不确定性漂浮基空间机械臂鲁棒控制方法研究
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摘要
随着人类空间活动的不断发展,在未来的空间活动中,将有大量的空间生产、空间加工、空间装配、空间维修等工作进行。这些工作不可能完全由宇航员完成,因为宇航员到太空成本高、风险大。因此必须充分利用空间机器人。而漂浮基空间机械臂由于采用自由漂浮工作模式,可节省燃料,延长使用寿命、降低成本。因此,国内外许多学者对此种空间机械臂的运动学、动力学、控制等方面进行了广泛的研究。
空间机械臂在环境恶劣的太空中工作,会受到许多不确定性因素影响。讨论具有不确定性的漂浮基空间机械臂的动力学、控制等问题具有理论与实际意义,同时也比较复杂。因此,本文主要针对受自身参数不确定和外部干扰影响的不确定性漂浮基空间机械臂系统,对其动力学与控制方面进行研究。
本文首先基于扩展机械臂模型,采用Lagrange方程法,考虑时变参数、外部干扰等不确定性因素,建立任务空间中漂浮基空间机械臂的动力学模型,分析了载体受到的干扰对机械臂产生的影响。并对漂浮基空间机械臂的运动特性(非完整性和姿态干扰特性)进行仿真研究。
其次,针对存在时变参数(滑变参数和跳变参数)和外部干扰的不确定性漂浮基空间机械臂系统,采用经艾格尼西箕舌线修改的σ?修改法对自适应控制器进行鲁棒性修改,分析修改后的自适应鲁棒控制器对时变参数(滑变参数和跳变参数)和外部干扰的鲁棒性。
最后,针对不确定性漂浮基空间机械臂系统,假设时变参数的变化范围、外部干扰的界已知,设计变结构鲁棒控制器,对其进行边界层修改以消除颤振现象。然后,针对时变参数的变化范围、外部干扰界未知的情况,结合自适应控制和变结构鲁棒控制方法设计自适应变结构控制器,同时对其进行了稳定性和鲁棒性分析。
另外,本文利用Matlab的GUI工具设计了仿真界面,该仿真界面集成了漂浮基空间机械臂的运动特性仿真、自适应鲁棒控制仿真和变结构鲁棒控制仿真。对所提的控制算法进行仿真研究,并对仿真结果进行对比分析,验证所提方法的有效性。
With the development of people’s space activities, more and more works such as manufacture, machining, assemblage, maintenance in space will be developed in the future. These works can’t be completed only by astronauts because of high cost and high risk of sending people to the space. Therefore people should take full advantage of space robots. Free floating is one of the most important control modes. This mode can reduce the usage of expensive fuel, extend the life of the space robots and cut a lot of cost. Therefore, there are lots of literatures all over the world addressing the kinematics, dynamics and control method of this kind of space robots.
The atrocious surroundings of the space make space robots be disturbed by many uncertain factors. By far, there have been few literatures addressing the dynamics and control method of space manipulators with uncertainties. Therefore, in this thesis, the dynamics and control method of float-vehicle space manipulators with uncertainties (including parameters uncertainty and external disturbances) will be studied.
Firstly, based on the extended robot model of You-Liang Gu, using Lagrange method, considering the uncertainties of parameters and external disturbances, this thesis deduced the dynamic equation of float-vehicle space manipulators in task space, and discovered the action on manipulators, produced by the disturbances the base affected. Moreover the kinematics characters such as nonholonomic character and attitude-disturb character were studied by simulating.
Secondly, based on the dynamic equation in task space of float-vehicle space manipulators with time varying parameters and external disturbances, considering time varying parameters(smooth and jump ) and external disturbances, in order to improve the robustness of the controller, this thesis modified the adaptive controller usingσ? modify method and analyzed the robustness of the system.
Finally, for float-vehicle space manipulators with time varying parameters and external disturbances, assuming that the bounds of parameters and external disturbances are known, this thesis designed a variable structure controller, and used boundary-layer-modify method to eliminate“chattering”. At last, for the case that the bounds of parameters and external disturbances are not known, this thesis designed an adaptive variable structure controller.
Meanwhile, the stability and effectivity of each kind of proposed controller were proved both with theoretic and simulation study. For the convenience of simulation study, this thesis designed a simulation interface using GUI tools of Matlab. The simulation interface integrates the simulation study of kinematic character analysis, adaptive robust control method and adaptive variable structure control method. By analyzing the simulation result, the effectivity of every proposed controller was validated.
