基于LMI移动机器人鲁棒控制研究
|
摘要
如果将机器人看作是一种能够扩展人类工作能力的有效工具，那么人类在认识和改造世界的过程中就不能没有机器人。移动机器人是机器人家族中的一个重要分支，也是进一步扩展机器人应用领域的重要研究发展方向，因此对移动机器人运动控制问题的研究，一直受到普遍关注。
本文针对近年来在移动机器人运动控制方面的热点问题——包含不确定扰动输入的完整约束轮式移动机器人的运动控制和干扰抑制问题——进行了深入和细致的研究。该研究课题以中国科学院沈阳自动化研究所机器人学开放实验室的全方位自主移动机器人作为被控制对象，它是由正交轮结构组成的完整约束移动机器人，也是在平坦环境下工作的自主机器人的理想载体。主要研究结果如下：
1．线性化方法的研究：总结了非线性控制理论与应用中几种解决线性化问题的思想和方法。针对移动机器人控制领域中一类多输入多输出仿射非线性系统，简化了一种基于平衡流形的近似线性化状态反馈镇定算法，并用此算法解决了一类完整约束轮式移动机器人的镇定问题。
2．降阶方法的研究：简要介绍了模型和控制器降阶的几种常用方法，并且针对一类包含不确定扰动输入的移动机器人系统，根据数学模型自身的特点，提出了满足鲁棒性的降阶控制器设计的充分条件及相关推论。
3．基于LMI的H_∞控制问题研究：根据降阶方法研究中给出的定理及推论，提出了一种基于LMI通过局部反馈H_∞控制实现整个系统对不确定扰动具有鲁棒性的算法，并用此算法解决了机器人控制领域中一类结构特殊的含有不确定扰动多输入多输出线性时不变高阶系统的H_∞控制问题。
4．通过仿真实验，分析并验证了论文中提出的定理、推论及算法的合理性和有效件。
Since robot can be viewed as an effective extension of human's motor ability, it is sure to be indispensable in the course of recognition and exploration of the world. Due to its important role in theory and application, the motion control of mobile robot has been given enough attention by researchers in the world.
In this thesis, the problems of motion control and perturbance restraint to a wheeled mobile robot with holonomic constraints including uncertain inputs, the pop problems in the field of motion control to mobile robot in recent years, are investigated deeply and thoughtfully. The orthogonal-wheeled mobile robot of the key robotics Lab in Shenyang institute of automation Chinese academy of sciences is the controlled object. It is a mobile robot with holonomic constrains composed of orthogonal-wheels and a ideal carrier in flat surroundings. The main conclusions are given as follows:
1. Investigation to the method of linearization: Summarizing the idea and the method of linearization. Considering a MIMO nonlinear system, an approximate linearizing stability via state feedback algorithm based on balanced flow pattern is simplified and applying this algorithm to a mobile robot with holonomic constraints.
2. Investigation to the method of order-decreasing: Simply introducing the idea and the method of order-decreasing for model and control. Considering a class of MIMO high-order LTI system including uncertain inputs in robot control field, according to the composition of the mathematics model, sufficient conditions and deduction for designing an order-decreasing control that meeting the robust quality are presented.
3. Investigation to the method of H control based on LMI: According to the sufficient conditions and deduction presented in the investigation to the method of order-decreasing, a new algorithm to solve H control problem for a kind of MIMO high-order LTT system is also proposed. Then apply this algorithm to a wheeled mobile robot with holonomic constraints.
