全方位移动下肢康复机器人的运动控制方法研究
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摘要
全球老龄化问题日益严峻，各种疾病、运动损伤及交通事故所引发的下肢运动功能障碍患者显著增加，这类患者除了早期的手术治疗和必要的药物治疗外，正确、科学的康复训练对于患者运动功能恢复将起到重要作用。本文以辽宁省教育厅项目和辽宁省自然科学基金项目为依托，对全方位移动下肢康复机器人的运动学、动力学建模，康复训练过程中机器人发生重心偏移时的轨迹跟踪控制进行了深入研究。该项研究目前在国内正处于起步阶段，具有广阔的发展空间，将为全方位移动下肢康复机器人系统早日应用奠定理论及技术基础。
全方位移动下肢康复机器人是一强耦合、非线性且含有诸多不确定因素的复杂系统。执行机构的机械误差、自身质量和转动惯量、环境、轮与地面的打滑和摩擦、机械震动等都会对机器人运动特性产生影响。尤其，受负载因素影响全方位移动机器人在辅助患者进行康复训练时重心位置是不确定的，重心偏移时机器人的运动控制已成为此类康复机器人亟待解决的一个重要问题。论文主要研究工作包括以下四个方面：
（1）全方位移动下肢康复机器人考虑重心偏移时数学模型的建立。结合全方位轮式移动下肢康复机器人的机构特点进行运动学和动力学分析，分别讨论康复机器人理想空载情况、考虑荷重变化但未产生重心偏移以及考虑荷重变化并产生重心偏移时全方位移动下肢康复机器人运动学模型和动力学模型的建立。
（2）针对全方位移动下肢康复机器人提出一种目标轨道加速度、速度信息有效利用的新型控制器设计。为设计该控制器，改进描述全方位移动下肢康复机器人重心偏移时动力学模型，利用系统模型中物理矩阵之间的关系等式，提出一种全新的控制器设计策略。控制器中有效包含目标轨道的加速度、速度信息，可以实现快速、准确地跟踪效果。并在满足患者质量定常、重心偏移定常可知条件下，基于Lyapunov定理证明了此控制律的稳定性。对全方位移动下肢康复机器人所提出的这种将目标轨道加速度、速度信息有效融入控制器设计的方法，通过与常规PD控制器设计方法对比进行了深入的仿真研究，验证了设计方法的有效性。
（3）针对全方位移动下肢康复机器人重心未知、时变偏移提出一种鲁棒补偿控制策略。考虑实际康复机器人训练过程中重心往往是时变且未知的，进一步提出一种有针对性解决重心偏移模型中含有时变未知项的鲁棒控制策略，通过设计一个具有H∞跟踪性能的鲁棒补偿控制器来补偿系统中的未知时变部分，既有效地改善了康复机器人重心时变偏移时的运动性能，同时又使系统具有良好的抗干扰能力。另外，该控制器设计基于全方位移动下肢康复机器人四轮控制力的限定约束关系，对系统重心偏移动力学模型进行改进描述，打破了以往全方位移动下肢康复机器人控制器设计严重依赖系统模型中的重心时变项和控制力的不可独立性，为全方位移动下肢康复机器人重心偏移时控制器设计提供了一个新的解决问题思路。
（4）全方位移动下肢康复机器人实验平台及轨迹跟踪控制实验。基于日本高知工科大学“步行王”全方位移动下肢康复机器人样机，摄像机和上位计算机组成的实验平台，对本文所提出的有效利用全方位移动下肢康复机器人目标轨道加速度、速度信息的控制方法和有效针对重心未知、时变偏移所提出的鲁棒补偿控制方法分别进行了直线轨迹跟踪控制实验研究，实验验证了本文所提出的运动控制策略具有可行性。
全方位移动下肢康复机器人的研制及其运动控制算法的研究在国内尚起步，算法的有效性对康复机器人的硬件、联机、可靠性、实时性等方面均有极高要求。本论文研究旨在针对重心偏移时控制器设计改善康复运动的训练效果，为我国下肢康复机器人领域的发展起到微薄推动作用。
The global population aging is increasingly serious and patients with lower-limbdysfunction caused by various diseases, injuries and traffic accidents have increasedsignificantly. Correct, scientific rehabilitation for these patients plays an important role, inaddition to early treatments and necessary drug treatments. In this dissertation, the kinematic,dynamic modeling of an omnidirectional lower-limb rehabilitation robot and the trajectorytracking control under the centre-of-gravity shift during walking training are studied based onthe research projects of Liaoning Provincial Department of Education and Liaoning ProvincialNatural Science Foundation. This research, which our country is short of, so has a broad outlookand can provide theoretical and technical base for the application of the omnidirectional lower-limb rehabilitation robot.
The omnidirectional lower-limb rehabilitation robot is a strongly coupled, complexnonlinear system including many uncertainties. The robot’s motion is affected by mechanicalerrors of actuators, mass and inertia, environments, the sliding and friction between the wheeland ground and mechanical vibration. Especially, the center of gravity of the omnidirectionalmobile robot during rehabilitation affected by load factors is uncertain. The motion control todeal with the centre-of-gravity shift has become an important problem in such field. Thisdissertation mainly includes the following aspects:
(1) Mathematical modeling of omnidirectional lower-limb rehabilitation robot with regardfor centre-of-gravity shift. Combined with the analyzing of the kinematics and dynamicscharacteristics of a four wheeled omnidirectional robot, the models of the robot kinematics anddynamics are established, respectively the ideal case with no load, with consideration of themass of the load, but not consideration of the centre-of-gravity shift and with regard for thecentre-of-gravity shift.
(2) For the omnidirectional lower-limb rehabilitation robot, a new controller by using theacceleration and velocity information effectively of the target trajectory is proposed. This new controller is proposed by using the relation equations of certain physical matrices of the systemdynamic model perfectly. By including the acceleration and velocity information, the speed ofcvergence and accuracy of the tracking error are well improved. The stability of this controllerwas proved by Lyapunov theorem under the condition of the constant mass of the patient. Thecontroller was simulated to verify the correctness by comparison with PD controller.
(3) A robust control strategy under the unknown and time-varying of the centre-of-gravityis proposed. Considering that the centre-of-gravity of the robot is always unknown and time-varying, a robust compensation control strategy aimed to solve the time-varying and unknownof the centre-of-gravity shift is developed. By developing an adaptive robust controller withH∞tracking performance to eliminate the time-varying and unkown part of the system, themotion performance and the interference suppression of the rehabilitation robot has both beenimproved. Based on specifying constraint relationship on four wheels’ control force, the newstrategy broke the previous limitation and dependence of the controller to the time-varyingmatrix of the system model.
