem are proved to be asymptotic stable.Based on the idea that the displacement of the manipulator end can be measured by laser displacement sensor and the information can derive the vibration of the state. The feedback control methods with backstepping design based on observer are proposed. The system stability is analyzed and simulation results are given.According to the research experience in manipulator systems, flexible multibody systems and distributed parameter systems and through studying on mathematics, mechanics and control theory, the conclusion and the perspective of future research are given at the end of the paper.