4. The simulation results demonstrate the efficiency of the sufficient conditions, deduction and method.
本文针对近年来在移动机器人运动控制方面的热点问题——包含不确定扰动输入的完整约束轮式移动机器人的运动控制和干扰抑制问题——进行了深入和细致的研究。该研究课题以中国科学院沈阳自动化研究所机器人学开放实验室的全方位自主移动机器人作为被控制对象，它是由正交轮结构组成的完整约束移动机器人，也是在平坦环境下工作的自主机器人的理想载体。主要研究结果如下：
1．线性化方法的研究：总结了非线性控制理论与应用中几种解决线性化问题的思想和方法。针对移动机器人控制领域中一类多输入多输出仿射非线性系统，简化了一种基于平衡流形的近似线性化状态反馈镇定算法，并用此算法解决了一类完整约束轮式移动机器人的镇定问题。
2．降阶方法的研究：简要介绍了模型和控制器降阶的几种常用方法，并且针对一类包含不确定扰动输入的移动机器人系统，根据数学模型自身的特点，提出了满足鲁棒性的降阶控制器设计的充分条件及相关推论。
3．基于LMI的H_∞控制问题研究：根据降阶方法研究中给出的定理及推论，提出了一种基于LMI通过局部反馈H_∞控制实现整个系统对不确定扰动具有鲁棒性的算法，并用此算法解决了机器人控制领域中一类结构特殊的含有不确定扰动多输入多输出线性时不变高阶系统的H_∞控制问题。
4．通过仿真实验，分析并验证了论文中提出的定理、推论及算法的合理性和有效件。
Since robot can be viewed as an effective extension of human's motor ability, it is sure to be indispensable in the course of recognition and exploration of the world. Due to its important role in theory and application, the motion control of mobile robot has been given enough attention by researchers in the world.
In this thesis, the problems of motion control and perturbance restraint to a wheeled mobile robot with holonomic constraints including uncertain inputs, the pop problems in the field of motion control to mobile robot in recent years, are investigated deeply and thoughtfully. The orthogonal-wheeled mobile robot of the key robotics Lab in Shenyang institute of automation Chinese academy of sciences is the controlled object. It is a mobile robot with holonomic constrains composed of orthogonal-wheels and a ideal carrier in flat surroundings. The main conclusions are given as follows:
1. Investigation to the method of linearization: Summarizing the idea and the method of linearization. Considering a MIMO nonlinear system, an approximate linearizing stability via state feedback algorithm based on balanced flow pattern is simplified and applying this algorithm to a mobile robot with holonomic constraints.
2. Investigation to the method of order-decreasing: Simply introducing the idea and the method of order-decreasing for model and control. Considering a class of MIMO high-order LTI system including uncertain inputs in robot control field, according to the composition of the mathematics model, sufficient conditions and deduction for designing an order-decreasing control that meeting the robust quality are presented.
3. Investigation to the method of H control based on LMI: According to the sufficient conditions and deduction presented in the investigation to the method of order-decreasing, a new algorithm to solve H control problem for a kind of MIMO high-order LTT system is also proposed. Then apply this algorithm to a wheeled mobile robot with holonomic constraints.
4. The simulation results demonstrate the efficiency of the sufficient conditions, deduction and method.
引文
[1] 蔡自兴．机器人学．北京：清华大学出版社，2000
[2] 谈大龙．关于我国智能机器人研究的几点想法．机器人，1992，14(4)：47～49
[3] 孙增圻，严隽薇，钱宗华．机器人智能控制．太原：山西教育出版社，1995
[4] Steven, M. Lavall and Seth A. Hutchinson. An objective-based framework for motion planning under sensing and control uncertainty. Int. J. Robotics Research, pp19-42, 1998
[5] Th. Fraichard and R. Mermond. Path planning with uncertainty for car-like robots. IEEE Int. Conference on Robot and Automation, pp27-32, 1998
[6] M. Khatib, B. Bouilly, T. Simeon, R. Chatila. Indoor navigation with uncertainty using sense-based motions. Proceedings of the 1997 IEEE International Conference on Robotics & Automation, pp3379-3384, 1997