(4) Experimental platform and research on trajectory tracking control of theomnidirectional lower-limb rehabilitation robot. Based on the platform consisting of the robotdesigned by Kochi University of Technology, the camera and the computer, the feasibilities ofthe above proposed trajectory tracking control algorithms of chapter3and chapter4arevalidated through tracking basic line trajectory.
The research on the omnidirectional lower-limb rehabilitation robot and its motion controlalgorithms are yet to start in our country. The effectiveness of the algorithms is also closelyrelated to the hardware of robot, online, reliability and real-time. The purpose of this dissertationis to improve the effect of rehabilitation based on control methods during the centre-of-gravityshift and to provide modest promotion to the development of lower-limb rehabilitation robot.
全方位移动下肢康复机器人是一强耦合、非线性且含有诸多不确定因素的复杂系统。执行机构的机械误差、自身质量和转动惯量、环境、轮与地面的打滑和摩擦、机械震动等都会对机器人运动特性产生影响。尤其，受负载因素影响全方位移动机器人在辅助患者进行康复训练时重心位置是不确定的，重心偏移时机器人的运动控制已成为此类康复机器人亟待解决的一个重要问题。论文主要研究工作包括以下四个方面：
（1）全方位移动下肢康复机器人考虑重心偏移时数学模型的建立。结合全方位轮式移动下肢康复机器人的机构特点进行运动学和动力学分析，分别讨论康复机器人理想空载情况、考虑荷重变化但未产生重心偏移以及考虑荷重变化并产生重心偏移时全方位移动下肢康复机器人运动学模型和动力学模型的建立。
（2）针对全方位移动下肢康复机器人提出一种目标轨道加速度、速度信息有效利用的新型控制器设计。为设计该控制器，改进描述全方位移动下肢康复机器人重心偏移时动力学模型，利用系统模型中物理矩阵之间的关系等式，提出一种全新的控制器设计策略。控制器中有效包含目标轨道的加速度、速度信息，可以实现快速、准确地跟踪效果。并在满足患者质量定常、重心偏移定常可知条件下，基于Lyapunov定理证明了此控制律的稳定性。对全方位移动下肢康复机器人所提出的这种将目标轨道加速度、速度信息有效融入控制器设计的方法，通过与常规PD控制器设计方法对比进行了深入的仿真研究，验证了设计方法的有效性。
（3）针对全方位移动下肢康复机器人重心未知、时变偏移提出一种鲁棒补偿控制策略。考虑实际康复机器人训练过程中重心往往是时变且未知的，进一步提出一种有针对性解决重心偏移模型中含有时变未知项的鲁棒控制策略，通过设计一个具有H∞跟踪性能的鲁棒补偿控制器来补偿系统中的未知时变部分，既有效地改善了康复机器人重心时变偏移时的运动性能，同时又使系统具有良好的抗干扰能力。另外，该控制器设计基于全方位移动下肢康复机器人四轮控制力的限定约束关系，对系统重心偏移动力学模型进行改进描述，打破了以往全方位移动下肢康复机器人控制器设计严重依赖系统模型中的重心时变项和控制力的不可独立性，为全方位移动下肢康复机器人重心偏移时控制器设计提供了一个新的解决问题思路。
（4）全方位移动下肢康复机器人实验平台及轨迹跟踪控制实验。基于日本高知工科大学“步行王”全方位移动下肢康复机器人样机，摄像机和上位计算机组成的实验平台，对本文所提出的有效利用全方位移动下肢康复机器人目标轨道加速度、速度信息的控制方法和有效针对重心未知、时变偏移所提出的鲁棒补偿控制方法分别进行了直线轨迹跟踪控制实验研究，实验验证了本文所提出的运动控制策略具有可行性。
全方位移动下肢康复机器人的研制及其运动控制算法的研究在国内尚起步，算法的有效性对康复机器人的硬件、联机、可靠性、实时性等方面均有极高要求。本论文研究旨在针对重心偏移时控制器设计改善康复运动的训练效果，为我国下肢康复机器人领域的发展起到微薄推动作用。
The global population aging is increasingly serious and patients with lower-limbdysfunction caused by various diseases, injuries and traffic accidents have increasedsignificantly. Correct, scientific rehabilitation for these patients plays an important role, inaddition to early treatments and necessary drug treatments. In this dissertation, the kinematic,dynamic modeling of an omnidirectional lower-limb rehabilitation robot and the trajectorytracking control under the centre-of-gravity shift during walking training are studied based onthe research projects of Liaoning Provincial Department of Education and Liaoning ProvincialNatural Science Foundation. This research, which our country is short of, so has a broad outlookand can provide theoretical and technical base for the application of the omnidirectional lower-limb rehabilitation robot.
The omnidirectional lower-limb rehabilitation robot is a strongly coupled, complexnonlinear system including many uncertainties. The robot’s motion is affected by mechanicalerrors of actuators, mass and inertia, environments, the sliding and friction between the wheeland ground and mechanical vibration. Especially, the center of gravity of the omnidirectionalmobile robot during rehabilitation affected by load factors is uncertain. The motion control todeal with the centre-of-gravity shift has become an important problem in such field. Thisdissertation mainly includes the following aspects:
(1) Mathematical modeling of omnidirectional lower-limb rehabilitation robot with regardfor centre-of-gravity shift. Combined with the analyzing of the kinematics and dynamicscharacteristics of a four wheeled omnidirectional robot, the models of the robot kinematics anddynamics are established, respectively the ideal case with no load, with consideration of themass of the load, but not consideration of the centre-of-gravity shift and with regard for thecentre-of-gravity shift.
(2) For the omnidirectional lower-limb rehabilitation robot, a new controller by using theacceleration and velocity information effectively of the target trajectory is proposed. This new controller is proposed by using the relation equations of certain physical matrices of the systemdynamic model perfectly. By including the acceleration and velocity information, the speed ofcvergence and accuracy of the tracking error are well improved. The stability of this controllerwas proved by Lyapunov theorem under the condition of the constant mass of the patient. Thecontroller was simulated to verify the correctness by comparison with PD controller.
(3) A robust control strategy under the unknown and time-varying of the centre-of-gravityis proposed. Considering that the centre-of-gravity of the robot is always unknown and time-varying, a robust compensation control strategy aimed to solve the time-varying and unknownof the centre-of-gravity shift is developed. By developing an adaptive robust controller withH∞tracking performance to eliminate the time-varying and unkown part of the system, themotion performance and the interference suppression of the rehabilitation robot has both beenimproved. Based on specifying constraint relationship on four wheels’ control force, the newstrategy broke the previous limitation and dependence of the controller to the time-varyingmatrix of the system model.
