柔性机器人动力学建模和仿真
摘要
柔性机器人系统是一个典型的多柔体系统，其动力学问题与一般刚体系统动力学有本质的差别，表现为大位移刚性运动和小位移变形运动之间的强烈耦合，其动力学问题是当今世界学术界公认的热门难题，被称为新世纪给力学提出的挑战性课题。而高效的动力学仿真软件工具对理论研究和工程设计都十分重要。本文根据多柔体系统动力学理论，提出创新的考虑柔性铰机器人动力学建模方法和新颖的全柔机器人(铰与杆件全柔)动力学建模方法。通过数值模拟算例研究柔性对机器人动力学响应的影响，从而使得机器人动力学和控制理论更加完善。
本文工作主要体现在以下几方面：
1．推导出柔性铰机器人和全柔机器人的动力学方程
2．对动力学方程进行有效的求解
3．编制动力学数值仿真软件
4．对算例进行计算以及分析其动力学特性
The system of a flexible robot is a typical multi-body system. Its dynamic problem is quite different from the dynamic problem of a multi-rigid-body system. The dynamic analysis of flexible robots is complicated by the coupling between the large overall rigid motion and the small elastic deformation. Its dynamic problem is academically difficult. It is a challenging problem. The dynamics simulation software package is very important in research and the design of products. Based on the theories of multi-body systems, This paper presented the mathematical model of flexible-joint robots and the mathematical model of flexible robots(flexible-link and flexible-joint). From a numerical simulation, we can find the effect of flexibility on dynamic response. And the theory of dynamic and control is more perfect.
The work of this dissertation is shown as follows:
1. The paper established dynamic equations of flexible-joint robots and flexible robots(flexible-joint and flexible-link);
2. The established dynamic equations are solved effectively;
3. A software of numerical simulation is complied;
4. Examples are given and the dynamic properties of corresponding robots are studied;
本文工作主要体现在以下几方面：
1．推导出柔性铰机器人和全柔机器人的动力学方程
2．对动力学方程进行有效的求解
3．编制动力学数值仿真软件
4．对算例进行计算以及分析其动力学特性
The system of a flexible robot is a typical multi-body system. Its dynamic problem is quite different from the dynamic problem of a multi-rigid-body system. The dynamic analysis of flexible robots is complicated by the coupling between the large overall rigid motion and the small elastic deformation. Its dynamic problem is academically difficult. It is a challenging problem. The dynamics simulation software package is very important in research and the design of products. Based on the theories of multi-body systems, This paper presented the mathematical model of flexible-joint robots and the mathematical model of flexible robots(flexible-link and flexible-joint). From a numerical simulation, we can find the effect of flexibility on dynamic response. And the theory of dynamic and control is more perfect.
The work of this dissertation is shown as follows:
1. The paper established dynamic equations of flexible-joint robots and flexible robots(flexible-joint and flexible-link);
2. The established dynamic equations are solved effectively;
3. A software of numerical simulation is complied;
4. Examples are given and the dynamic properties of corresponding robots are studied;
引文
1 赵锡芳等．机器人动力学．上海：上海交通大学出版社，1992
2 黄文虎，邵成勋．多柔体系统动力学．北京：科学出版社，1996
3 Turcic D A, Midha A. Dynamic analysis of elastic mechanism system, Part Ⅰ: applications. ASME. J. of Dynamic Systems, Measurements and control. 1984(i06): 243-248
4 Linkins P W. Finite element appendage equations for hybrid coordinate dynamic analysis. Journal of Solids & Structures. 1972(8): 709-731
5 Ryan R R. Dynamics of flexible beams undergoing large overall motions. American Astronomical Society. 1987, pp. 87-437
6 Kane T R, Ryan R R, Banerjee A K. Dynamics of a cantilever beam attached to a moving base. Journal of Guidance, Control & Dynamics. Vol. 10, No. 2, (1987), pp. 139-151
