类车移动机器人轨迹跟踪控制方法研究
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摘要
近年来,随着机器人技术的发展,移动机器人轨迹跟踪问题受到了人们越来越多的关注。前轮转向、后轮驱动的轮式类车移动机器人与四轮汽车的运动学模型相近,因此对轮式类车移动机器人的轨迹跟踪控制问题的研究在汽车自动驾驶、智能交通等方面具有重要的意义。轮式类车移动机器人具有的非完整运动学约束特性给轨迹跟踪控制的研究带来了挑战。
首先研究了在低速或参数变化不大时轮式类车移动机器人的横向轨迹跟踪控制问题。分别采用经典PID、径向基函数(RBF)神经网络自适应PID和模糊自整定PID三种方法对机器人轨迹跟踪过程实现了横向控制。在纵向跟踪速度方面,基于预瞄控制理论,设计了模糊速度控制器。其次,根据类车移动机器人的运动学模型,采用反步法(Backstepping)设计了一种类车移动机器人全局轨迹跟踪控制器,并利用Lyapunov理论证明了系统的全局稳定性。考虑到机器人的运动学约束,控制率中引入了机器人速度受限策略,保证了机器人运动平滑。
利用MATLAB仿真环境,对三种横向跟踪控制和Backstepping方法进行了仿真研究,分析、比较了几种控制方法的优点及适用性。论文最后给出了基于视觉的类车机器人轨迹跟踪的初步实验,结果表明该文所用方法可以很好地跟踪地面铺设的轨迹线。
With the development of robot technology, the trajectory-tracking problem of mobile robot is paid more and more attention. A wheeled car-like mobile robot, which is steered by two front wheels and driven by two rear wheels, has similar kinematic model to that of a four-wheel car. So the study on the trajectory-tracking problem of the wheeled car-like mobile robot is significant for automatic drive of car as well as intelligent transportation. Due to the intrinsic non-holonomic kinematical constraints of car-like robot, it is challenging to control the robot track the given trajectory.
Firstly, the lateral trajectory-tracking problem is studied when the robot moves in low speed or parameters change little. Three methods, which include the classic PID, radial basis function (RBF) neural network based adaptive PID and fuzzy self-tuning PID, are adopted for the mobile robot to realize lateral control of trajectory tracking. To control the longitudinal speed of the robot, a fuzzy speed controller is designed based on the preview control theory. Secondly, a global asymptotically stable tracking controller is designed using the backstepping method on the basis of the kinematic model of the car-like robot. Meanwhile, the Lyapunov theory is used to verify the stability of the controller.Considering the kinematic constraints, the speed limited strategy is introduced to ensure the smooth motion of the robot.
The validity of three lateral control methods as well as the backstepping method is simulated with MATLAB. The merit and applicability of each method are analyzed and compared. Finally, initial trajectory-tracking experiments are implemented, in which a CMOS camera is used to acquire trajectory information. Experimental results show that, with the methods presented in this paper, the robot can track the paved trajectory well.
首先研究了在低速或参数变化不大时轮式类车移动机器人的横向轨迹跟踪控制问题。分别采用经典PID、径向基函数(RBF)神经网络自适应PID和模糊自整定PID三种方法对机器人轨迹跟踪过程实现了横向控制。在纵向跟踪速度方面,基于预瞄控制理论,设计了模糊速度控制器。其次,根据类车移动机器人的运动学模型,采用反步法(Backstepping)设计了一种类车移动机器人全局轨迹跟踪控制器,并利用Lyapunov理论证明了系统的全局稳定性。考虑到机器人的运动学约束,控制率中引入了机器人速度受限策略,保证了机器人运动平滑。
利用MATLAB仿真环境,对三种横向跟踪控制和Backstepping方法进行了仿真研究,分析、比较了几种控制方法的优点及适用性。论文最后给出了基于视觉的类车机器人轨迹跟踪的初步实验,结果表明该文所用方法可以很好地跟踪地面铺设的轨迹线。
With the development of robot technology, the trajectory-tracking problem of mobile robot is paid more and more attention. A wheeled car-like mobile robot, which is steered by two front wheels and driven by two rear wheels, has similar kinematic model to that of a four-wheel car. So the study on the trajectory-tracking problem of the wheeled car-like mobile robot is significant for automatic drive of car as well as intelligent transportation. Due to the intrinsic non-holonomic kinematical constraints of car-like robot, it is challenging to control the robot track the given trajectory.