(4) Experimental platform and research on trajectory tracking control of theomnidirectional lower-limb rehabilitation robot. Based on the platform consisting of the robotdesigned by Kochi University of Technology, the camera and the computer, the feasibilities ofthe above proposed trajectory tracking control algorithms of chapter3and chapter4arevalidated through tracking basic line trajectory.
The research on the omnidirectional lower-limb rehabilitation robot and its motion controlalgorithms are yet to start in our country. The effectiveness of the algorithms is also closelyrelated to the hardware of robot, online, reliability and real-time. The purpose of this dissertationis to improve the effect of rehabilitation based on control methods during the centre-of-gravityshift and to provide modest promotion to the development of lower-limb rehabilitation robot.
引文
[1]杜鹏,翟振武.陈卫.中国人口老龄化百年发展趋势.人口研究.2005,(06):90-93.
[2]郑晓瑛,陈立新.中国人口老龄化特点及政策思考.中国全科医学.2006,9(23):1920-1923.
[3]中国人口老龄化发展趋势预测研究报告.2007:2-4.
[4] Fougere M, Merette M. Population aging and ecnomic growth in seven OECD countries. Ecnomicmodelling.1999,16(3):411-427.
[5]马尔萨斯.人口论.北京:北京大学出版社.2008.
[6]黄松波,吕秀东.康复对重度偏瘫的脑卒中受训者运动功能恢复的影响.中国康复医学杂志.2000,1(4):58-59.
[7]范晓华,宫艺,刘俊兰.早期康复对脊髓损伤患者步行功能恢复的临床观察.中国康复理论与实践.2004,10(7):421-422.
[8]金德文,张济川.康复工程学的研究与发展.现代康复.2000,4(1):1-4.
[9]赵凯,吴建贤,高晓平等.综合康复对脊髓损伤患者机体功能恢复的影响.安徽医学.2009,30(3):10-12.
[10]缪鸿石.康复医学理论与实践.上海:上海科学技术出版社.2000.
[11] Swinnen E, Duerinck S, Baeyens J P. Effectiveness of robot-assisted gait training in persons withspinal cord injury: a systematic review. Journal of rehabilitation medicine.2010,42:127-130.
[12] Fasoli S E, Krebs H I, Stein J. Effects of robotic therapy on recovery in chronic stroke. Arch PhysMed Rehabil.2003,84:477-482.
[13]张付祥,付宜利,王树国.康复机器人研究进展.河北工业科技.2005,22(2):100-105.
[14]吕广明,孙立宁,彭龙刚.康复机器人技术发展现状及关键技术分析.哈尔滨工业大学学报.2004,36(9):31-35.
[15]邓志东,程振波.我国助老助残机器人产业与技术发展现状调研.机器人技术与应用.2009,2:20-24.
[16]颜庆.下肢康复机器人控制及实验研究：(硕士学位论文).哈尔滨:哈尔滨工程大学.2004.
[17]胡涛,金俏,李学谦.减重步行训练对脊髓损伤患者下肢行走能力的影响.青海医药杂志.2008,38(5):29-31.
[18] Hesse S, Konrad M, Uhlenbrock D E. Treadmill walking with partial body weight support versusfloor walking in hemiparetic subjects. Arch Phys Med Rehabil.1999:421-427.
[19] Chen F, Yu Y, Ge Y J, et al. A PAWL for enhancing strength and endurance during walking usinginteraction force and dynamical information. Proceedings of ROBIO, Kunming,2006.
[20] Bernhardt M, Frey M, Colombo G, et al. Hybrid force-position control yields cooperative behaviorof the rehabilitation robot LOKOMAT. Proceedings of ICORR, Chicago,2005.
[21] Lunenburger L, Colombo G, Riener R, et al. Biofeedback in gait training with the robotic orthosisLokomat. Proceedings of EMBC, Zurich, Switzerland,2004.
[22] Dietz V, Mueller R, Colombo G. Locomotor activity in spinal man:significance of afferent inputfrom joint and load receptors. Brain.2002,125(12):2626-2634.
[23] Stefan H. A mechanized gait trainer for restoration of gait. Joural of rehabilitation research anddevelopment..2000,37(6):701-708.
[24] Stefan H. Locomotor therapy in neurorehabilitation. Neurorehabilitation.2001,16:133-139.
[25] Schmidt H, Stefan H, Rolf B, et al. Haptic Walker-a novel haptic foot device. ACM transactions onapplied perception.2005,2(2):166-180.
[26] Henning S, Cordula W, Rolf B, et al. Gait rehabilitation machines based on programmablefootplates. Journal of NeuroEngineering and Rehabilitation.2007(2):25-28.
[27] Deutsch J, Latonio J, Burdea G, et al. Post-stroke Rehabilitation with the Rutgers Ankle System-ACase Study. Presence: Teleoperators&Virtual Environment,2001(4):416-430.
[28] Deutsch J, Latonio J, Burdea G, et al. Poststroke rehabilitation with the rutgers ankle system-A casestudy[A]. Presence. MIT press.2001,10(4):420-435.
[29] Girone M, Bnrdea G, Bonzit M., et al. A stewart platform-based system for ankle telerehabilitation.Autonomous robots.2001,10(3):203-212.
[30]谢欲晓,白伟,张羽.下肢康复训练机器人的研究现状与趋势.中国医疗器械信息.2010,16(2):5-8.
[31]刘更谦,高金莲,杨四新,何春燕,张小俊.踝关节康复训练并联机构构型及其运动学分析.机电产品开发与创新.2005,18(5):13-15.
[32] Peshkin M, Brown D A, Santos-Munne J J. Kine assist: a robotic overground gait and balancetraining device. Proceedings of ICORR Chicago,2005.
[33] Patton J L, Brown D, Lewis E. Motility evaluation of a novel overground functional mobility toolfor post stroke rehabilitation. Proceedings of ICORR, Netherlands,2007.
[34] http://intron.kz.tsukuba.ac.jp/gaitmaster/gaitmaster_j.html[OL].
[35]王硕玉,河田,井上,石田,木村.全方向移动型步行训练机.第17回生命支援学会学术演讲会论文集.2001:48.
[36] Wang S Y, Kawata K, Inoue Y, et al. Omni-directional mobile walker for rehabilitation of walkingwhich can prevent tipping over. Japan Society of Mechanical Engineers Symposium on WelfareEngineering.2003(39):145-146.
[37] Wang S Y, Inoue H, Kawata K, et al. Developing the omni-directional mobile walker and verifyingits effect of increasing in the muscle power. JSME Symposium on Welfare Engineering2007.2007:176-177.
[38]张秀峰,季林红,王景新.辅助上肢运动康复机器人技术研究.清华大学学报(自然科学版).2006,46(11):1864-1867.