7 Chen C, Shabana A A, Rismantab-Sany J. Generalized constraint and joint reaction forces in the inverse dynamics of spatial flexible mechanical system. Journal of Mechanical Design. 1994(i16):777-784
8 陆佑方等．柔性多体系统动力学．北京：高等教育出版社，1996
9 Bae D S, Haug E J. A recursive formulation for constrained machine system dynamics: Part Ⅰ: open loop systems. Mech Struct & Mach. Vol. 15, No. 3, (1987),pp. 359-382
10 潘振宽，洪嘉振，刘延柱．链状柔性多体机器人动力学研究．固体力学学报．Vol．14，No．4，(1993)，pp．323-329
11 于清，洪嘉振．静力校正模态在闭环柔性多体系统动力学仿真中的应用．多体系统动力学与控制．北京：北京理工大学出版社，1996，27-30
12 Spong M W. The control of Flexible Robots, A survey in New Trends and Application of Distributed Parameter Control Systems. New York, Marcel Dekker publisher, 1991
13 Xi F, Fentor R G. Coupling Effect of A Flexible Link and A Flexible
Joint. Int. J. of Robotic Research. Vol. 13, No. 5, (1994),pp. 443-453
14 Benati M, Morro R. Formulation of equations of motion for a chain of flexible links using Hamilton' sprinciple. ASME. J. DN. Sys. Measurement Control. Vol.116, No. 1, (1994),pp. 81-88
15 Tsuneo Y, Koh H. Modeling of Flexible Manipulators Using Virtual Rigid Links and Passive Joints. Robotics Research. Vol. 15, No. 3, (1996), pp. 290-299
16 Chang L W and Hamilton J F. Dynamics of robotic manipulators with flexible links. ASME. J. DN. Sys. Measurement Control. Vol. 113, No. 1, (1991), pp. 54-59
17 Edelstein E, Rosen A. Nonlinear Dynamics of a Flexible Multirod (Multibeam) System. ASME. J. DN. Sys. Measurement Control. Vol. 120, No. 2, (1998),pp. 224-231
18 吴立成，陆震．一种柔性机器人的子杆法建模方法．机器人．Vol．22，No．5，(2000)，pp．344-349
19 Xi F, Fentor R G. On flexible links manipulators: modeling and analysis using the algebra of rotations. Int J of Robotic Research. Vol. 12, No. 4, (1994),pp. 371-381
20 Angeles J. Fundamentals of Robotic Mechanical System: Theory, Methods, and Algorithms, Springer-Verlag. New York, 2002
21 Fu K S, Gonzalez R C, and Lee C S G. Robotics: Control, Sensing, Vision, and Intelligent, McGraw-Hill, Inc., New York, 1987
22 Jankowski K P, Van Brussel H. Inverse Dynamics Task Control of Flexible Joint Robots—Part Ⅰ: Continuous-Time Approach, Part Ⅱ: Discrete-Time Approach, Mech. Mach. Theory. Vol. 28, No. 6,(1993), pp. 741-762
23 Jonker B. A Finite Element Dynamic Analysis of Flexible Manipulators, International J. of Robotics Research. Vol. 9, No. 4, (1990),pp. 59-74
24 Spong M W. Modeling and Control of Elastic Joint Robots, ASME J. of
Dynamic Systems Measurement Control. vol. 109, No. 4, (1987),pp. 310-319
25 边宇枢、陆震．柔性机器人动力学建模的一种方法．北京航空航天大学学报．Vol．25，No．4，(1999)，pp．486-490
26 Barbieri E, Ozg Uner U. Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link. Journal Dynamic Systems, Measurement, and Control, Vol. 110, No. 4, (1988),pp. 416-421
27 Cait Y, Miklavcivc M, Maccluer C R. Radcliffe C J. A Natural Model Expansion for the Flexible Robot Arm Problem via a Self-Adjoint Formulation IEEE Transaction on Robotics and Automation. Vol. 6, No. 5, (1990),pp. 601-603
28 Morgul O. Orientation and Stabilization of a Flexible beam Attached to a Rigid body: Planar Motion. IEEE Transactions on Automatic Control. Vol. 36, No. 8, (1991),pp. 953-962
29 Choura S, Jayasuriya S, Medick M A. On the Modeling, and Open-Loop Control of a Rotating Thin Flexible Beam, Journal of Dynamic Systems, Measurement, and Control. Vol. 113, No. 1, (1991),pp. 26-33
30 张策等．弹性连杆机构的分析与设计．北京：机械工业出版社，1989
31 Lowen G G and Chassapis C. The Elastic Behavior of Linkages: An Upadate, Mechanism & Machine Theory. Vol. 21, No. 1, (1986),pp. 33-42
32 Book W J. Recursive Lagrangian Dynamics of Flexible Manipulator Arms, Int J Robot Res. Vol. 3, No. 3, (1984),pp. 78-101.