空间机械臂在环境恶劣的太空中工作,会受到许多不确定性因素影响。讨论具有不确定性的漂浮基空间机械臂的动力学、控制等问题具有理论与实际意义,同时也比较复杂。因此,本文主要针对受自身参数不确定和外部干扰影响的不确定性漂浮基空间机械臂系统,对其动力学与控制方面进行研究。
本文首先基于扩展机械臂模型,采用Lagrange方程法,考虑时变参数、外部干扰等不确定性因素,建立任务空间中漂浮基空间机械臂的动力学模型,分析了载体受到的干扰对机械臂产生的影响。并对漂浮基空间机械臂的运动特性(非完整性和姿态干扰特性)进行仿真研究。
其次,针对存在时变参数(滑变参数和跳变参数)和外部干扰的不确定性漂浮基空间机械臂系统,采用经艾格尼西箕舌线修改的σ?修改法对自适应控制器进行鲁棒性修改,分析修改后的自适应鲁棒控制器对时变参数(滑变参数和跳变参数)和外部干扰的鲁棒性。
最后,针对不确定性漂浮基空间机械臂系统,假设时变参数的变化范围、外部干扰的界已知,设计变结构鲁棒控制器,对其进行边界层修改以消除颤振现象。然后,针对时变参数的变化范围、外部干扰界未知的情况,结合自适应控制和变结构鲁棒控制方法设计自适应变结构控制器,同时对其进行了稳定性和鲁棒性分析。
另外,本文利用Matlab的GUI工具设计了仿真界面,该仿真界面集成了漂浮基空间机械臂的运动特性仿真、自适应鲁棒控制仿真和变结构鲁棒控制仿真。对所提的控制算法进行仿真研究,并对仿真结果进行对比分析,验证所提方法的有效性。
With the development of people’s space activities, more and more works such as manufacture, machining, assemblage, maintenance in space will be developed in the future. These works can’t be completed only by astronauts because of high cost and high risk of sending people to the space. Therefore people should take full advantage of space robots. Free floating is one of the most important control modes. This mode can reduce the usage of expensive fuel, extend the life of the space robots and cut a lot of cost. Therefore, there are lots of literatures all over the world addressing the kinematics, dynamics and control method of this kind of space robots.
The atrocious surroundings of the space make space robots be disturbed by many uncertain factors. By far, there have been few literatures addressing the dynamics and control method of space manipulators with uncertainties. Therefore, in this thesis, the dynamics and control method of float-vehicle space manipulators with uncertainties (including parameters uncertainty and external disturbances) will be studied.
Firstly, based on the extended robot model of You-Liang Gu, using Lagrange method, considering the uncertainties of parameters and external disturbances, this thesis deduced the dynamic equation of float-vehicle space manipulators in task space, and discovered the action on manipulators, produced by the disturbances the base affected. Moreover the kinematics characters such as nonholonomic character and attitude-disturb character were studied by simulating.
Secondly, based on the dynamic equation in task space of float-vehicle space manipulators with time varying parameters and external disturbances, considering time varying parameters(smooth and jump ) and external disturbances, in order to improve the robustness of the controller, this thesis modified the adaptive controller usingσ? modify method and analyzed the robustness of the system.
Finally, for float-vehicle space manipulators with time varying parameters and external disturbances, assuming that the bounds of parameters and external disturbances are known, this thesis designed a variable structure controller, and used boundary-layer-modify method to eliminate“chattering”. At last, for the case that the bounds of parameters and external disturbances are not known, this thesis designed an adaptive variable structure controller.
Meanwhile, the stability and effectivity of each kind of proposed controller were proved both with theoretic and simulation study. For the convenience of simulation study, this thesis designed a simulation interface using GUI tools of Matlab. The simulation interface integrates the simulation study of kinematic character analysis, adaptive robust control method and adaptive variable structure control method. By analyzing the simulation result, the effectivity of every proposed controller was validated.
