Study On Trajectory And Vibration Control Of A Dual-manipulator System Handling A Flexible Payload

Recently, robot manipulator has been used in many fields. There are many scholars who have done much work in manipulating rigid payload, while there is little has been done in manipulating flexible payload. However, in many fields, such as car and air craft, shipbuilding and so on, flexible material has been widely used, and it is very hard for only one manipulator to do complex job, such as movement. So it is necessary to study on a dual-manipulator manipulate flexible payload. This paper is supported by the project of National Natural Science Foundation of China"Study on dynamic and control of a dual-manipulator system handing a flexible payload".In practice, one manipulator can only accomplish very finite kinds of work. It is difficulty for one manipulator to manipulate payload with such features: non-regular shape, too heavy , with degree of freedom or the process is too difficulty to operate. Such tasks always need more than one manipulator to cooperate. In cooperative control of flexible payload, not only the position and force of the end- point of the manipulator but also the cooperative motion between the end-point and the object are concerned. It is a synthesis problem of position, force, vibration and cooperative control. The dynamics of cooperating flexible manipulators is so complex that is very difficult to control them. In the present, there are many papers about manipulating rigid payload, however, there is little about the cooperative control of flexible payload both at home and abroad. So it is necessary to do research on cooperative control flexible payload.The dual-manipulator handling flexible payload system is a typical nonlinear system with distributed parameters. It must be expressed by the model of infinite mode essentially. For the convenience of research, this paper will use the combination of Lagrange formation and assumed-mode method to accomplish the dynamic model of the system. The principle of assumed-mode is using finite mode function to describe the movement of the system. The solution of continuous system can be expressed by the linear combination of all mode function. In this paper, assume the flexible object is a Euler beam, the connection method between the manipulator end and the beam is hinged support. Choose two order mode function, omit high order function. Use the beam that is not deformed as benchmark, solve the kinetic energy and elastic energy of the flexible body, build the kinetic model of the payload, analysis some characteristic of it. Generalized coordinate is composed of object coordination and two flexible coordinate. In this paper three kinds of coordinates will appear that are joint coordinates, end-effector coordinates and object coordinate. And introduce the relation among them. Based on object coordinate the rigid dynamic equation and vibration equation are listed. Analysis the characteristics of the entire cooperative system.For the reason of the flexible coordinate and the rigid coordinate strongly coupled, it is difficulty to control the system. Singular perturbation has been used to control flexible manipulator fairly well. Singular perturbation include boundary layer theory and multiple time scale theory. Through introducing a small perturbation parameter, we can obtain a slow subsystem which expressing the whole motion and a fast subsystem which expressing the elastic vibration. Thus facilitate the controller design. In this paper, we will continue to use it to control flexible payload, to decompose the dynamic model of the system.For slow subsystem, the dynamic model of it is similar to the rigid manipulator, so many control method that applicable to rigid manipulator is also applicable to control the slow subsystem. During the construction of dynamic model of the system, for the reason of omitting high order assumed mode, also the measurement errors of manipulator and flexible's mass, length, density and the effect of environment, all these coupled to make the dynamic model inaccurate. Fuzzy system has the property of universal approximation, it can approximate any kind of nonlinear function. Therefore during the controller design of the slow subsystem, we introduce a fuzzy system, it is used to approximate uncertain items. According to the slow subsystem we design an adaptive fuzzy sliding mode controller. By means of Lyapunov theory testify the validation of the control method. For the fast subsystem, its dynamic function is a linear function. For the control of fast subsystem actually is a zero adjustment problem. In this paper design a simple PD controller, construct an error function, make use of trajectory tracking is zero to control fast subsystem. Also by means of Lyapunov theory to testify the controller can guarantee the error function global asymptotic stability. By means of the relationship between slow variables and fast variables, we can change the control torque of fast subsystem from fast time scale to slow time scale, so we can obtain the whole control input of the entire system. Finally, simulations validate the effectiveness of the dynamic model and the controller.A dual-manipulator handling a flexible payload is a complex system. Its dynamic and control is a complex problem. In the paper only do some preliminary research. There is some deficiency during the process of doing research on it, for example, only use two order mode function to describe the vibration situation, assume the vibration coordinate can be measured, and so on. These need further research.