[39]胡宇川,季林红.一种偏瘫上肢复合运动的康复训练机器人.机械设计与制造.2004,(6):7-49.
[40]张立勋,颜庆.下肢康复训练机器人AVR单片机控制系统.机械与电子.2004,5(10):1-3.
[41]颜庆,张立勋.下肢康复训练机器人单片机控制系统设计.应用科技.2004,31(11):52-54.
[42]赵唯伟.卧式下肢康复机器人控制系统研究：(硕士学位论文).哈尔滨:哈尔滨工程大学.2007.
[43]董亦鸣.下肢康复医疗外骨骼训练控制系统研究与初步实现：(硕士学位论文).杭州:浙江大学.2008.
[44]赵铁石,于海波,戴建生.一种基于3-RSS/S并联机构的踝关节康复机器人.燕山大学学报.2008,29(6):471-475.
[45] Lefeber E, Nijmeijer H. Adaptive tracking control of nonholonomic systems: an example.Proceedings of CDC, Phoenix,1999.
[46] Wang D, Wang H. Adaptive stabilization of uncertain dynamic non-holonomicsystems.International Journal of Control.1999,72(18):1689-1700.
[47] Peng K, Yan T R, Li H Z. Adaptive admittance control of a robot manipulator under task spaceconstraint. Proceedings of ICRA, Anchorage, AK,2010.
[48] Tan R P, Wang S Y, Jiang Y L, et al. Adaptive Controller for Motion Control of an Omni-directional Walker. IEEE International Conference on Mechatronics and Automation.2010(7):156-161.
[49]董文杰,霍伟.受完整约束移动机器人的跟踪控制.自动化学报.2000,26(1):1-6.
[50]高为炳.变结构控制的理论及设计方法.北京:科学出版社:1996.
[51] Song Y D. Path tracking control of robot using varible structure method.控制理论与应用.1991,7(1):354-359.
[52] Young KD, Ozuguner U. Frequency shaping compensator for sliding mode. Int. J. Control.1993,57(5):1005～1019.
[53] Stepanenko Y, Cao Y, Chun Y S. Variable structure control of robotic manipulator with PID slidingsurface. Int. J. of robust and nonlinear control.1998,12(8):79-90.
[54] Man et al. A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators.Trans·IEEE on automatic control.1994,39(8):2462-2469.
[55] Slotine J J E. The robust control of robotic manipulators. Int. J.of robot and research.1985,12(4):49-54.
[56] ZAMES G. Feedback and optimal sensitivity model reference transformation, multiplicative semi-norms and approximation inverses. IEEE Trans. automat. contr,1981:301-320.
[57] Peterson I R, Hollot C V. A Riccati equation approach to the stabilization of uncertain linear systems.Automatica.1986,22(4):397-411.
[58] Tadmor G. Worst-case design in the Time domain: the maximum pinciple and the standardH∞problem. Syst. signal processing,1999,28:1190-1208.
[59] Andrea R D. Linear matrix inequality conditions for robustness and control design. InternationalJournal of Robust and Nonlinear Control.2001,11(6):541-554.
[60] Doyle J C, Glover K, Khargonekar P, et al. State space solutions to standardH2andH∞controlproblems. IEEE trans. aut. control.1999,(34):831-847.
[61]陈亚陵.H∞控制问题逼近解的状态空间法.厦门大学学报.1994(2):125-128.
[62] Glover K, Doyle J C. State-space formulae for all stabilizing controllersH∞norm bound andrelations to risk sensitivity. Systems&Control letters,1998:167-172.
[63] Stout L, Sawan M E. Application ofH∞theory to robot manipulators control. Proceedings of theconference on control application.1992:148-183.
[64] Shen T, Tamra T. RobustH∞control of uncertain nonlinear system via stated feedback. IEEE trans.on automatic control.1995,40(8):766-68
[65] Chung Y, Park C, Harashima F. A position control differential drive wheeled mobile robot. IEEEtransactions on industrial electronics.2001,48(4):853-863.
[66] Kraft L G, Campagna D P. A comparison between CMAC neural network control and twotraditional adaptive control systems. IEEE control systems magazine.1990,(4):36-43.
[67]段培水,邵惠鹤.基于广义基函数的CMAC学习算法的改进及收敛性分析.自动化学报.1999(2):53-62.
[68]吕广明,孙立宁,沈刚.基于CMAC神经网络的康复机器人的智能控制技术.哈尔滨工程大学学报.2006,27(5):662-665.
[69] Kwan C, Lewis F L. Robust backstepping control of Nonlinear Systems using neural networks.IEEE transaction on systems, man, cybernetics-part A: systems and humans.2000,30(6):753-765.
[70] Fierro R, Lewis F L. Control of a nonholonomic mobile robot using neural networks. NeuralNetworks.1998,9(4):589-600.
[71]王立新.模糊系统与模糊控制教程.北京:清华大学出版社:2003.
[72] Lim C M, Hiyama T. Application of fuzzy logic control to a manipulator. Robotics and automation.1991,7(5):688-691.
[73] Mandic N J, Scharf E M, Mamdani E H. Practical application of a heuristic fuzzy rule-basedcontroller to the dynamic control of a robot arm. IEEE Proceedings on control theory andapplications.1985,132:190-203.
[74] Buckley J J. Sugeno type controllers are universal controllers. Fuzzy sets and systems.1993,53(3):299-303.
[75]林雷.机器人模糊控制策略研究：(硕士学位论文).燕山:燕山大学.2008.
[76] Wang X L, Cui Y X, Huang J. Intelligent force/position control of robotic manipulators based onfuzzy logic. Journal of System Simulation.2007,19(11):2467-2471.
[77] Sahin T, Eroglu E, Zergeroglu E. An adaptive output feedback tracking control of robot manipulatorvia fuzzy logic based compensation. Advanced motion control,2006.9thIEEE internationalworkshop on.2006:681-686.
[78] Rusu P, Petriu E M, Whalen T E, et al. Behavior-based neuro-fuzzy controller for mobile robotnavigation. Instrumentation and measurement.2003,52(4):1335-1340.
[79]王洪斌,宋佐时.基于模糊神经网络的机器人逆运动学问题.系统仿真学报.2002,14(7):852-854.
[80] Yu W, Li X. Fuzzy identification using fuzzy neural networks with stable learning algorithms. IEEETransactions on fuzzy systems.2004,12(3):411-420.
[81] Zhao Y S, Zhang Y Q, Yang J, et al. Enhanced fuzzy sliding mode controller for roboticmanipulators. International journal of robotics and automation.2007,22(2):170-182.
[82] Ertugrual M, Kaynak O. Neuro sliding mode control of robotic manipulators. Mechatronics.2000,10(1-2):239-263.