Firstly, the lateral trajectory-tracking problem is studied when the robot moves in low speed or parameters change little. Three methods, which include the classic PID, radial basis function (RBF) neural network based adaptive PID and fuzzy self-tuning PID, are adopted for the mobile robot to realize lateral control of trajectory tracking. To control the longitudinal speed of the robot, a fuzzy speed controller is designed based on the preview control theory. Secondly, a global asymptotically stable tracking controller is designed using the backstepping method on the basis of the kinematic model of the car-like robot. Meanwhile, the Lyapunov theory is used to verify the stability of the controller.Considering the kinematic constraints, the speed limited strategy is introduced to ensure the smooth motion of the robot.
The validity of three lateral control methods as well as the backstepping method is simulated with MATLAB. The merit and applicability of each method are analyzed and compared. Finally, initial trajectory-tracking experiments are implemented, in which a CMOS camera is used to acquire trajectory information. Experimental results show that, with the methods presented in this paper, the robot can track the paved trajectory well.
引文
[1]蔡自兴,机器人学[M],北京:清华大学出版社,1993
[2]何发昌,邵远,多功能机器人的原理及应用[M],北京:高等教育出版社, 1996
[3] Saeed B.Niku著,孙富春等译,机器人学导论[M],北京:电子工业出版社,2004
[4]李磊,叶涛,谭民等,移动机器人技术研究现状与未来[J],机器人,2002,24(5):475-480
[5]章小兵,宋爱国,地面移动机器人研究现状及发展趋势[J],机器人技术与应用,2004,(2):21-25
[6]李佳宁,易建强,赵冬斌等,非完整移动机器人体系结构研究进展[J],机器人,2003, 25(7):756-760
[7]池瑞楠,非完整移动机器人的鲁棒轨迹跟踪控制研究[D],华南理工大学,2001
[8] Mills J. K., Goldenberg A. A. Force and Position Control of Manipulators during Constrained Motion Tasks. IEEE Robot. and Automat. Magzine, 1989, 15 (1):30-46.
[9]胡跃明,非线性控制系统理论与应用[M],北京:国防工业出版社,2002
[10]孙越,基于神经动力学的非完整移动机器人运动控制[D],大连理工大学,2007
[11]徐俊艳,非完整移动机器人轨迹跟踪和点镇定控制研究[D],中国科技大学,2004
[12] Yuan G. F. Tracking control of a mobile robot using neural dynamics based approaches:[dissertation]. Guelph: Univ. of Guelph, 2001.
[13]唐述博,非完整移动机器人点镇定和轨迹跟踪控制研究[D],大连理工大学,2005
[14] Andrea-Novel B, Campion G, Bastin G. Control of nonholonomic wheeled mobile robots by state feedback linearization. The International Journal of Robotics Research, 1995, 14(6):543-559.
[15] Samson C., Ait-Abderrahim K. Feedback control of a nonholonomic wheeled car in Cartesian space. Proceedings of IEEE International Conference on Robotics and Automation, Sacramento, CA, 1991:1136-1141.
[16]董文杰,霍伟,受非完整约束非完整移动机器人的跟踪控制[J],自动化学报,2000,26(1):1-6
[17]王丰尧,滑模变结构控制[M],北京:机械工业出版社,1995
[18] Yang Jung-Min, Choi In–Hwan, Kim Jong-Hwan. Sliding mode control of a nonholonomic wheeled mobile robot for trajectory tracking. Proceedings of IEEEInternational Conference on Robotics and Automation, Leuven, Belgium, 1998: 2983-2988.
[19] Yang Jung-Min, Kim Jong-Hwan. Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots. IEEE Transactions on Robotics and Automation, 1999, 15( 3): 578-587.
[20] Chwa Dong-Kyong, Seo Jin H., Kim Pyojac, et al. Sliding mode tracking control of nonholonomic wheeled mobile robots. Proceedings of the American Control Conference, Anchorage, A K, 2002: 3991-3996.
[21] Chwa Dong-kyong. Sliding-mode tracking control of nonholonomic wheeled mobile robots in Polar coordinates. IEEE Transactions on Control Systems Technology, 2004, 12(4): 637-644.
[22] Colbaugh R., Barany E., Glass K. Adaptive control of nonholonomic robotic systems. Journal of Robotics System, 1998, 15(7): 365-393.
