双足机器人欠驱动动态步行仿人运动控制研究
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摘要
双足机器人具有广阔的应用前景,是近年来机器人学领域的研究热点之一。但就目前发展水平来看,还远未达到人类期望的大范围动态步行水平,具体表现为运动性能较差,存在能耗高、速度低、环境适应能力低等问题。欠驱动双足机器人是为了研究快速、自然动态步行而提出的一种机器人结构。机器人没有脚掌,与地面点接触形成欠驱动系统,这给机器人的稳定控制带来巨大挑战。机器人不能形成稳定域,静止站立十分困难;需要通过不断变换支撑点位置实现动态平衡。但由于欠驱动机器人可以充分利用重力和惯性力,其步态具有高效、高速、动作自然等特点,为双足机器人运动控制研究提供了新的思路。
针对目前欠驱动双足机器人足地间接触假设性条件过多等问题,提出了一种从实际角度考虑的双足机器人行走动力学特性模型,包含足地间接触关系和反映人类自然行走的膝关节限制特性,为控制策略设计提供基础。
以“仿人”、“仿生”为指导,深入分析人类行走过程中的运动机理,运用仿人智能控制的研究方法,提出了欠驱动双足步行仿人运动控制方案。对双足动态步行这一复杂任务分解,研究仿人智能控制理论在步行控制中的特征选择、控制模态的确定等关键技术,实现欠驱动双足行走机器人高效能动态步行,并与其它典型控制策略开展仿真比较研究。
针对欠驱动双足机器人步行过程中环境不确定性问题,指出不摔倒是稳定性的重要表征,当双足步行过程受到干扰时,原有的步态模式不能继续保持,就需要进行调整以适应变化。通过模仿人的控制行为,实时判断系统出现的不稳定趋势,提出能够保持机器人不摔倒的稳定性监控方案,以适当的控制量对欠驱动双足行走机器人进行在线步态调整保证系统运行,分析了实现步态调整后双足机器人的稳定性。
充分利用开源软件的优越性,建立了一个通用的基于开源物理引擎的双足机器人步行控制研究仿真平台。通过抽象仿真平台的开发过程,设计了计算机与开发人员都可以理解的结构表以提高仿真平台的品质,进而设计双足机器人仿真平台的开发框架,在该框架下实现具有实用性的仿真平台,并注重开放性、灵活性和简洁性,为双足机器人仿真平台的设计者展示了一条快捷方便的开发途径。
设计了基于CAN总线集中式控制结构的双足机器人样机系统,解决关节实时驱动控制器和地面力测量装置中存在的软硬件设计问题,感知系统实时监测双足机器人自身状态的各项指标,同时从外界环境中采集各种有用信息,而双足机器人的控制系统则根据感知系统提供的各种信息,对驱动系统进行控制,使双足机器人实现双足步行功能,对关节控制器提出应用仿人智能控制策略以抑制驱动电机转矩脉动。
Biped robot is a focus in the field of robotics research in recent years for its broad potential application. But to the developmental level of biped technology,it achieves far from the expectation of human being for a wide range dynamic walking. To be more specific, movement capability of current biped robots is very poor,and the biped walking is slow, inefficient and poor adaptation to the environment.
So,underactuated biped robot is brought forward to research high speed and naturally dynamic walking.The robot has no soles and touches ground with points,which brings great challenges to biped stability control for its underactuated method.For example,it has no stable region,still standing is almost impossible and its supporting points may keep moving to achieve dynamic stability.But the greatest merit is that the underactuated biped robot can walk naturally with high speed and high efficiency for taking full advantage of gravity and inertia force. Therefore,the appearance of underactuated biped robot offers new methods for biped motion control.The main contributions of the dissertation include the following:
A more accurate model which can reflect the dynamics of the biped robot, including the contact method of the leg tip with the ground in line with the actual situation and the kneecap limit which can reflect the characteristics of human natural walking is presented to avoid current inappropriate assumptions and provided to be the basis for control strategy design.
With the Human-Simulated Intelligent Control method, the complex process of dynamic walking for underactuated biped robot is divided through in-depth analysis of human walking mechanism under the direction thought of“human-simulated”and“biologies-simulated”.The Human-Simulated motion control scheme is developed for underactuated biped robot.The key technology of characteristic selection and control mode decision are researched. A comparative study is carried out with other typical simulation and the efficient dynamic walking of underactuated biped robot is achieved.
When the underactuated biped robot is subjected to the environmental uncertainty, it will fall down or not,which is an important symbol of stability. When the underactuated biped robot is put in an uncertain environment, the biped robot can’t keep walking with the original gait patterns which need to be adjusted. By mimicking human behavior, the instability trend can be observed in real time. The stability supervision and control method which can maintain the robot not falling are presented through adjusting walking gait on line to maintain balance. The stability of the biped robot is analyzed after the walking gait adaptation.