[7] Latombe, Lazanas, Shekhar. Robot motion planning with uncertainty in control and sensing. Artificial Intell, Vol. (52), ppl-47, 1991
[8] Lozano-Perez, T. Mason, M. T. and Taylor, R. H. Automatic synthesis of fine-motion strategies for robots. Int. J. Robotics Research, pp3-24, 1984
[9] Laurent Dubois, Toshio Fukud. A approximate reasoning for the control of a robot in an uncertain environment a multi-model approach. Proceedings of the 1997 IEEE International Conference on Robotics & Automation, pp823-828, 1997
[10] Walcott, B. L. Zak, S. H. Combined observer-controller synthesis for nonlinear uncertain dynamical system. Proceedings of the 1987 American Control Conference, Vol. (2), pp868-873, 1997
[11] Dong Sun, James K. Mills. Adaptive learning control of robotic system with model uncertainty. Proceedings of the 1998 IEEE International Conference on Robotics & Automation, pp1847-1853, 1998
[12] T. Tsubouchi and M. Rude. Motion planning for mobile robots in a time-varying environment. J. of Robotics and Mechatrortics, Vol. (8), No. 1, ppl 5-24, 1996
[13] Doyle J C, Glover K, Khargonekar P P, Francis B A. State space solutions to standard H_2 and H_∞ control problems. IEEE Trans. Aut. Control, 1989, 34:831-847
[14] Kimum H, Lu Y, Kawatani R J. On the structure of H_∞ control systems and related extensions. IEEE Trans. Automat. Control, 1991, 36:653-667
[15] Stoorvogel A A. The singular HH_∞ conrtol with dynamic measurement feedback. SIAM J. Control Optimiz, 1991, 29:160-184
[16] Ball J A, Helton J W, Walker M L. H_∞ control for nonliner system with output feedback. IEEE Trans. Automat. Control, 1993, 38:546-559
[17] Glover K, Doyle J C. State-space formulae for all stabilizing controllers that satisfy anH_∞ norm bound and relations to risk sensitivity. Systems & Control Letters, 1988, 167-172
[18] Tadmor G. Worst-case design in the time domain: the maximum principle and the standard H_∞ problem. Syst. Signal Processing, 1989, 28:1190-1208
[19] Kimura H. Chain-scattering representation, J-lossless factorization and H_∞ control. Journal of Mathematical Systems, Estimation and Control, 1995, 5:204-255
[20] 冯纯伯，费树岷．非线性控制系统分析与设计．北京：电子工业出版社，1998
[21] 胡跃明．非线性控制系统理论与应用．北京：国防工业出版社，2002
[22] Vidyasagar M. Nonlinear Systems Analysis, Prentice-Hall, 1993
[23] Isidori A. Nonlinear control systems. 2nd Edition. New York: Springer-Verlag, 1989
[24] Brockett R W. Volterra series and geometry control theory. Automatica, 1976, 12: 167-176
[25] Jakubczyk B, Respondek W. On linearization of control systems. Bull A cad Polonaise Sci Ser Sci Math, 1980, 28:517-522
[26] 卢强，孙元章．电力系统非线性控制．北京：科学出版社，1993
[27] Charlet B, J Levine, R Marino. Dynamic feedback linearization and applications.to aircraft control. In: Proc 27th IEEE Conference on Decision control. Austin, 1988. 701-705
[28] Pei Hai-long, Zhou Qi-jie, Leung T P. Approximate linearization of nonlinear systems: A neural network approach. In: Proc of the 1996 IEEE International Symposium on Intelligent Control. Dearborn, 1996. 444-449
[29] Hauser J. Nonlinear control via uniform system approximation. Syst Contr Lett, 1991,17:145-154
[30] Baumann W T, Rugh W J. Feedback control of nonlinear systems by extended linearization. IEEE Trans A C, 1986, 31:40-46
[31] Krener A J. Approximate linearization by state feedback and coordinate changes. Syst Contr Lett, 1984, 5:181-185
[32] Hunt L R, Turi. A new algorithm for constructing approximate transformations for nonlinear systems. IEEE Trans A C, 1993, 38:1553-1556
