机械臂协调操作柔性负载系统轨迹与振动控制方法研究
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摘要
本文以机械臂协调操作柔性负载系统为研究对象,通过系统模型的建立、奇异摄动分解、自适应模糊滑模控制器和模糊补偿控制器的设计等手段,采用理论研究与Matlab仿真相结合的方式对柔性负载的轨迹与振动控制进行了研究。
首先,以简支梁为研究对象,采用了Lagrange方程和假设模态法相结合的方法建立了柔性负载的动力学模型,并且分析了模型特性。给出了关节角坐标,末端执行器坐标以及物体坐标之间的转换关系,在物体坐标系下建立了整个协调系统的动力学方程。其次,基于奇异摄动理论对建立的动力学模型进行分解,得到了表征大范围刚性运动的慢变子系统和表征小幅弹性振动的快变子系统。再次,在考虑系统参数存在不确定性情况下,针对慢变子系统设计了自适应模糊滑模控制器,针对快变子系统则采取了PD控制和模糊补偿控制相结合的控制方法。最后,通过仿真研究验证了所设计控制方法能够很好的对柔性负载的轨迹和振动进行控制。
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.
首先,以简支梁为研究对象,采用了Lagrange方程和假设模态法相结合的方法建立了柔性负载的动力学模型,并且分析了模型特性。给出了关节角坐标,末端执行器坐标以及物体坐标之间的转换关系,在物体坐标系下建立了整个协调系统的动力学方程。其次,基于奇异摄动理论对建立的动力学模型进行分解,得到了表征大范围刚性运动的慢变子系统和表征小幅弹性振动的快变子系统。再次,在考虑系统参数存在不确定性情况下,针对慢变子系统设计了自适应模糊滑模控制器,针对快变子系统则采取了PD控制和模糊补偿控制相结合的控制方法。最后,通过仿真研究验证了所设计控制方法能够很好的对柔性负载的轨迹和振动进行控制。
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.
引文
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[2] LI YUANCHUN, TANG BAOJIAN, SHI ZHIXIA, et al. Experimental Study for Trajectory of a Two-link Flexible Manipulator[J]. International Journal of System Science, 2000,31(1): 3-9
[3]李元春,陆佑方,唐保健,等.双连杆柔性机械臂轨迹跟踪的鲁棒控制[J].自动化学报,1999,25(3): 330-336
[4]刘名治,刘春霞.柔性机械臂动力学建模和控制研究[J].力学进展,2001,31(1):1-8
[5] YUKAWA T, UCHIYAMA M, INOOKA H, et al. Handling of a Constrained Flexible Object by a Robot[C]//International Conference on Robotics and Automation, New York: IEEE Press,1995: 324-329
[6] WU JIANQING, LUO ZHIWEI, YAMAKITA M, et al. Scheduled Control of Robot Manipulators for Contact Tasks on Uncertain Flexible Objects[J]. International Workshop on Advanced Motion Control, 1996, (2):512-517
[7] WU JIANQING, LUO ZHIWEI, GAIN K, et al. Scheduled Control for Robot Manipulator's Contact Tasks on Flexible Environments[C]//IEEE International Conference on Systems, Man and Cybernetics, New York: IEEE Press, 1996:41-46
[8] LAI R, OHKAWA F. Digital Control of A Manipulator Handling Flexible Objects[C]// The World Congress on Intelligent Control and Automation, New York: IEEE Press,2004: 455-459
[9] FAHANTIDIS N, PARASCHIDIS K, V.PETIDIS, et al. Robot Handling of Flat Textile Materials[J]. IEEE Robotics &Automation Magazine,1997,4(1): 34-41
[10] NAKAGAKI H, KITAGAKI K, OGASAWARA T, et al. Study of Deformation and Insertion Tasks of a Flexible Wire[C]//IEEE International Conference on Robotics and Automation Albuquerque, New York: IEEE Press, 1997:2397-2402
[11] HIRAI S, WAKAMATSU H, IWATA K, et al. Modeling of Deformable Thin Parts for Their Manipulation[J]. IEEE International Conference on Robotics and Automation, New York: IEEE Press, 1994: 2595-2560
[12] ARAI F, RONG L, FUKUDA T, et al. Trajectory Control of Flexible Plate Using Neural Network[J]. IEEE Transaction on Control Systems Technology,1993:155-159
[13] ZHENG YUAN F, PEI R, CHEN C, et al. Strategies for Automatic Assembly of Deformable Objects[C]// Proceedings of the International Conference on Robotics and Automation, New York: IEEE Press,1991: 2598-2603
[14] CHEN MING Z., ZHENG YUAN F. Vibration-free Movement of Deformable Beams by Robot Manipulator[C]//International Conference on Robotics and Automation, New York: IEEE Press, 1993: 456-461
[15] JAIN S, FARSHAD. Vibration Suppression of Unknown Flexible Payloads for Robotic Arms Using a Wrist-mounted Force/Torque Sensor[J]. Transactions on Control Systems Technology, 1995,3(2):189-200
[16] ZHOU T, ZU J W, GOLDENBERG A A, et al. Vibration Controllability of Flexible Robot-Payload System[C]//IEEE International Conference on Robotics and Automation, New York: IEEE Press, 2000:1484-1489
[17] ZHOU T, GOLDENBERG A A, ZU J W, et al. Model Force Based Input Shaper for Vibration Suppression of Flexible Payload[C]//IEEE International Conference on Robotics and Automation, New York: IEEE Press, 2002: 2430-2335
[18] JIANG ZHAOHUI. Workspace Adaptive Control of Flexible Robot Arms[C]// Proceedings of the first International Conference on Machine Learning and Cybernetics, New York: IEEE Press, 2002 : 1863-1868
[19] TIAN LIANFANG. Fuzzy Neuro Controller for a Two-Link Right-Flexible Manipulator System[C]// Proceedings of the 9th International Conference on Neural Information Processing, New York: IEEE Press, 2002 : 1867-1871
[20] PENG GUANGZHENG, WANG XUESONG, YANG XUE, et al. Study on Fuzzy PD Control of Planar Two-link Flexible Manipulator[C]// Proceeding of IEEE TENCON02, New York: IEEE Press, 2002:1542-1545
[21] HUANG LOULIN, ZRIBI M, CHAN S P, et al. Control of Two Robotic Manipulators Moving a Constrained Object[C]// Proceedings of the 33rd Conference on Decision and Control, New York: IEEE Press, 1994: 2419-2424
[22] CHIU CHIAN-SONG, LIAN KUANG-YOW. Adaptive Tracking Control for Both Constrained and Coordinated Manipulator Systems[C]// Proceedings of the 38th Conference on Decision & Control, New York: IEEE Press, 1999:1260-1266
[23] ZRIBI M, KARKOUB M, HUANG LOULIN, et al. Modeling and Control of Two Robotic Manipulators Handling a Constrained Object[J]. Applied Mathematical Modeling, 2000: 881-898
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