引文
1柳长安,李国栋,吴克河,洪炳熔.自由飞行空间机器人研究综述.机器人. 2002. 24(4):380~383
2葛景华.双臂空间机器人运动学、动力学及控制.福州大学硕士学位论文. 2005:7~10
3 Z. Vafa, S. Dubowsky. The Kinematics and Dynamics of Space Manipulators, The Virtural Manipulator Approach. International Journal of Robotics Research. 1990,9(4):3~21
4 Y. Umetani, K. Yoshida. Resolved Motion Rate Control of Space Manipulators with Generalized Jacobian Matrix. IEEE Transactions on Robotics and Automation. 1989,5(3):303~314
5 S. K. Saha. A Unified Approach to Space Robot Kinematics. IEEE Transactions on Robotics and Automation. 1996,12(3):401~405
6 K. Yamada, K. Ysuchiya. Efficient Computation Algorithms for Manipulator Control of a Space Robot. Transactions of the Society of Instrument and Control Engineers. 1990,26(7):31~38
7 E. Papadopoulos, S. Dubowsky.On the Nature of Control Algorithms for Space Manipulators. IEEE International Conference on Robotics and Automation. 1990,2:1102~1108
8梁斌,刘良栋,李庚田, Xu Yangsheng.空间机器人的动力学等价机械臂.自动化学报. 1998,24(6):761~767
9 E. Papadopoulos, S. Dubowsky. Coordinated Manipulator/Spacecraft Motion Control for Space Robotic Systems. IEEE International Conference on Robotics and Automation. 1991,2:1696~1702
10 S. Dubowsky, E. Papadopoulos.The Kinematics, Dynamics, and Control of Free-Flying and Free-Floating Space Robotic Systems. IEEE Transactions on Robotics and Automation. 1993,9(5):531~543
11袁景阳,柳长安,李瑰贤.有外力作用的多臂自由飞行空间机器人协调操作动力学特性.宇航学报. 2006,27(3):541~545
12 Y. L. Gu, Y. Xu. A Normal Form Augmentation Approach to Adaptive Control of Space Robot Systems, IEEE International Conference on Robotics and Automation, 1993,2: 731~737
13 O. Parlaktuna, M. Ozkan. Adaptive Control of Free-floating Space Robots in Cartesian Coordinates. Advanced Robotics. 2004,18(9):943~959
14张燕红,林兆荣.姿态受控漂浮基空间机器人系统协调运动的反演滑模控制.山东理工大学学报(自然科学版). 2008,22(3):5~9
15 D. Nenchev, Y. Umetani, Kazuya Yoshida. Analysis of a Redundant Free-Flying Spacecraft/Manipulator System. IEEE Transactions on Robotics and Automation. 1992,8(1):1~6
16 D. N. Nenchev, K. Yoshida, M. Uchiyama. Reaction Null-Space Based Control of Flexible Structure Mounted Manipulating Systems. IEEE CDC, Kobe, Japan. 1996,4:4118~4123
17 Y. Xu, T. Kanade, J.J. Lee. Parameterization Control of Space and Adaptive Robot System. IEEE Transactions on Aerospace and Electronic Systems. 1994,30(2):435~451
18 M.W. Walker. Adaptive Control of Space-Based Robot Manipulators. IEEE Transactions on Robotics and Automation. 1992,7(6):828~835
19马保离,霍伟.空间机器人系统的自适应控制.控制理论与应用. 1996,13(2):191~197
20 M. Walker, L. Wee. Adaptive Control Strategy for Space Based Robot Manipulators. IEEE Conference on Robotics and Automation. 1991,2:1673~1680
21 L.Ehrenwald, M. Guelman. Integrated Adaptive Control of Space Manipulators. Journal of Guidance Control and Dynamics. 1998,21(1):156~163
22王昊瀛,王景,吴宏鑫.平面型两关节空间机器人的自适应轨迹控制.航天控制. 1999,(3):13~19
23王景,王昊瀛,刘良栋,梁斌.空间机械臂的鲁棒复合自适应控制.自动化学报. 2002, 28(3):378~384
24 Yangsheng Xu, et al. Robust Control of Free-Floating Space Robot Systems. International Journal of Control. 1995,61(2):261~277
25陈力,刘延柱.参数不确定空间机械臂系统的变结构鲁棒控制.空间科学学报. 1998,18(2):174~179
26陈力.带滑移铰空间机器人惯性空间轨迹跟踪的鲁棒混合自适应控制.工程力学. 2004,21(3):174~179
27陈力.漂浮基带滑移铰空间机器人相对轨迹运动的变结构鲁棒控制.机械科学与技术. 2004,23(6):705~709
28王景,刘良栋,梁斌.任务空间内空间机械臂的一种鲁棒自适应控制.航天控制. 2000,1:37~43
29 Chu Zhongyi, Sun Fuchun, Cui Jing. Disturbance Observer-Based Robust Control of Free-Floating Space Manipulators. IEEE System Journal. 2008,2(1):114~119