[23] Singh S. N. Adaptive model following control of nonlinear robotic systems. IEEE Transactions on Automatic Control, 1985, 30(11): 1099-1100
[24]杨俊华,吴捷,胡跃明,反步方法原理及在非线性鲁棒控制中的应用[J],控制与决策,2002,17(增刊):641-653
[25]吴卫国,陈辉堂,王月娟,移动机器人的全局轨迹跟踪控制[J],自动化学报,2001,27(3): 326-331
[26] Jiang Z. P., Nijmeijer. Tracking control of mobile robots: a case study in backstepping. Automatica, 1997, 33(7): 1393-1399
[27]陈卫东,唐得志,王海涛等,基于Backstepping的机器人鲁棒跟踪控制[J],系统仿真学报,2004,16(4):837-841
[28]易继错,侯媛彬,智能控制技术[M],北京:北京工业大学出版社, 1999
[29]张吉礼,模糊-神经网络控制原理与工程应用[M],哈尔滨:哈尔滨工业大学出版社,2004
[30]郭毓,吴益飞,胡维礼,机器人模糊神经网络控制研究进展,中国人工智能学会第11届全国学术年会论文集(下), 2005:1134-1138
[31]隋海美,基于神经网络的机器人控制研究[D],南京理工大学,2003
[32]施维,轮式移动机器人轨迹跟踪控制研究[D],南京理工大学,2006
[33]徐晶晶,自主式移动机器人路径跟踪及仿真的研究[D],北京交通大学,2006
[34]高峻峣,龚建伟,熊光明,轮式机器人横向纵向统一遗传模糊神经网络控制研究[J],计算机测量与控制,2004,12(5):443-445
[35]龚建伟,高峻峣,陆际联,轮式移动机器人大转向航向跟踪控制[J],北京理工大学学报,2000,20(6): 715-719
[36]龚建伟,黄文宇,陆际联,轮式移动机器人航向跟踪预估控制算法[J],机器人,2001,23 (3):193-196
[37]王峰,移动式机器人转向的模糊控制[D],北京:北京理工大学,1998
[38]陶永华,新型PID控制及其应用[M],北京:机械工业出版社,1998
[39]刘素芹,刘新平,戚平等,PID与模糊控制算法的比较及其改进[J],控制工程,2003,10(1):51-52
[40] Sbarbaro D., Segovia J. P., Alcozer S., et al. Application of radial basis network technology to process control. IEEE Transactions on Control Systems Technology, 2000, 8 (1):14-22.
[41] Wai Rong-Jong. Tracking control based on neural network strategy for robot manipulator. Neurocomputing, 2003, 51: 425-445.
[42] Fierro R., Lewis F. L. Control of Nonholonomic Mobile Robot Using Neural Networks.IEEE Transactions on Neural Networks, 1998, 9(4): 589-600.
[43] Simon Haykin,神经网络原理[M],北京:机械工业出版社,2004
[44]杨林,任雪梅,黄鸿,基于RBF网络自整定PID控制的应用研究[J],计算机仿真,2006,23(1):270-273
[45]姬小飞,孟令柏,申东日等,基于RBF神经网络多步预测的自适应PID控制[J],甘肃科学学报,2003,15(2):72-75
[46]启宏杰,尔联洁,刘强等,基于神经网络自适应稳定PID控制方法的研究[J].北京航空航天大学学报,2001,27 (2):153-156
[47]李广军,张翠芳,申元霞,基于RBF神经网络的PID整定[J],佳木斯大学学报,2005,23(3):354-357
[48]李绍铭,刘寅虎,基于改进型RBF神经网络辨识的PID控制[J],自动化与仪表,2006,21(5):40-43
[49]吴卫兵,基于RBF在线辨识的神经网络PID控制及其应用[J],冶金动力,2006,116(4):84-86
[50]高健,黄心汉,彭刚等,基于Fuzzy PID的移动机器人运动控制研究[J],控制工程,2004,11(6):525-528
[51] Lee T. H., Lam H. K., Leung F. H. F., et al. A practical fuzzy logic controller for the path tracking of Wheeled Mobile Robots. IEEE Control System Magazine, 2003, 14(6): 60-65
[52] WANG Yang-Yu, YU Wen-Ge, De-Jie, et al. A fuzzy parameters adaptive PID controller design of digital positional servo system. Proceedings of 2002 International Conference on Machine Learning and Cybernetics, 2002, 23(9): 310-314
[53]庄利峰,杨慧中,模糊自适应PID控制器的设计及应用[J],自动化与仪表,2005(1):37-39
[54]李友善,李华,模糊控制理论及其在过程控制中应用[M],北京:国防工业出版社,1993
[55]王冬雪,神经模糊控制器在锅炉控制中的应用与研究[D],2004,大连海事大学
[56]高健,基于视觉移动机器人控制研究[D],华中科技大学,2005
[57]李士勇,模糊控制和智能控制理论与应用[M],哈尔滨:哈尔滨工业大学出版社,1990
[58]李庆中,顾伟康,叶秀清等,移动机器人路径跟踪的智能预瞄控制方法研究[J],机器人,2002,24(3):252-255
[59]李万玉,董介春,移动机器人路径跟踪控制方法的研究[J],青岛大学学报2004,17 (2):36-40
[60]高振海,管欣,李谦等,基于预瞄跟随理论的驾驶员跟随汽车日标速度的控制模型[J],吉林人大学学报(工学版),2002,32 (1):1-5
[61] Brockett R.W. Asymptotic stability and feedback stabilization, In Differential Geometric Control Theory, Brockett R.W, Millman R.S., Sussman H.J. eds, Birkhauser, Boston, 1983: 181-191.