33 De Luca A, and Siciliano B. Closed-form Dynamics Model of Planar Multilink Lightweight Robots. IEEE Trans Sys Man Cybernet. Vol. SMC-21, No. 4,(1991),pp. 826-839
34 Hastings G G and Book W J, Verification of a Linear Dynamic Model for Flexible Robotic Manipulators, Proc IEEE Int Conf Robot Automation. 1986:1024-1029
35 Connelly J D, Huston R L. The dynamics of flexible multibody system:a finite segment approach. Computer & Structures. 1994(50):259-262
36 Ider S K, Amirouche F M L. Nonlinear modeling of flexible multibody system dynamics subjected to variable constrains. Journal of Applied Mechanics. 1989(56):444-450
37 Yu Qing, Hong jiazhen. Static correction modes in dynamic simulation of flexible multibody systems with closed loops. Journal for Shanghai Jiaotong University. 1997(1):17-20
38 Matsuno, Yamamoto, etc. Dynamic hybrid position/force control of a planar two-link structurally flexible manipulator. J of Robotic Systems. Vol. 11, No. 5, (1994),pp. 355-366
39 Cannon R H, Schmits E. Initial experiments on the endpoint control of a flexible one-link robot. The Robotics Research. 1985(3):62-57
40 Chapnik B, Heppler J, Aplevich J. Modelling impact on a one link flexible robot arm. IEEE Transactions on Robotics and Automatic. Vol.7, No. 4, (1991),pp. 479-488
41 赵平，薛克宗．空间柔性机械臂三维动力学数值仿真．工程力学．Vol．13，No．1，(1996)，pp．103-114
42 费从宇，邵成勋．柔性机械臂刚柔耦合运动的摄动分析．应用力学学报．Vol．10，No．3，(1993)，pp．43-48
43 洪嘉振．多体系统动力学-理论、计算方法和应用．上海：上海交大出版社，1992
44 窦建武，余跃庆．柔性机器人协调操作的力可操作性研究．北京工业大学学报．Vol．26，No．3，(2000)，pp．10-15
45 潘振宽，洪嘉振．柔性机械臂动力学方程单向递推组集方法．力学学报．Vol．25，No．3，(1993)，pp．327-333
46 洪嘉振，蒋丽忠．柔性多体系统刚-柔耦合动力学．力学进展．Vol．30，No．1，(2000)，pp．15-20
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48 刘宏昭，曹惟庆．多柔体系统动力学的一种数值求解方法．计算机结构力学及其应用．Vol．8，No．3，(1991)，pp．316-325
49 刘迎春，余跃庆．柔性机器人协调操作柔性负载的动力学模型．机械科学与技术．Vol．21，No．4，(2002)，pp．565-568
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2 黄文虎，邵成勋．多柔体系统动力学．北京：科学出版社，1996
3 Turcic D A, Midha A. Dynamic analysis of elastic mechanism system, Part Ⅰ: applications. ASME. J. of Dynamic Systems, Measurements and control. 1984(i06): 243-248
4 Linkins P W. Finite element appendage equations for hybrid coordinate dynamic analysis. Journal of Solids & Structures. 1972(8): 709-731
5 Ryan R R. Dynamics of flexible beams undergoing large overall motions. American Astronomical Society. 1987, pp. 87-437
6 Kane T R, Ryan R R, Banerjee A K. Dynamics of a cantilever beam attached to a moving base. Journal of Guidance, Control & Dynamics. Vol. 10, No. 2, (1987), pp. 139-151
7 Chen C, Shabana A A, Rismantab-Sany J. Generalized constraint and joint reaction forces in the inverse dynamics of spatial flexible mechanical system. Journal of Mechanical Design. 1994(i16):777-784