An ODE (Open Dynamics Engine) based integration solution of the wide range dynamic walking for biped robot simulator is presented to get an universal simulator. The development procedure of the ODE based biped robot simulator is abstracted and the advantage of open source is taken. The structure of a biped robot is described by a robot structure table that can be understood by simulator designers and the computer to improve the performance of the simulator. Then the development framework of a biped robot simulation platform is designed and the simulation platform is realized. The simulation platform is focused on openness, flexibility and simplicity and shown a convenient way for the designer of the biped robot simulation platform.
The centralized control system of biped robot prototype platform based on CAN bus is designed. The design of hardware and software of the real-time controller for driving joint is presented,so do with the measuring device of contact force of ground. The biped robot's own state is monitored in real-time and a variety of useful information of the environment is collected by the sensing system. The underactuated biped robot controls the drive system with the information to achieve biped walking. A HSIC control strategy is also presented to reduce the torque ripple of drive motor.
针对目前欠驱动双足机器人足地间接触假设性条件过多等问题,提出了一种从实际角度考虑的双足机器人行走动力学特性模型,包含足地间接触关系和反映人类自然行走的膝关节限制特性,为控制策略设计提供基础。
以“仿人”、“仿生”为指导,深入分析人类行走过程中的运动机理,运用仿人智能控制的研究方法,提出了欠驱动双足步行仿人运动控制方案。对双足动态步行这一复杂任务分解,研究仿人智能控制理论在步行控制中的特征选择、控制模态的确定等关键技术,实现欠驱动双足行走机器人高效能动态步行,并与其它典型控制策略开展仿真比较研究。
针对欠驱动双足机器人步行过程中环境不确定性问题,指出不摔倒是稳定性的重要表征,当双足步行过程受到干扰时,原有的步态模式不能继续保持,就需要进行调整以适应变化。通过模仿人的控制行为,实时判断系统出现的不稳定趋势,提出能够保持机器人不摔倒的稳定性监控方案,以适当的控制量对欠驱动双足行走机器人进行在线步态调整保证系统运行,分析了实现步态调整后双足机器人的稳定性。
充分利用开源软件的优越性,建立了一个通用的基于开源物理引擎的双足机器人步行控制研究仿真平台。通过抽象仿真平台的开发过程,设计了计算机与开发人员都可以理解的结构表以提高仿真平台的品质,进而设计双足机器人仿真平台的开发框架,在该框架下实现具有实用性的仿真平台,并注重开放性、灵活性和简洁性,为双足机器人仿真平台的设计者展示了一条快捷方便的开发途径。
设计了基于CAN总线集中式控制结构的双足机器人样机系统,解决关节实时驱动控制器和地面力测量装置中存在的软硬件设计问题,感知系统实时监测双足机器人自身状态的各项指标,同时从外界环境中采集各种有用信息,而双足机器人的控制系统则根据感知系统提供的各种信息,对驱动系统进行控制,使双足机器人实现双足步行功能,对关节控制器提出应用仿人智能控制策略以抑制驱动电机转矩脉动。
Biped robot is a focus in the field of robotics research in recent years for its broad potential application. But to the developmental level of biped technology,it achieves far from the expectation of human being for a wide range dynamic walking. To be more specific, movement capability of current biped robots is very poor,and the biped walking is slow, inefficient and poor adaptation to the environment.
So,underactuated biped robot is brought forward to research high speed and naturally dynamic walking.The robot has no soles and touches ground with points,which brings great challenges to biped stability control for its underactuated method.For example,it has no stable region,still standing is almost impossible and its supporting points may keep moving to achieve dynamic stability.But the greatest merit is that the underactuated biped robot can walk naturally with high speed and high efficiency for taking full advantage of gravity and inertia force. Therefore,the appearance of underactuated biped robot offers new methods for biped motion control.The main contributions of the dissertation include the following:
A more accurate model which can reflect the dynamics of the biped robot, including the contact method of the leg tip with the ground in line with the actual situation and the kneecap limit which can reflect the characteristics of human natural walking is presented to avoid current inappropriate assumptions and provided to be the basis for control strategy design.
With the Human-Simulated Intelligent Control method, the complex process of dynamic walking for underactuated biped robot is divided through in-depth analysis of human walking mechanism under the direction thought of“human-simulated”and“biologies-simulated”.The Human-Simulated motion control scheme is developed for underactuated biped robot.The key technology of characteristic selection and control mode decision are researched. A comparative study is carried out with other typical simulation and the efficient dynamic walking of underactuated biped robot is achieved.
When the underactuated biped robot is subjected to the environmental uncertainty, it will fall down or not,which is an important symbol of stability. When the underactuated biped robot is put in an uncertain environment, the biped robot can’t keep walking with the original gait patterns which need to be adjusted. By mimicking human behavior, the instability trend can be observed in real time. The stability supervision and control method which can maintain the robot not falling are presented through adjusting walking gait on line to maintain balance. The stability of the biped robot is analyzed after the walking gait adaptation.