[62] Komanovsky H., MacClamroch N. H. Developments in nonholonomic control systems. IEEE Control Systems Magazine. 1995, 15(6):20-36.
[63] Samson C., Ait-Abderrahim K. Feedback control of a nonholonomic wheeled cart in Cartesian space. In: Proc. of IEEE Int. Conf. on Robotics and Automation, 1991, 1136-1141
[64] Kanayama Y., Kimura Y. et al. A stable tracking control method for an autonomous mobile robot. In: Proc. of IEEE Int. Conf. on Robotics and Automation, 1990, 384-389
[65] Andrea-Novel, Campion G., Bastin G. Control of nonholonomic wheeled mobile robots by state feedback linearization. Int. J. of Robotics Research, 1995, 543-559.
[66] Kristic M., Kanellakopoulos I., Kokotovic P. V. Nonlinear and Adaptive Control Design. New York: John Wiley, Inc, 1995.
[67]张海鹏,鲁棒滑模反步控制法及其在减摇鳍中的应用[D],哈尔滨工程大学,2004
[68]徐俊艳,张培仁,程剑锋,基于Backstepping时变反馈和PID控制的移动机器人实时轨迹跟踪控制研究[J],电机与控制学报,2004,8(1):35-43
[69]徐俊艳,张培仁,非完整轮式移动机器人轨迹跟踪控制研究[J],中国科学技术大学学报,2004,34(3):376-380
[70]刘松良,朱铁夫,郁万鹏,Backstepping控制理论及在非线性飞控系统中的应用[J],飞机设计,2007,27(4):48-52
[71]刘金琨,先进PID控制MATLAB仿真[M],北京:电子工业出版社,2006
[2]何发昌,邵远,多功能机器人的原理及应用[M],北京:高等教育出版社, 1996
[3] Saeed B.Niku著,孙富春等译,机器人学导论[M],北京:电子工业出版社,2004
[4]李磊,叶涛,谭民等,移动机器人技术研究现状与未来[J],机器人,2002,24(5):475-480
[5]章小兵,宋爱国,地面移动机器人研究现状及发展趋势[J],机器人技术与应用,2004,(2):21-25
[6]李佳宁,易建强,赵冬斌等,非完整移动机器人体系结构研究进展[J],机器人,2003, 25(7):756-760
[7]池瑞楠,非完整移动机器人的鲁棒轨迹跟踪控制研究[D],华南理工大学,2001
[8] Mills J. K., Goldenberg A. A. Force and Position Control of Manipulators during Constrained Motion Tasks. IEEE Robot. and Automat. Magzine, 1989, 15 (1):30-46.
[9]胡跃明,非线性控制系统理论与应用[M],北京:国防工业出版社,2002
[10]孙越,基于神经动力学的非完整移动机器人运动控制[D],大连理工大学,2007
[11]徐俊艳,非完整移动机器人轨迹跟踪和点镇定控制研究[D],中国科技大学,2004
[12] Yuan G. F. Tracking control of a mobile robot using neural dynamics based approaches:[dissertation]. Guelph: Univ. of Guelph, 2001.
[13]唐述博,非完整移动机器人点镇定和轨迹跟踪控制研究[D],大连理工大学,2005
[14] Andrea-Novel B, Campion G, Bastin G. Control of nonholonomic wheeled mobile robots by state feedback linearization. The International Journal of Robotics Research, 1995, 14(6):543-559.