[83] Morbidi F, Prattichizzo D. Sliding mode formation tracking control of a tractor and trailer-carsystem. Proceedings of robotics: Science and Systems, Atlanta, Georgia,2007.
[84] Erbatur K, Kaynak O. Use of adaptive fuzzy systems in parameter tuning of sliding-modecontrollers. IEEE/ASME trans. mechatronics.2001,6(4):474-482.
[85]王耀南,孙炜.基于模糊神经网络的机器人自学习控制.电机与控制学报.2001,5(2):92-102.
[86]金耀初,蒋静坪.一类非线性系统的模糊变结构控制及应用.控制与决策.1992,7(1):36-40.
[87] Kim S H, Park C K, Harashima F. Adaptive fuzzy controller design for trajectory tracking of a2D.O.F. wheeled mobile robot using genetic algorithm. Proceedings of IROS, Victoria, Canada,1998.
[88] Kim M S, Shin J H., Hong S G, et al. Designing a robust adaptive dynamic controller fornonholonomic mobile robots under modeling uncertainty and disturbances. Mechatronics.2003,13(5):507-519.
[89] Wilson D G, Robinett. R D I. Robust adaptive backstepping control for a nonholonomic mobilerobot. Proceedings of International Conference on Systems, Man and Cybernetics, Tucson, AZ,2001.
[90] Wang Z P, Ge S S, Lee T H. Adaptive neural network control of a wheeled mobile robot violatingthe pure nonholonomic constraint. Proceedings of CDC, Nassau, Bahamas,2004.
[91]王越超,景兴建.轮式非完整移动机器人控制.机器人.2000,22(7):724-729.
[92] Zhao Y, Bement L. Kinematics, dynamics and control of wheeled mobile robots. Proceedings of1992IEEE conference on robotics and automation.1992:91-96.
[93]吕世增,张大卫,刘海年.基于吴方法的6R机器人逆运动学旋量方程求解.机械工程学报.2010,46(17):37-39.
[94]位耀光,庞旭欣,王库等.基于雅克比矩阵的机械臂逆运动学求解.中国电机工程学会2010年学术年会论文集.2010.
[95] Eghtesada M, Necsulescu D S. Study of the internal dynamics of an autonomous mobile robot.Robotics and Autonomous Systems.2006,12(54):342-349.
[96] Lin C T, Georgee Lee C S. Fault-tolerant reconfigurable architecture for robot kinematics anddynamics computations. IEEE Transactions on System, Man, Cybernetics.1991,21(5):983-989.
[97] Lin S K. Dynamics of the manipulator with closed chain. IEEE Transactions on Robotics andAutomation.1990,6(4):496-501.
[98] Nilanjan C, Ashitava G. Kinematics of wheeled mobile robots on uneven terrain. Mechanism andMachine Theory2004,39(12):1273-1287.
[99] Dixon W E, Dawson D M, Zergeroglu E, et al. Adaptive tracking control of a wheeled mobile robotvia an uncalibrated camera system. Systems, Man, and Cybernetics.2001,31(3):341-352.
[100] Zhu X C, Dong G H, Hu D W,et al. Robust stabilization of wheeled mobile robots moving onuncertain uneven surface. Proceedings of ISDA, Jinan,2006.
[101]蔡广文等.中风康复训练手册.北京:世界图书出版公司.2009.
[102]熊有伦.机器人技术基础.武汉:华中理工大学出版社.1996.
[103] Pin F G, Killough S M. A new family of omnidirectional and holonomic wheeled platforms formobile. Transactions on Robo ti cs and automation.1994,(10):480-489.
[104] Muir P E, Neuman C P. Kinematic modeling of wheeled mobile robots. Journal of robotics andsystem.1987,(4):281-340.
[105] Killough S M,et al. Design of an omnidirectional and holonomic wheeled platform prototype.Proceedings of the1992IEEE international conference on robotics and automation.1992:84-90.
[106] Gilles M, Cyril N, Gerard P, et al. Omnidirectional robot with spherical orthogonal wheels:concepts and analyses. Proceedings of the2006IEEE international conference on robotics andautomation.2006:3374-3379.
[107] Martin U, Karl I. Kinematic analysis and control of an omnidirectional mobile robot. Proceedingsof IROS, San Diego, CA,2007.
[108] Joseph A, Carl M, Ashitava G. Modeling of wheeled mobile robotsusing dextrous manipulationkinematics. Proceedings of WCECS, San Francisco,2007.
[109] Jain A, Rodriguez G. Diagonalized Lagrangian robot dynamics. IEEE Transactions on robotics andautomation.1995,11(4):571-579.
[110]陈根良,王皓,来新民,林宗钦.基于广义坐标形式牛顿-欧拉方法的空间并联机构动力学正问题分析.机械工程学报.2009,45(7):41-47.
[111] Nuknlwuthiopas W, Laowattana N, Maneewarn T. Dynamic modeling of an one-wheel robot byusing Kane's method. IEEE IC1T'02, Bangkok, Thailand,2002:524529.
[112] Mal B L, Tso S K. Robust discontinuous exponential regulation of dynamic nonholonomicwheeled mobile robots with parameter uncertainties. Robust and nonlinear control.2008,18(9):960-974.
[113] Shen T L, Tamura K, Kaminaga H, et al. Robust nonlinear control of parametric uncertain systemswith unknown friction and its application to a pneumatic control valve. Journal of dynamic systems,measurement and control.2000,122(6):257-262.
[114]周景雷,张维海.带有摩擦的机器人鲁棒控制.机械工程学报.2007,43(9):102-106.
[115] Laurent D, Toshio F. A approximate reasoning for the control of a robot in an uncertainenvironment a multi-model approach. Proceedings of the1997IEEE international conference onrobotics&automation.1997:823-828.
[116] Nemoto Y, Egawa S, Koseki A, et al. Power-assisted walking support system for elderly, Proc. ofthe20thAnnual International Conference of IEEE Engineering in Medicine and Biology Society,vol.5, pp.2693-2695,1998.
[117] Tan R P, Wang S Y, Jiang Y L, et al. Motion control of an omini-directional walker using adaptivecontrol method. ICIC Express Letters, vol.4, No.6(A), pp.2195-2199,2010.
[118] Tan R P, Wang S Y, Jiang Y L, et al. Adaptive control for omini-directional walker: improvementof dynamic model. Proceeding of the2011IEEE International Conference on Mechatronics andAutomation. pp.325-330,2011.
[119] Slotine J J, Li W. Applied nonlinear control. Mill Valley, CA, Prentice Hall,1991.
[120] Chen B S, Lee C H, Chang Y C.H∞tracking design of uncertain nonlinear SISO systems:adaptive fuzzy approach. IEEE transactions on System, Man and Cybernetics: part B,1996,26(1):32-43.