8 陆佑方等．柔性多体系统动力学．北京：高等教育出版社，1996
9 Bae D S, Haug E J. A recursive formulation for constrained machine system dynamics: Part Ⅰ: open loop systems. Mech Struct & Mach. Vol. 15, No. 3, (1987),pp. 359-382
10 潘振宽，洪嘉振，刘延柱．链状柔性多体机器人动力学研究．固体力学学报．Vol．14，No．4，(1993)，pp．323-329
11 于清，洪嘉振．静力校正模态在闭环柔性多体系统动力学仿真中的应用．多体系统动力学与控制．北京：北京理工大学出版社，1996，27-30
12 Spong M W. The control of Flexible Robots, A survey in New Trends and Application of Distributed Parameter Control Systems. New York, Marcel Dekker publisher, 1991
13 Xi F, Fentor R G. Coupling Effect of A Flexible Link and A Flexible
Joint. Int. J. of Robotic Research. Vol. 13, No. 5, (1994),pp. 443-453
14 Benati M, Morro R. Formulation of equations of motion for a chain of flexible links using Hamilton' sprinciple. ASME. J. DN. Sys. Measurement Control. Vol.116, No. 1, (1994),pp. 81-88
15 Tsuneo Y, Koh H. Modeling of Flexible Manipulators Using Virtual Rigid Links and Passive Joints. Robotics Research. Vol. 15, No. 3, (1996), pp. 290-299
16 Chang L W and Hamilton J F. Dynamics of robotic manipulators with flexible links. ASME. J. DN. Sys. Measurement Control. Vol. 113, No. 1, (1991), pp. 54-59
17 Edelstein E, Rosen A. Nonlinear Dynamics of a Flexible Multirod (Multibeam) System. ASME. J. DN. Sys. Measurement Control. Vol. 120, No. 2, (1998),pp. 224-231
18 吴立成，陆震．一种柔性机器人的子杆法建模方法．机器人．Vol．22，No．5，(2000)，pp．344-349
19 Xi F, Fentor R G. On flexible links manipulators: modeling and analysis using the algebra of rotations. Int J of Robotic Research. Vol. 12, No. 4, (1994),pp. 371-381
20 Angeles J. Fundamentals of Robotic Mechanical System: Theory, Methods, and Algorithms, Springer-Verlag. New York, 2002
21 Fu K S, Gonzalez R C, and Lee C S G. Robotics: Control, Sensing, Vision, and Intelligent, McGraw-Hill, Inc., New York, 1987
22 Jankowski K P, Van Brussel H. Inverse Dynamics Task Control of Flexible Joint Robots—Part Ⅰ: Continuous-Time Approach, Part Ⅱ: Discrete-Time Approach, Mech. Mach. Theory. Vol. 28, No. 6,(1993), pp. 741-762
23 Jonker B. A Finite Element Dynamic Analysis of Flexible Manipulators, International J. of Robotics Research. Vol. 9, No. 4, (1990),pp. 59-74
24 Spong M W. Modeling and Control of Elastic Joint Robots, ASME J. of
Dynamic Systems Measurement Control. vol. 109, No. 4, (1987),pp. 310-319
25 边宇枢、陆震．柔性机器人动力学建模的一种方法．北京航空航天大学学报．Vol．25，No．4，(1999)，pp．486-490
26 Barbieri E, Ozg Uner U. Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link. Journal Dynamic Systems, Measurement, and Control, Vol. 110, No. 4, (1988),pp. 416-421