[15] Samson C., Ait-Abderrahim K. Feedback control of a nonholonomic wheeled car in Cartesian space. Proceedings of IEEE International Conference on Robotics and Automation, Sacramento, CA, 1991:1136-1141.
[16]董文杰,霍伟,受非完整约束非完整移动机器人的跟踪控制[J],自动化学报,2000,26(1):1-6
[17]王丰尧,滑模变结构控制[M],北京:机械工业出版社,1995
[18] Yang Jung-Min, Choi In–Hwan, Kim Jong-Hwan. Sliding mode control of a nonholonomic wheeled mobile robot for trajectory tracking. Proceedings of IEEEInternational Conference on Robotics and Automation, Leuven, Belgium, 1998: 2983-2988.
[19] Yang Jung-Min, Kim Jong-Hwan. Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots. IEEE Transactions on Robotics and Automation, 1999, 15( 3): 578-587.
[20] Chwa Dong-Kyong, Seo Jin H., Kim Pyojac, et al. Sliding mode tracking control of nonholonomic wheeled mobile robots. Proceedings of the American Control Conference, Anchorage, A K, 2002: 3991-3996.
[21] Chwa Dong-kyong. Sliding-mode tracking control of nonholonomic wheeled mobile robots in Polar coordinates. IEEE Transactions on Control Systems Technology, 2004, 12(4): 637-644.
[22] Colbaugh R., Barany E., Glass K. Adaptive control of nonholonomic robotic systems. Journal of Robotics System, 1998, 15(7): 365-393.
[23] Singh S. N. Adaptive model following control of nonlinear robotic systems. IEEE Transactions on Automatic Control, 1985, 30(11): 1099-1100
[24]杨俊华,吴捷,胡跃明,反步方法原理及在非线性鲁棒控制中的应用[J],控制与决策,2002,17(增刊):641-653
[25]吴卫国,陈辉堂,王月娟,移动机器人的全局轨迹跟踪控制[J],自动化学报,2001,27(3): 326-331
[26] Jiang Z. P., Nijmeijer. Tracking control of mobile robots: a case study in backstepping. Automatica, 1997, 33(7): 1393-1399
[27]陈卫东,唐得志,王海涛等,基于Backstepping的机器人鲁棒跟踪控制[J],系统仿真学报,2004,16(4):837-841
[28]易继错,侯媛彬,智能控制技术[M],北京:北京工业大学出版社, 1999
[29]张吉礼,模糊-神经网络控制原理与工程应用[M],哈尔滨:哈尔滨工业大学出版社,2004
[30]郭毓,吴益飞,胡维礼,机器人模糊神经网络控制研究进展,中国人工智能学会第11届全国学术年会论文集(下), 2005:1134-1138
[31]隋海美,基于神经网络的机器人控制研究[D],南京理工大学,2003
[32]施维,轮式移动机器人轨迹跟踪控制研究[D],南京理工大学,2006
[33]徐晶晶,自主式移动机器人路径跟踪及仿真的研究[D],北京交通大学,2006
[34]高峻峣,龚建伟,熊光明,轮式机器人横向纵向统一遗传模糊神经网络控制研究[J],计算机测量与控制,2004,12(5):443-445
[35]龚建伟,高峻峣,陆际联,轮式移动机器人大转向航向跟踪控制[J],北京理工大学学报,2000,20(6): 715-719
[36]龚建伟,黄文宇,陆际联,轮式移动机器人航向跟踪预估控制算法[J],机器人,2001,23 (3):193-196
[37]王峰,移动式机器人转向的模糊控制[D],北京:北京理工大学,1998
[38]陶永华,新型PID控制及其应用[M],北京:机械工业出版社,1998
[39]刘素芹,刘新平,戚平等,PID与模糊控制算法的比较及其改进[J],控制工程,2003,10(1):51-52
[40] Sbarbaro D., Segovia J. P., Alcozer S., et al. Application of radial basis network technology to process control. IEEE Transactions on Control Systems Technology, 2000, 8 (1):14-22.
[41] Wai Rong-Jong. Tracking control based on neural network strategy for robot manipulator. Neurocomputing, 2003, 51: 425-445.
[42] Fierro R., Lewis F. L. Control of Nonholonomic Mobile Robot Using Neural Networks.IEEE Transactions on Neural Networks, 1998, 9(4): 589-600.