30 B.M. Feng, G.C. Ma et al. Adaptive Robust Control of Space Robot in Task Space. Proceedings of IEEE International Conference on Mechatronics and Automation, Luoyang, China, 2006:1571~1576
31丰保民,马广程,温奇咏.任务空间内空间机器人鲁棒智能控制器设计.宇航学报. 2007,28(4):914~919
32郭益深,陈力.漂浮基姿态受控空间机械臂关节运动的自适应神经网络控制.空间科学学报. 2008,28(2):173~179
33郭益深,陈力.具有外部扰动的空间刚性机械臂姿态与末端爪手协调运动的Terminal滑模控制算法设计.应用数学和力学. 2008,29(5):525~532
34 S.A. Moosavian, M.R. Homaeinejad. Control of Space Free-Flying Robots Using Regulated Sliding Mode Controller. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, 2006:3131~3136
35代颖,施颂椒.综合的机器人鲁棒自适应控制.上海交通大学学报. 1999,33(10):1272~1275
36代颖,施颂椒,郑南宁.一类关于不确定性机器人的鲁棒控制策略研究.自动化学报. 1999,25(2):204~209
37 J.J. Slotine, W. Li. On the Adaptive Control of Manipulators. International Journal of Robotics Research. 1987,6(3):49~59
38 C. Abdallah, D. Dawson, P. Dorato, M. Jamshidi. Survey of Robust Control for Rigid Robots. Control Systems Magazine, IEEE. 1991,11(2):24~30
39 J-J.E.Slotine. the Robust Control of Robot Manipulators. International Journal of Robotics Research. 1985,4:49~64
40 J-J.E.Slotine, S.S.Sastry. Tracking Control of Nonlinear Systems Using Sliding Surfaces with Applications to Robot Manipulators. International Journal of Control. 1983,38:465~492
41 T. Furuta, K. Tomiyama. Sliding Mode Controller with Time-Varying Hypeplane. IEEE/RSJ International Conference on Intelligent Robots and Systems. 1996,2:576~581
42 K. Kreutz. On Manipulator Control by Exact Linearization. IEEE Transaction of Automation and Control. 1989,34:763~767
43 L. Bascetta, P. Rocco. Revising the Robust Control Design for Rigid Robot Manipulators. IEEE International Conference on Robotics and Automation. 2007:4478~4483
44 Guangjun Liu, A.A. Goldenberg. Uncertainty Decomposition-Based Robust Control of Robot Manipulators. IEEE Transactions on Control Systems Technology. 1996,4(4):384~393
45 P.R. Pagilla, Yongliang Zhu. Adaptive Control of Mechanical Systems with Time-Varying Parameters and Disturbances. Transaction of the ASME. 2004,126:520~530
46 S. Torres, J.A. Méndez, et al. Efficient Control of Robot Manipulators with Model Disturbances. Proceedings of the 45th CDC, San Diego, CA, USA, 2006:2931~2936
47 J. J. Slotine, Weiping Li. Applied Nonlinear Control.程代展.机械工业出版社, 2006:130~131
48 J. J. Slotine, W.P. Li. Composite Adaptive Control of Robot Manipulators. Automatica. 1989,25(4):509~519
49 R. Ortega, M.W. Spong. Adaptive Motion Control of Rigid Robots: a Tutorial Automatica. 1989,25(6):877~888
50 R. Ortega, Y. Tang. Robustness of Adaptive Controllers-a Survey. Automatica. 1989,25(5):651~677
51 J.S. Reed, P.A. Ioannou. Instability Analysis and Robust Adaptive Control of Robotic Manipulators. Proceedings of the 27th CDC, Austin, Texas, 1988:1607~1612
52 T. Furuta, K. Tomiyama. Sliding Mode Controller with Time-Varying Hyperplane. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Osaka, 1996:576~581
53 S. S. You, J. L. Hall. Model-Based Approach with Adaptive Bounds of Robust Controllers for Robot Manipulators. IEEE International Conference on Systems, Man and Cybernetics, San Antonio, TX, 1994:1279~1284
54宋佐时.基于计算力矩结构的不确定性机器人控制策略研究.燕山大学工学硕士学位论文. 2002:22~43
55 Y.H. Chen, C.Y. Kuo. Fundamental Properties of Rigid Serial Manipulators for Control Design. Proceedings of the American Control Conference, San Diego, California, 1999:3003~3007