27 Cait Y, Miklavcivc M, Maccluer C R. Radcliffe C J. A Natural Model Expansion for the Flexible Robot Arm Problem via a Self-Adjoint Formulation IEEE Transaction on Robotics and Automation. Vol. 6, No. 5, (1990),pp. 601-603
28 Morgul O. Orientation and Stabilization of a Flexible beam Attached to a Rigid body: Planar Motion. IEEE Transactions on Automatic Control. Vol. 36, No. 8, (1991),pp. 953-962
29 Choura S, Jayasuriya S, Medick M A. On the Modeling, and Open-Loop Control of a Rotating Thin Flexible Beam, Journal of Dynamic Systems, Measurement, and Control. Vol. 113, No. 1, (1991),pp. 26-33
30 张策等．弹性连杆机构的分析与设计．北京：机械工业出版社，1989
31 Lowen G G and Chassapis C. The Elastic Behavior of Linkages: An Upadate, Mechanism & Machine Theory. Vol. 21, No. 1, (1986),pp. 33-42
32 Book W J. Recursive Lagrangian Dynamics of Flexible Manipulator Arms, Int J Robot Res. Vol. 3, No. 3, (1984),pp. 78-101.
33 De Luca A, and Siciliano B. Closed-form Dynamics Model of Planar Multilink Lightweight Robots. IEEE Trans Sys Man Cybernet. Vol. SMC-21, No. 4,(1991),pp. 826-839
34 Hastings G G and Book W J, Verification of a Linear Dynamic Model for Flexible Robotic Manipulators, Proc IEEE Int Conf Robot Automation. 1986:1024-1029
35 Connelly J D, Huston R L. The dynamics of flexible multibody system:a finite segment approach. Computer & Structures. 1994(50):259-262
36 Ider S K, Amirouche F M L. Nonlinear modeling of flexible multibody system dynamics subjected to variable constrains. Journal of Applied Mechanics. 1989(56):444-450
37 Yu Qing, Hong jiazhen. Static correction modes in dynamic simulation of flexible multibody systems with closed loops. Journal for Shanghai Jiaotong University. 1997(1):17-20
38 Matsuno, Yamamoto, etc. Dynamic hybrid position/force control of a planar two-link structurally flexible manipulator. J of Robotic Systems. Vol. 11, No. 5, (1994),pp. 355-366
39 Cannon R H, Schmits E. Initial experiments on the endpoint control of a flexible one-link robot. The Robotics Research. 1985(3):62-57
40 Chapnik B, Heppler J, Aplevich J. Modelling impact on a one link flexible robot arm. IEEE Transactions on Robotics and Automatic. Vol.7, No. 4, (1991),pp. 479-488
41 赵平，薛克宗．空间柔性机械臂三维动力学数值仿真．工程力学．Vol．13，No．1，(1996)，pp．103-114
42 费从宇，邵成勋．柔性机械臂刚柔耦合运动的摄动分析．应用力学学报．Vol．10，No．3，(1993)，pp．43-48
43 洪嘉振．多体系统动力学-理论、计算方法和应用．上海：上海交大出版社，1992
44 窦建武，余跃庆．柔性机器人协调操作的力可操作性研究．北京工业大学学报．Vol．26，No．3，(2000)，pp．10-15
45 潘振宽，洪嘉振．柔性机械臂动力学方程单向递推组集方法．力学学报．Vol．25，No．3，(1993)，pp．327-333
46 洪嘉振，蒋丽忠．柔性多体系统刚-柔耦合动力学．力学进展．Vol．30，No．1，(2000)，pp．15-20
47 王成国，梁国平．多柔性体系统动力学的有限元法．工程力学．Vol．16，No．2，(1999)，pp．22-28
48 刘宏昭，曹惟庆．多柔体系统动力学的一种数值求解方法．计算机结构力学及其应用．Vol．8，No．3，(1991)，pp．316-325
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