[33] Ghannadan R, Blandenship G. Adaptive control of nonlinear systems via approximate lineadzation. IEEE Trans A C, 1996, 41: 618-625
[34] Doyle F J, Frank Allgower, Mantled Morari, A normal form approximate input-output linearization for maximum phase nonlinear SISO systems. IEEE Trans A C,1996, 41:305-309
[35] Hauser J, S Sastry, P Kokotovic. Nonlinear control via approximate input-output linearization: the ball and beam example. IEEE Trans A C, 1992, 37:392-398
[36] 郭朝晖．非线性系统的鲁棒控制及应用．浙江大学博士学位论文，1997
[37] Bultheel, A. and Van Baral, M. Pade techniques for model reduction in linear system theory: a survey, Journal of Computation and Applied Mathematics, Vol. 14, 1986, 401-438
[38] Mahmoud M S, Singh M G. Large scale systems modeling. Oxford: Pergamon Press, 1981:123-143
[39] Jamshidi M. Large-scale systems modeling and control. New York: North-Holland, 1983:165-180
[40] Chen B S, Cheng Y M. A structure-specified H_∞ optimal control design for practical application: a genetic approach. IEEE Trans. On Control System Technology. 1998, 6(6): 707-718
[41] 李孝安，戴冠中．一种基于遗传算法与进化编程的系统辨识方法．控制与决策，1996，11(3)：404-407
[42] 黄炯等．基于遗传算法的系统在线辨识．信息与控制，1996，25(3)：171-176
[43] 孙秀霞，毛剑琴．基于凸优化和投影原理的降阶控制器设计方法研究．控制与决策，2000，15(4)：458-460
[44] 祝小平，陈士橹．一种简便的模型降阶处理方法．南京航空航天大学学报，1994，26(4)：464-470
[45] Li Y, Tan K C, Gong M. Global structure evolution and local parameter learning for control system model reduction. In: Dasgupta D, Michalewicz Z, Eds. Evolutionary Algorithms in Engineering Applications[C]. Berlin: Springer-Vedag, 1997, 345-360
[46] Grigoriadis K M, Skelton R E. Low order control design for LMI problems using alternating projection methods. Automatica, 1995, 32(8): 1117-1125
[47] Swei S M, Rorea M A. System order reduction in robust stabilization problems. Int. J Contr, 1994, 60(2): 223-241
[48] Palhares R M, Peres P L D. Robust H_∞ filtering design with pole placement constraint via LMIs. Journal of Optimization Theory and Applications, 1999, 102(2): 239-261
[49] Oliveira M C, Geromel J C, Bemussou J. An LMI optimization approach to multi- objective conrtoller design for discrete-time systems. Proceedings of the 38th IEEE Conference on Decision & Control, Phoenix, Arizona, 1999, 3611-3616
[50] Chilali M, Gahinet P, Apkarian P. Robust pole placement in LMI regions. IEEE Trans. On Automatic Control, 1999, 44(12): 2257-2270
[51] 褚健，俞立，苏宏业．鲁棒控制理论及应用．浙江：浙江大学出版社，2000
[52] 冯纯伯，田玉平，忻欣．鲁棒控制系统设计．江苏：东南大学出版社，1995
[53] Esfahani S H, Petersen I R. An LMI approach to output-feedback guaranteed cost control for uncertain time-delay systems. International Journal of Robust and Nonlinear Control, 2000, 10(2): 157-174
[54] Gahinet P, Nemirovski A, Laub A J, Chilali M. LMI control toolbox-for use with matlab, The MATH Works Inc, 1995
[55] 俞立．鲁棒控制_—线性矩阵不等式处理方法．北京：清华大学出版社，2002
[56] Stephen B, Eric F, Laurent E G, Venkataramanan B. Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics, Philadelphia, 1994
[57] 刘开周．移动机器人具有不确定性时扰动建模与鲁棒控制．沈阳工业大学硕士论文，2002
[58] 邱尚涛等．现代工程数学及应用．北京：中国电力出版社，2001
[59] 谢学书，钟宜生．H_∞控制理论．北京：清华大学出版社，1994
[60] 申铁龙．H_∞控制理论及应用．北京：清华大学出版社，1996
[61] Latombe J C. Robot motion planning. Boston Kluwer Academic, 1991
[2] 谈大龙．关于我国智能机器人研究的几点想法．机器人，1992，14(4)：47～49
[3] 孙增圻，严隽薇，钱宗华．机器人智能控制．太原：山西教育出版社，1995
[4] Steven, M. Lavall and Seth A. Hutchinson. An objective-based framework for motion planning under sensing and control uncertainty. Int. J. Robotics Research, pp19-42, 1998