2葛景华.双臂空间机器人运动学、动力学及控制.福州大学硕士学位论文. 2005:7~10
3 Z. Vafa, S. Dubowsky. The Kinematics and Dynamics of Space Manipulators, The Virtural Manipulator Approach. International Journal of Robotics Research. 1990,9(4):3~21
4 Y. Umetani, K. Yoshida. Resolved Motion Rate Control of Space Manipulators with Generalized Jacobian Matrix. IEEE Transactions on Robotics and Automation. 1989,5(3):303~314
5 S. K. Saha. A Unified Approach to Space Robot Kinematics. IEEE Transactions on Robotics and Automation. 1996,12(3):401~405
6 K. Yamada, K. Ysuchiya. Efficient Computation Algorithms for Manipulator Control of a Space Robot. Transactions of the Society of Instrument and Control Engineers. 1990,26(7):31~38
7 E. Papadopoulos, S. Dubowsky.On the Nature of Control Algorithms for Space Manipulators. IEEE International Conference on Robotics and Automation. 1990,2:1102~1108
8梁斌,刘良栋,李庚田, Xu Yangsheng.空间机器人的动力学等价机械臂.自动化学报. 1998,24(6):761~767
9 E. Papadopoulos, S. Dubowsky. Coordinated Manipulator/Spacecraft Motion Control for Space Robotic Systems. IEEE International Conference on Robotics and Automation. 1991,2:1696~1702
10 S. Dubowsky, E. Papadopoulos.The Kinematics, Dynamics, and Control of Free-Flying and Free-Floating Space Robotic Systems. IEEE Transactions on Robotics and Automation. 1993,9(5):531~543
11袁景阳,柳长安,李瑰贤.有外力作用的多臂自由飞行空间机器人协调操作动力学特性.宇航学报. 2006,27(3):541~545
12 Y. L. Gu, Y. Xu. A Normal Form Augmentation Approach to Adaptive Control of Space Robot Systems, IEEE International Conference on Robotics and Automation, 1993,2: 731~737
13 O. Parlaktuna, M. Ozkan. Adaptive Control of Free-floating Space Robots in Cartesian Coordinates. Advanced Robotics. 2004,18(9):943~959
14张燕红,林兆荣.姿态受控漂浮基空间机器人系统协调运动的反演滑模控制.山东理工大学学报(自然科学版). 2008,22(3):5~9
15 D. Nenchev, Y. Umetani, Kazuya Yoshida. Analysis of a Redundant Free-Flying Spacecraft/Manipulator System. IEEE Transactions on Robotics and Automation. 1992,8(1):1~6
16 D. N. Nenchev, K. Yoshida, M. Uchiyama. Reaction Null-Space Based Control of Flexible Structure Mounted Manipulating Systems. IEEE CDC, Kobe, Japan. 1996,4:4118~4123
17 Y. Xu, T. Kanade, J.J. Lee. Parameterization Control of Space and Adaptive Robot System. IEEE Transactions on Aerospace and Electronic Systems. 1994,30(2):435~451
18 M.W. Walker. Adaptive Control of Space-Based Robot Manipulators. IEEE Transactions on Robotics and Automation. 1992,7(6):828~835
19马保离,霍伟.空间机器人系统的自适应控制.控制理论与应用. 1996,13(2):191~197
20 M. Walker, L. Wee. Adaptive Control Strategy for Space Based Robot Manipulators. IEEE Conference on Robotics and Automation. 1991,2:1673~1680
21 L.Ehrenwald, M. Guelman. Integrated Adaptive Control of Space Manipulators. Journal of Guidance Control and Dynamics. 1998,21(1):156~163
22王昊瀛,王景,吴宏鑫.平面型两关节空间机器人的自适应轨迹控制.航天控制. 1999,(3):13~19
23王景,王昊瀛,刘良栋,梁斌.空间机械臂的鲁棒复合自适应控制.自动化学报. 2002, 28(3):378~384
24 Yangsheng Xu, et al. Robust Control of Free-Floating Space Robot Systems. International Journal of Control. 1995,61(2):261~277
25陈力,刘延柱.参数不确定空间机械臂系统的变结构鲁棒控制.空间科学学报. 1998,18(2):174~179
26陈力.带滑移铰空间机器人惯性空间轨迹跟踪的鲁棒混合自适应控制.工程力学. 2004,21(3):174~179
27陈力.漂浮基带滑移铰空间机器人相对轨迹运动的变结构鲁棒控制.机械科学与技术. 2004,23(6):705~709
28王景,刘良栋,梁斌.任务空间内空间机械臂的一种鲁棒自适应控制.航天控制. 2000,1:37~43
29 Chu Zhongyi, Sun Fuchun, Cui Jing. Disturbance Observer-Based Robust Control of Free-Floating Space Manipulators. IEEE System Journal. 2008,2(1):114~119