[121]刘艳伟.非完整约束轮式移动机器人鲁棒控制：(硕士学位论文).沈阳:沈阳工业大学.2005.
[122] Andrew H, Dudley S, Erick H. Roll-over shapes of human locomotor systems: effects of walkingspeed. Clinical Biomechanics.2004,19(4):407-414.
[2]郑晓瑛,陈立新.中国人口老龄化特点及政策思考.中国全科医学.2006,9(23):1920-1923.
[3]中国人口老龄化发展趋势预测研究报告.2007:2-4.
[4] Fougere M, Merette M. Population aging and ecnomic growth in seven OECD countries. Ecnomicmodelling.1999,16(3):411-427.
[5]马尔萨斯.人口论.北京:北京大学出版社.2008.
[6]黄松波,吕秀东.康复对重度偏瘫的脑卒中受训者运动功能恢复的影响.中国康复医学杂志.2000,1(4):58-59.
[7]范晓华,宫艺,刘俊兰.早期康复对脊髓损伤患者步行功能恢复的临床观察.中国康复理论与实践.2004,10(7):421-422.
[8]金德文,张济川.康复工程学的研究与发展.现代康复.2000,4(1):1-4.
[9]赵凯,吴建贤,高晓平等.综合康复对脊髓损伤患者机体功能恢复的影响.安徽医学.2009,30(3):10-12.
[10]缪鸿石.康复医学理论与实践.上海:上海科学技术出版社.2000.
[11] Swinnen E, Duerinck S, Baeyens J P. Effectiveness of robot-assisted gait training in persons withspinal cord injury: a systematic review. Journal of rehabilitation medicine.2010,42:127-130.
[12] Fasoli S E, Krebs H I, Stein J. Effects of robotic therapy on recovery in chronic stroke. Arch PhysMed Rehabil.2003,84:477-482.
[13]张付祥,付宜利,王树国.康复机器人研究进展.河北工业科技.2005,22(2):100-105.
[14]吕广明,孙立宁,彭龙刚.康复机器人技术发展现状及关键技术分析.哈尔滨工业大学学报.2004,36(9):31-35.
[15]邓志东,程振波.我国助老助残机器人产业与技术发展现状调研.机器人技术与应用.2009,2:20-24.
[16]颜庆.下肢康复机器人控制及实验研究：(硕士学位论文).哈尔滨:哈尔滨工程大学.2004.
[17]胡涛,金俏,李学谦.减重步行训练对脊髓损伤患者下肢行走能力的影响.青海医药杂志.2008,38(5):29-31.
[18] Hesse S, Konrad M, Uhlenbrock D E. Treadmill walking with partial body weight support versusfloor walking in hemiparetic subjects. Arch Phys Med Rehabil.1999:421-427.
[19] Chen F, Yu Y, Ge Y J, et al. A PAWL for enhancing strength and endurance during walking usinginteraction force and dynamical information. Proceedings of ROBIO, Kunming,2006.
[20] Bernhardt M, Frey M, Colombo G, et al. Hybrid force-position control yields cooperative behaviorof the rehabilitation robot LOKOMAT. Proceedings of ICORR, Chicago,2005.
[21] Lunenburger L, Colombo G, Riener R, et al. Biofeedback in gait training with the robotic orthosisLokomat. Proceedings of EMBC, Zurich, Switzerland,2004.
[22] Dietz V, Mueller R, Colombo G. Locomotor activity in spinal man:significance of afferent inputfrom joint and load receptors. Brain.2002,125(12):2626-2634.
[23] Stefan H. A mechanized gait trainer for restoration of gait. Joural of rehabilitation research anddevelopment..2000,37(6):701-708.
[24] Stefan H. Locomotor therapy in neurorehabilitation. Neurorehabilitation.2001,16:133-139.
[25] Schmidt H, Stefan H, Rolf B, et al. Haptic Walker-a novel haptic foot device. ACM transactions onapplied perception.2005,2(2):166-180.
[26] Henning S, Cordula W, Rolf B, et al. Gait rehabilitation machines based on programmablefootplates. Journal of NeuroEngineering and Rehabilitation.2007(2):25-28.
[27] Deutsch J, Latonio J, Burdea G, et al. Post-stroke Rehabilitation with the Rutgers Ankle System-ACase Study. Presence: Teleoperators&Virtual Environment,2001(4):416-430.
[28] Deutsch J, Latonio J, Burdea G, et al. Poststroke rehabilitation with the rutgers ankle system-A casestudy[A]. Presence. MIT press.2001,10(4):420-435.
[29] Girone M, Bnrdea G, Bonzit M., et al. A stewart platform-based system for ankle telerehabilitation.Autonomous robots.2001,10(3):203-212.
[30]谢欲晓,白伟,张羽.下肢康复训练机器人的研究现状与趋势.中国医疗器械信息.2010,16(2):5-8.
[31]刘更谦,高金莲,杨四新,何春燕,张小俊.踝关节康复训练并联机构构型及其运动学分析.机电产品开发与创新.2005,18(5):13-15.
[32] Peshkin M, Brown D A, Santos-Munne J J. Kine assist: a robotic overground gait and balancetraining device. Proceedings of ICORR Chicago,2005.
[33] Patton J L, Brown D, Lewis E. Motility evaluation of a novel overground functional mobility toolfor post stroke rehabilitation. Proceedings of ICORR, Netherlands,2007.
[34] http://intron.kz.tsukuba.ac.jp/gaitmaster/gaitmaster_j.html[OL].
[35]王硕玉,河田,井上,石田,木村.全方向移动型步行训练机.第17回生命支援学会学术演讲会论文集.2001:48.
[36] Wang S Y, Kawata K, Inoue Y, et al. Omni-directional mobile walker for rehabilitation of walkingwhich can prevent tipping over. Japan Society of Mechanical Engineers Symposium on WelfareEngineering.2003(39):145-146.
[37] Wang S Y, Inoue H, Kawata K, et al. Developing the omni-directional mobile walker and verifyingits effect of increasing in the muscle power. JSME Symposium on Welfare Engineering2007.2007:176-177.
[38]张秀峰,季林红,王景新.辅助上肢运动康复机器人技术研究.清华大学学报(自然科学版).2006,46(11):1864-1867.
[39]胡宇川,季林红.一种偏瘫上肢复合运动的康复训练机器人.机械设计与制造.2004,(6):7-49.
[40]张立勋,颜庆.下肢康复训练机器人AVR单片机控制系统.机械与电子.2004,5(10):1-3.
[41]颜庆,张立勋.下肢康复训练机器人单片机控制系统设计.应用科技.2004,31(11):52-54.