[5] Th. Fraichard and R. Mermond. Path planning with uncertainty for car-like robots. IEEE Int. Conference on Robot and Automation, pp27-32, 1998
[6] M. Khatib, B. Bouilly, T. Simeon, R. Chatila. Indoor navigation with uncertainty using sense-based motions. Proceedings of the 1997 IEEE International Conference on Robotics & Automation, pp3379-3384, 1997
[7] Latombe, Lazanas, Shekhar. Robot motion planning with uncertainty in control and sensing. Artificial Intell, Vol. (52), ppl-47, 1991
[8] Lozano-Perez, T. Mason, M. T. and Taylor, R. H. Automatic synthesis of fine-motion strategies for robots. Int. J. Robotics Research, pp3-24, 1984
[9] Laurent Dubois, Toshio Fukud. A approximate reasoning for the control of a robot in an uncertain environment a multi-model approach. Proceedings of the 1997 IEEE International Conference on Robotics & Automation, pp823-828, 1997
[10] Walcott, B. L. Zak, S. H. Combined observer-controller synthesis for nonlinear uncertain dynamical system. Proceedings of the 1987 American Control Conference, Vol. (2), pp868-873, 1997
[11] Dong Sun, James K. Mills. Adaptive learning control of robotic system with model uncertainty. Proceedings of the 1998 IEEE International Conference on Robotics & Automation, pp1847-1853, 1998
[12] T. Tsubouchi and M. Rude. Motion planning for mobile robots in a time-varying environment. J. of Robotics and Mechatrortics, Vol. (8), No. 1, ppl 5-24, 1996
[13] Doyle J C, Glover K, Khargonekar P P, Francis B A. State space solutions to standard H_2 and H_∞ control problems. IEEE Trans. Aut. Control, 1989, 34:831-847
[14] Kimum H, Lu Y, Kawatani R J. On the structure of H_∞ control systems and related extensions. IEEE Trans. Automat. Control, 1991, 36:653-667
[15] Stoorvogel A A. The singular HH_∞ conrtol with dynamic measurement feedback. SIAM J. Control Optimiz, 1991, 29:160-184
[16] Ball J A, Helton J W, Walker M L. H_∞ control for nonliner system with output feedback. IEEE Trans. Automat. Control, 1993, 38:546-559
[17] Glover K, Doyle J C. State-space formulae for all stabilizing controllers that satisfy anH_∞ norm bound and relations to risk sensitivity. Systems & Control Letters, 1988, 167-172
[18] Tadmor G. Worst-case design in the time domain: the maximum principle and the standard H_∞ problem. Syst. Signal Processing, 1989, 28:1190-1208
[19] Kimura H. Chain-scattering representation, J-lossless factorization and H_∞ control. Journal of Mathematical Systems, Estimation and Control, 1995, 5:204-255
[20] 冯纯伯，费树岷．非线性控制系统分析与设计．北京：电子工业出版社，1998
[21] 胡跃明．非线性控制系统理论与应用．北京：国防工业出版社，2002
[22] Vidyasagar M. Nonlinear Systems Analysis, Prentice-Hall, 1993
[23] Isidori A. Nonlinear control systems. 2nd Edition. New York: Springer-Verlag, 1989
[24] Brockett R W. Volterra series and geometry control theory. Automatica, 1976, 12: 167-176
[25] Jakubczyk B, Respondek W. On linearization of control systems. Bull A cad Polonaise Sci Ser Sci Math, 1980, 28:517-522
[26] 卢强，孙元章．电力系统非线性控制．北京：科学出版社，1993
[27] Charlet B, J Levine, R Marino. Dynamic feedback linearization and applications.to aircraft control. In: Proc 27th IEEE Conference on Decision control. Austin, 1988. 701-705
[28] Pei Hai-long, Zhou Qi-jie, Leung T P. Approximate linearization of nonlinear systems: A neural network approach. In: Proc of the 1996 IEEE International Symposium on Intelligent Control. Dearborn, 1996. 444-449
[29] Hauser J. Nonlinear control via uniform system approximation. Syst Contr Lett, 1991,17:145-154