30 B.M. Feng, G.C. Ma et al. Adaptive Robust Control of Space Robot in Task Space. Proceedings of IEEE International Conference on Mechatronics and Automation, Luoyang, China, 2006:1571~1576
31丰保民,马广程,温奇咏.任务空间内空间机器人鲁棒智能控制器设计.宇航学报. 2007,28(4):914~919
32郭益深,陈力.漂浮基姿态受控空间机械臂关节运动的自适应神经网络控制.空间科学学报. 2008,28(2):173~179
33郭益深,陈力.具有外部扰动的空间刚性机械臂姿态与末端爪手协调运动的Terminal滑模控制算法设计.应用数学和力学. 2008,29(5):525~532
34 S.A. Moosavian, M.R. Homaeinejad. Control of Space Free-Flying Robots Using Regulated Sliding Mode Controller. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, 2006:3131~3136
35代颖,施颂椒.综合的机器人鲁棒自适应控制.上海交通大学学报. 1999,33(10):1272~1275
36代颖,施颂椒,郑南宁.一类关于不确定性机器人的鲁棒控制策略研究.自动化学报. 1999,25(2):204~209
37 J.J. Slotine, W. Li. On the Adaptive Control of Manipulators. International Journal of Robotics Research. 1987,6(3):49~59
38 C. Abdallah, D. Dawson, P. Dorato, M. Jamshidi. Survey of Robust Control for Rigid Robots. Control Systems Magazine, IEEE. 1991,11(2):24~30
39 J-J.E.Slotine. the Robust Control of Robot Manipulators. International Journal of Robotics Research. 1985,4:49~64
40 J-J.E.Slotine, S.S.Sastry. Tracking Control of Nonlinear Systems Using Sliding Surfaces with Applications to Robot Manipulators. International Journal of Control. 1983,38:465~492
41 T. Furuta, K. Tomiyama. Sliding Mode Controller with Time-Varying Hypeplane. IEEE/RSJ International Conference on Intelligent Robots and Systems. 1996,2:576~581
42 K. Kreutz. On Manipulator Control by Exact Linearization. IEEE Transaction of Automation and Control. 1989,34:763~767
43 L. Bascetta, P. Rocco. Revising the Robust Control Design for Rigid Robot Manipulators. IEEE International Conference on Robotics and Automation. 2007:4478~4483
44 Guangjun Liu, A.A. Goldenberg. Uncertainty Decomposition-Based Robust Control of Robot Manipulators. IEEE Transactions on Control Systems Technology. 1996,4(4):384~393
45 P.R. Pagilla, Yongliang Zhu. Adaptive Control of Mechanical Systems with Time-Varying Parameters and Disturbances. Transaction of the ASME. 2004,126:520~530
46 S. Torres, J.A. Méndez, et al. Efficient Control of Robot Manipulators with Model Disturbances. Proceedings of the 45th CDC, San Diego, CA, USA, 2006:2931~2936
47 J. J. Slotine, Weiping Li. Applied Nonlinear Control.程代展.机械工业出版社, 2006:130~131
48 J. J. Slotine, W.P. Li. Composite Adaptive Control of Robot Manipulators. Automatica. 1989,25(4):509~519
49 R. Ortega, M.W. Spong. Adaptive Motion Control of Rigid Robots: a Tutorial Automatica. 1989,25(6):877~888
50 R. Ortega, Y. Tang. Robustness of Adaptive Controllers-a Survey. Automatica. 1989,25(5):651~677
51 J.S. Reed, P.A. Ioannou. Instability Analysis and Robust Adaptive Control of Robotic Manipulators. Proceedings of the 27th CDC, Austin, Texas, 1988:1607~1612
52 T. Furuta, K. Tomiyama. Sliding Mode Controller with Time-Varying Hyperplane. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Osaka, 1996:576~581
53 S. S. You, J. L. Hall. Model-Based Approach with Adaptive Bounds of Robust Controllers for Robot Manipulators. IEEE International Conference on Systems, Man and Cybernetics, San Antonio, TX, 1994:1279~1284
54宋佐时.基于计算力矩结构的不确定性机器人控制策略研究.燕山大学工学硕士学位论文. 2002:22~43
55 Y.H. Chen, C.Y. Kuo. Fundamental Properties of Rigid Serial Manipulators for Control Design. Proceedings of the American Control Conference, San Diego, California, 1999:3003~3007