[42]赵唯伟.卧式下肢康复机器人控制系统研究：(硕士学位论文).哈尔滨:哈尔滨工程大学.2007.
[43]董亦鸣.下肢康复医疗外骨骼训练控制系统研究与初步实现：(硕士学位论文).杭州:浙江大学.2008.
[44]赵铁石,于海波,戴建生.一种基于3-RSS/S并联机构的踝关节康复机器人.燕山大学学报.2008,29(6):471-475.
[45] Lefeber E, Nijmeijer H. Adaptive tracking control of nonholonomic systems: an example.Proceedings of CDC, Phoenix,1999.
[46] Wang D, Wang H. Adaptive stabilization of uncertain dynamic non-holonomicsystems.International Journal of Control.1999,72(18):1689-1700.
[47] Peng K, Yan T R, Li H Z. Adaptive admittance control of a robot manipulator under task spaceconstraint. Proceedings of ICRA, Anchorage, AK,2010.
[48] Tan R P, Wang S Y, Jiang Y L, et al. Adaptive Controller for Motion Control of an Omni-directional Walker. IEEE International Conference on Mechatronics and Automation.2010(7):156-161.
[49]董文杰,霍伟.受完整约束移动机器人的跟踪控制.自动化学报.2000,26(1):1-6.
[50]高为炳.变结构控制的理论及设计方法.北京:科学出版社:1996.
[51] Song Y D. Path tracking control of robot using varible structure method.控制理论与应用.1991,7(1):354-359.
[52] Young KD, Ozuguner U. Frequency shaping compensator for sliding mode. Int. J. Control.1993,57(5):1005～1019.
[53] Stepanenko Y, Cao Y, Chun Y S. Variable structure control of robotic manipulator with PID slidingsurface. Int. J. of robust and nonlinear control.1998,12(8):79-90.
[54] Man et al. A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators.Trans·IEEE on automatic control.1994,39(8):2462-2469.
[55] Slotine J J E. The robust control of robotic manipulators. Int. J.of robot and research.1985,12(4):49-54.
[56] ZAMES G. Feedback and optimal sensitivity model reference transformation, multiplicative semi-norms and approximation inverses. IEEE Trans. automat. contr,1981:301-320.
[57] Peterson I R, Hollot C V. A Riccati equation approach to the stabilization of uncertain linear systems.Automatica.1986,22(4):397-411.
[58] Tadmor G. Worst-case design in the Time domain: the maximum pinciple and the standardH∞problem. Syst. signal processing,1999,28:1190-1208.
[59] Andrea R D. Linear matrix inequality conditions for robustness and control design. InternationalJournal of Robust and Nonlinear Control.2001,11(6):541-554.
[60] Doyle J C, Glover K, Khargonekar P, et al. State space solutions to standardH2andH∞controlproblems. IEEE trans. aut. control.1999,(34):831-847.
[61]陈亚陵.H∞控制问题逼近解的状态空间法.厦门大学学报.1994(2):125-128.
[62] Glover K, Doyle J C. State-space formulae for all stabilizing controllersH∞norm bound andrelations to risk sensitivity. Systems&Control letters,1998:167-172.
[63] Stout L, Sawan M E. Application ofH∞theory to robot manipulators control. Proceedings of theconference on control application.1992:148-183.
[64] Shen T, Tamra T. RobustH∞control of uncertain nonlinear system via stated feedback. IEEE trans.on automatic control.1995,40(8):766-68
[65] Chung Y, Park C, Harashima F. A position control differential drive wheeled mobile robot. IEEEtransactions on industrial electronics.2001,48(4):853-863.
[66] Kraft L G, Campagna D P. A comparison between CMAC neural network control and twotraditional adaptive control systems. IEEE control systems magazine.1990,(4):36-43.
[67]段培水,邵惠鹤.基于广义基函数的CMAC学习算法的改进及收敛性分析.自动化学报.1999(2):53-62.
[68]吕广明,孙立宁,沈刚.基于CMAC神经网络的康复机器人的智能控制技术.哈尔滨工程大学学报.2006,27(5):662-665.
[69] Kwan C, Lewis F L. Robust backstepping control of Nonlinear Systems using neural networks.IEEE transaction on systems, man, cybernetics-part A: systems and humans.2000,30(6):753-765.
[70] Fierro R, Lewis F L. Control of a nonholonomic mobile robot using neural networks. NeuralNetworks.1998,9(4):589-600.
[71]王立新.模糊系统与模糊控制教程.北京:清华大学出版社:2003.
[72] Lim C M, Hiyama T. Application of fuzzy logic control to a manipulator. Robotics and automation.1991,7(5):688-691.
[73] Mandic N J, Scharf E M, Mamdani E H. Practical application of a heuristic fuzzy rule-basedcontroller to the dynamic control of a robot arm. IEEE Proceedings on control theory andapplications.1985,132:190-203.
[74] Buckley J J. Sugeno type controllers are universal controllers. Fuzzy sets and systems.1993,53(3):299-303.
[75]林雷.机器人模糊控制策略研究：(硕士学位论文).燕山:燕山大学.2008.
[76] Wang X L, Cui Y X, Huang J. Intelligent force/position control of robotic manipulators based onfuzzy logic. Journal of System Simulation.2007,19(11):2467-2471.
[77] Sahin T, Eroglu E, Zergeroglu E. An adaptive output feedback tracking control of robot manipulatorvia fuzzy logic based compensation. Advanced motion control,2006.9thIEEE internationalworkshop on.2006:681-686.
[78] Rusu P, Petriu E M, Whalen T E, et al. Behavior-based neuro-fuzzy controller for mobile robotnavigation. Instrumentation and measurement.2003,52(4):1335-1340.
[79]王洪斌,宋佐时.基于模糊神经网络的机器人逆运动学问题.系统仿真学报.2002,14(7):852-854.
[80] Yu W, Li X. Fuzzy identification using fuzzy neural networks with stable learning algorithms. IEEETransactions on fuzzy systems.2004,12(3):411-420.
[81] Zhao Y S, Zhang Y Q, Yang J, et al. Enhanced fuzzy sliding mode controller for roboticmanipulators. International journal of robotics and automation.2007,22(2):170-182.
[82] Ertugrual M, Kaynak O. Neuro sliding mode control of robotic manipulators. Mechatronics.2000,10(1-2):239-263.
[83] Morbidi F, Prattichizzo D. Sliding mode formation tracking control of a tractor and trailer-carsystem. Proceedings of robotics: Science and Systems, Atlanta, Georgia,2007.
[84] Erbatur K, Kaynak O. Use of adaptive fuzzy systems in parameter tuning of sliding-modecontrollers. IEEE/ASME trans. mechatronics.2001,6(4):474-482.