[30] Baumann W T, Rugh W J. Feedback control of nonlinear systems by extended linearization. IEEE Trans A C, 1986, 31:40-46
[31] Krener A J. Approximate linearization by state feedback and coordinate changes. Syst Contr Lett, 1984, 5:181-185
[32] Hunt L R, Turi. A new algorithm for constructing approximate transformations for nonlinear systems. IEEE Trans A C, 1993, 38:1553-1556
[33] Ghannadan R, Blandenship G. Adaptive control of nonlinear systems via approximate lineadzation. IEEE Trans A C, 1996, 41: 618-625
[34] Doyle F J, Frank Allgower, Mantled Morari, A normal form approximate input-output linearization for maximum phase nonlinear SISO systems. IEEE Trans A C,1996, 41:305-309
[35] Hauser J, S Sastry, P Kokotovic. Nonlinear control via approximate input-output linearization: the ball and beam example. IEEE Trans A C, 1992, 37:392-398
[36] 郭朝晖．非线性系统的鲁棒控制及应用．浙江大学博士学位论文，1997
[37] Bultheel, A. and Van Baral, M. Pade techniques for model reduction in linear system theory: a survey, Journal of Computation and Applied Mathematics, Vol. 14, 1986, 401-438
[38] Mahmoud M S, Singh M G. Large scale systems modeling. Oxford: Pergamon Press, 1981:123-143
[39] Jamshidi M. Large-scale systems modeling and control. New York: North-Holland, 1983:165-180
[40] Chen B S, Cheng Y M. A structure-specified H_∞ optimal control design for practical application: a genetic approach. IEEE Trans. On Control System Technology. 1998, 6(6): 707-718
[41] 李孝安，戴冠中．一种基于遗传算法与进化编程的系统辨识方法．控制与决策，1996，11(3)：404-407
[42] 黄炯等．基于遗传算法的系统在线辨识．信息与控制，1996，25(3)：171-176
[43] 孙秀霞，毛剑琴．基于凸优化和投影原理的降阶控制器设计方法研究．控制与决策，2000，15(4)：458-460
[44] 祝小平，陈士橹．一种简便的模型降阶处理方法．南京航空航天大学学报，1994，26(4)：464-470
[45] Li Y, Tan K C, Gong M. Global structure evolution and local parameter learning for control system model reduction. In: Dasgupta D, Michalewicz Z, Eds. Evolutionary Algorithms in Engineering Applications[C]. Berlin: Springer-Vedag, 1997, 345-360
[46] Grigoriadis K M, Skelton R E. Low order control design for LMI problems using alternating projection methods. Automatica, 1995, 32(8): 1117-1125
[47] Swei S M, Rorea M A. System order reduction in robust stabilization problems. Int. J Contr, 1994, 60(2): 223-241
[48] Palhares R M, Peres P L D. Robust H_∞ filtering design with pole placement constraint via LMIs. Journal of Optimization Theory and Applications, 1999, 102(2): 239-261
[49] Oliveira M C, Geromel J C, Bemussou J. An LMI optimization approach to multi- objective conrtoller design for discrete-time systems. Proceedings of the 38th IEEE Conference on Decision & Control, Phoenix, Arizona, 1999, 3611-3616
[50] Chilali M, Gahinet P, Apkarian P. Robust pole placement in LMI regions. IEEE Trans. On Automatic Control, 1999, 44(12): 2257-2270
[51] 褚健，俞立，苏宏业．鲁棒控制理论及应用．浙江：浙江大学出版社，2000
[52] 冯纯伯，田玉平，忻欣．鲁棒控制系统设计．江苏：东南大学出版社，1995
[53] Esfahani S H, Petersen I R. An LMI approach to output-feedback guaranteed cost control for uncertain time-delay systems. International Journal of Robust and Nonlinear Control, 2000, 10(2): 157-174
[54] Gahinet P, Nemirovski A, Laub A J, Chilali M. LMI control toolbox-for use with matlab, The MATH Works Inc, 1995
[55] 俞立．鲁棒控制_—线性矩阵不等式处理方法．北京：清华大学出版社，2002
[56] Stephen B, Eric F, Laurent E G, Venkataramanan B. Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics, Philadelphia, 1994
[57] 刘开周．移动机器人具有不确定性时扰动建模与鲁棒控制．沈阳工业大学硕士论文，2002
[58] 邱尚涛等．现代工程数学及应用．北京：中国电力出版社，2001
[59] 谢学书，钟宜生．H_∞控制理论．北京：清华大学出版社，1994
[60] 申铁龙．H_∞控制理论及应用．北京：清华大学出版社，1996
[61] Latombe J C. Robot motion planning. Boston Kluwer Academic, 1991