[43] Simon Haykin,神经网络原理[M],北京:机械工业出版社,2004
[44]杨林,任雪梅,黄鸿,基于RBF网络自整定PID控制的应用研究[J],计算机仿真,2006,23(1):270-273
[45]姬小飞,孟令柏,申东日等,基于RBF神经网络多步预测的自适应PID控制[J],甘肃科学学报,2003,15(2):72-75
[46]启宏杰,尔联洁,刘强等,基于神经网络自适应稳定PID控制方法的研究[J].北京航空航天大学学报,2001,27 (2):153-156
[47]李广军,张翠芳,申元霞,基于RBF神经网络的PID整定[J],佳木斯大学学报,2005,23(3):354-357
[48]李绍铭,刘寅虎,基于改进型RBF神经网络辨识的PID控制[J],自动化与仪表,2006,21(5):40-43
[49]吴卫兵,基于RBF在线辨识的神经网络PID控制及其应用[J],冶金动力,2006,116(4):84-86
[50]高健,黄心汉,彭刚等,基于Fuzzy PID的移动机器人运动控制研究[J],控制工程,2004,11(6):525-528
[51] Lee T. H., Lam H. K., Leung F. H. F., et al. A practical fuzzy logic controller for the path tracking of Wheeled Mobile Robots. IEEE Control System Magazine, 2003, 14(6): 60-65
[52] WANG Yang-Yu, YU Wen-Ge, De-Jie, et al. A fuzzy parameters adaptive PID controller design of digital positional servo system. Proceedings of 2002 International Conference on Machine Learning and Cybernetics, 2002, 23(9): 310-314
[53]庄利峰,杨慧中,模糊自适应PID控制器的设计及应用[J],自动化与仪表,2005(1):37-39
[54]李友善,李华,模糊控制理论及其在过程控制中应用[M],北京:国防工业出版社,1993
[55]王冬雪,神经模糊控制器在锅炉控制中的应用与研究[D],2004,大连海事大学
[56]高健,基于视觉移动机器人控制研究[D],华中科技大学,2005
[57]李士勇,模糊控制和智能控制理论与应用[M],哈尔滨:哈尔滨工业大学出版社,1990
[58]李庆中,顾伟康,叶秀清等,移动机器人路径跟踪的智能预瞄控制方法研究[J],机器人,2002,24(3):252-255
[59]李万玉,董介春,移动机器人路径跟踪控制方法的研究[J],青岛大学学报2004,17 (2):36-40
[60]高振海,管欣,李谦等,基于预瞄跟随理论的驾驶员跟随汽车日标速度的控制模型[J],吉林人大学学报(工学版),2002,32 (1):1-5
[61] Brockett R.W. Asymptotic stability and feedback stabilization, In Differential Geometric Control Theory, Brockett R.W, Millman R.S., Sussman H.J. eds, Birkhauser, Boston, 1983: 181-191.
[62] Komanovsky H., MacClamroch N. H. Developments in nonholonomic control systems. IEEE Control Systems Magazine. 1995, 15(6):20-36.
[63] Samson C., Ait-Abderrahim K. Feedback control of a nonholonomic wheeled cart in Cartesian space. In: Proc. of IEEE Int. Conf. on Robotics and Automation, 1991, 1136-1141
[64] Kanayama Y., Kimura Y. et al. A stable tracking control method for an autonomous mobile robot. In: Proc. of IEEE Int. Conf. on Robotics and Automation, 1990, 384-389
[65] Andrea-Novel, Campion G., Bastin G. Control of nonholonomic wheeled mobile robots by state feedback linearization. Int. J. of Robotics Research, 1995, 543-559.
[66] Kristic M., Kanellakopoulos I., Kokotovic P. V. Nonlinear and Adaptive Control Design. New York: John Wiley, Inc, 1995.
[67]张海鹏,鲁棒滑模反步控制法及其在减摇鳍中的应用[D],哈尔滨工程大学,2004
[68]徐俊艳,张培仁,程剑锋,基于Backstepping时变反馈和PID控制的移动机器人实时轨迹跟踪控制研究[J],电机与控制学报,2004,8(1):35-43
[69]徐俊艳,张培仁,非完整轮式移动机器人轨迹跟踪控制研究[J],中国科学技术大学学报,2004,34(3):376-380
[70]刘松良,朱铁夫,郁万鹏,Backstepping控制理论及在非线性飞控系统中的应用[J],飞机设计,2007,27(4):48-52
[71]刘金琨,先进PID控制MATLAB仿真[M],北京:电子工业出版社,2006