[85]王耀南,孙炜.基于模糊神经网络的机器人自学习控制.电机与控制学报.2001,5(2):92-102.
[86]金耀初,蒋静坪.一类非线性系统的模糊变结构控制及应用.控制与决策.1992,7(1):36-40.
[87] Kim S H, Park C K, Harashima F. Adaptive fuzzy controller design for trajectory tracking of a2D.O.F. wheeled mobile robot using genetic algorithm. Proceedings of IROS, Victoria, Canada,1998.
[88] Kim M S, Shin J H., Hong S G, et al. Designing a robust adaptive dynamic controller fornonholonomic mobile robots under modeling uncertainty and disturbances. Mechatronics.2003,13(5):507-519.
[89] Wilson D G, Robinett. R D I. Robust adaptive backstepping control for a nonholonomic mobilerobot. Proceedings of International Conference on Systems, Man and Cybernetics, Tucson, AZ,2001.
[90] Wang Z P, Ge S S, Lee T H. Adaptive neural network control of a wheeled mobile robot violatingthe pure nonholonomic constraint. Proceedings of CDC, Nassau, Bahamas,2004.
[91]王越超,景兴建.轮式非完整移动机器人控制.机器人.2000,22(7):724-729.
[92] Zhao Y, Bement L. Kinematics, dynamics and control of wheeled mobile robots. Proceedings of1992IEEE conference on robotics and automation.1992:91-96.
[93]吕世增,张大卫,刘海年.基于吴方法的6R机器人逆运动学旋量方程求解.机械工程学报.2010,46(17):37-39.
[94]位耀光,庞旭欣,王库等.基于雅克比矩阵的机械臂逆运动学求解.中国电机工程学会2010年学术年会论文集.2010.
[95] Eghtesada M, Necsulescu D S. Study of the internal dynamics of an autonomous mobile robot.Robotics and Autonomous Systems.2006,12(54):342-349.
[96] Lin C T, Georgee Lee C S. Fault-tolerant reconfigurable architecture for robot kinematics anddynamics computations. IEEE Transactions on System, Man, Cybernetics.1991,21(5):983-989.
[97] Lin S K. Dynamics of the manipulator with closed chain. IEEE Transactions on Robotics andAutomation.1990,6(4):496-501.
[98] Nilanjan C, Ashitava G. Kinematics of wheeled mobile robots on uneven terrain. Mechanism andMachine Theory2004,39(12):1273-1287.
[99] Dixon W E, Dawson D M, Zergeroglu E, et al. Adaptive tracking control of a wheeled mobile robotvia an uncalibrated camera system. Systems, Man, and Cybernetics.2001,31(3):341-352.
[100] Zhu X C, Dong G H, Hu D W,et al. Robust stabilization of wheeled mobile robots moving onuncertain uneven surface. Proceedings of ISDA, Jinan,2006.
[101]蔡广文等.中风康复训练手册.北京:世界图书出版公司.2009.
[102]熊有伦.机器人技术基础.武汉:华中理工大学出版社.1996.
[103] Pin F G, Killough S M. A new family of omnidirectional and holonomic wheeled platforms formobile. Transactions on Robo ti cs and automation.1994,(10):480-489.
[104] Muir P E, Neuman C P. Kinematic modeling of wheeled mobile robots. Journal of robotics andsystem.1987,(4):281-340.
[105] Killough S M,et al. Design of an omnidirectional and holonomic wheeled platform prototype.Proceedings of the1992IEEE international conference on robotics and automation.1992:84-90.
[106] Gilles M, Cyril N, Gerard P, et al. Omnidirectional robot with spherical orthogonal wheels:concepts and analyses. Proceedings of the2006IEEE international conference on robotics andautomation.2006:3374-3379.
[107] Martin U, Karl I. Kinematic analysis and control of an omnidirectional mobile robot. Proceedingsof IROS, San Diego, CA,2007.
[108] Joseph A, Carl M, Ashitava G. Modeling of wheeled mobile robotsusing dextrous manipulationkinematics. Proceedings of WCECS, San Francisco,2007.
[109] Jain A, Rodriguez G. Diagonalized Lagrangian robot dynamics. IEEE Transactions on robotics andautomation.1995,11(4):571-579.
[110]陈根良,王皓,来新民,林宗钦.基于广义坐标形式牛顿-欧拉方法的空间并联机构动力学正问题分析.机械工程学报.2009,45(7):41-47.
[111] Nuknlwuthiopas W, Laowattana N, Maneewarn T. Dynamic modeling of an one-wheel robot byusing Kane's method. IEEE IC1T'02, Bangkok, Thailand,2002:524529.
[112] Mal B L, Tso S K. Robust discontinuous exponential regulation of dynamic nonholonomicwheeled mobile robots with parameter uncertainties. Robust and nonlinear control.2008,18(9):960-974.
[113] Shen T L, Tamura K, Kaminaga H, et al. Robust nonlinear control of parametric uncertain systemswith unknown friction and its application to a pneumatic control valve. Journal of dynamic systems,measurement and control.2000,122(6):257-262.
[114]周景雷,张维海.带有摩擦的机器人鲁棒控制.机械工程学报.2007,43(9):102-106.
[115] Laurent D, Toshio F. A approximate reasoning for the control of a robot in an uncertainenvironment a multi-model approach. Proceedings of the1997IEEE international conference onrobotics&automation.1997:823-828.
[116] Nemoto Y, Egawa S, Koseki A, et al. Power-assisted walking support system for elderly, Proc. ofthe20thAnnual International Conference of IEEE Engineering in Medicine and Biology Society,vol.5, pp.2693-2695,1998.
[117] Tan R P, Wang S Y, Jiang Y L, et al. Motion control of an omini-directional walker using adaptivecontrol method. ICIC Express Letters, vol.4, No.6(A), pp.2195-2199,2010.
[118] Tan R P, Wang S Y, Jiang Y L, et al. Adaptive control for omini-directional walker: improvementof dynamic model. Proceeding of the2011IEEE International Conference on Mechatronics andAutomation. pp.325-330,2011.
[119] Slotine J J, Li W. Applied nonlinear control. Mill Valley, CA, Prentice Hall,1991.
[120] Chen B S, Lee C H, Chang Y C.H∞tracking design of uncertain nonlinear SISO systems:adaptive fuzzy approach. IEEE transactions on System, Man and Cybernetics: part B,1996,26(1):32-43.
[121]刘艳伟.非完整约束轮式移动机器人鲁棒控制：(硕士学位论文).沈阳:沈阳工业大学.2005.
[122] Andrew H, Dudley S, Erick H. Roll-over shapes of human locomotor systems: effects of walkingspeed. Clinical Biomechanics.2004,19(4):407-414.