An ODE (Open Dynamics Engine) based integration solution of the wide range dynamic walking for biped robot simulator is presented to get an universal simulator. The development procedure of the ODE based biped robot simulator is abstracted and the advantage of open source is taken. The structure of a biped robot is described by a robot structure table that can be understood by simulator designers and the computer to improve the performance of the simulator. Then the development framework of a biped robot simulation platform is designed and the simulation platform is realized. The simulation platform is focused on openness, flexibility and simplicity and shown a convenient way for the designer of the biped robot simulation platform.
The centralized control system of biped robot prototype platform based on CAN bus is designed. The design of hardware and software of the real-time controller for driving joint is presented,so do with the measuring device of contact force of ground. The biped robot's own state is monitored in real-time and a variety of useful information of the environment is collected by the sensing system. The underactuated biped robot controls the drive system with the information to achieve biped walking. A HSIC control strategy is also presented to reduce the torque ripple of drive motor.
引文
[1] Pfeiffer F. Dynamical systems of variable structure[C]. Proc. of the International Conference on Dynamics, Vibration and Control. Beijing, China.1990:668-681.
[2] Pratt J E. Exploiting Inherent robustness and natural dynamics in the control of bipedal walking robots[D]. USA: MIT, 2002.
[3] Hurmuzlu Y, Genot F, Brogliato B. Modeling, stability and control of biped robots—a general framework[J]. Automatica. 2004, 40(10):1647-1664.
[4] Hofmann A. Robust execution of bipedal walking tasks from biomechanical principles: [D]. USA: MIT, 2006.
[5] Vukobratovic M, Juricic D. Contribution to the synthesis of biped gait[J]. IEEE Transactions on Bio-Medical Engineering, 1969, 16(1) :1-6.
[6] Hemami H, Weimer F, Koozekanani S. Some aspects of the inverted pendulum problem for modeling of locomotion systems[J].. IEEE Transactions on Automatic and Control, 1973, 18(6):658-661.
[7] Kato I, Tsuiki H. The hydraulically powered biped walking machine with a high carrying capacity[C]. Proc. of the International Symposium on External Control of Human Extremities. Dubrovnik, Yugoslavia. September 1972:410-421.
[8] Lim H, Takanishi A. Biped walking robots created at Waseda University: WL and WABIAN family[J]. Phil. Trans. R. Soc. A, 2007, 365:49–64.
[9] Takanishi A, Ishida M, Yamazaki Y, et al. The realization of dynamic walking by the biped walking robot WL-10RD[C]. Proc. of the International Conference on Advanced Robotics. Tokyo, Japan. September 1985: 459-466.
[10] Yamaguchi J, Takanishi A. Development of a leg part of a humanoid robot—development of a biped walking robot adapting to the humans’normal living floor[J]. Autonomous Robots. 1997, 4(4):369-385.
[11] Yamaguchi J, Soga E, Inoue S, et al. Development of a bipedal humanoid robot control method of whole body cooperative dynamic biped walking[C]. Proc. of the IEEE International Conference on Robotics and Automation. Detroit, USA. April 1999:368-374.
[12] Furusho J, Moritsuka H, Masubuchi M. Low order modeling of biped locomotion system using local feedback[J]. Transactions of the Society of Japan Instrument and Control Engineers. 1981, 17(5):596-601.
[13] Furusho J, Masubuchi M. Control of a dynamical biped locomotion system for steadywalking[J]. Journal of Dynamic Systems, Measurement, and Control. 1986, 108(6):111-118.
[14] Furusho J, Sano A. Sensor-based control of a nine-link biped[J]. International Journal of Robotics Research, 1990, 9(2):83-98.
[15] Furusho J, Masubuchi M. A theoretically motivated reduced order model for the control of dynamic biped locomotion[J]. Journal of Dynamic Systems, Measurement, and Control. 1987, 109(6):155-163.
[16] Zheng Y F, Hemami H. Impact effect of biped contact with the environment[J]. IEEE Transactions on Systems, Man, and Cybernetics. 1984, 14(3):437-443.
[17] Zheng Y F, Fred R S. Design and motion control of practical biped robots[J]. International Journal of Robotics and Automation. 1988, 3(2):70-77.
[18] Zheng Y F, Shen J. Gait Synthesis for the SD-2 biped robot to climb sloping surface[J]. IEEE Transactions on Robotics and Automation. 1990, 6(1):86-96.
[19] Kajita S, Tani K, Kobayashi A. Dynamic walk control of a biped robot along the potential energy conserving orbit[C]. Proc. of the International Workshop on Intelligent Robots and Systems, 1990:789-794.
[20] Kajita S, Tani K. Experimental study of biped dynamic walking[J]. IEEE Control Systems Magazine. 1996, 16(1):13-19.
[21] Sakagami Y, Watanabe R, Aoyama C, et al. The intelligent ASIMO: System overview and integration[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Lausanne, Switzerland. October 2002:2478-2483.
[22] Kaneko K, Kanehiro F, Kajita S, et al. Design of prototype humanoid robotics platform for HRP[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Lausanne, Switzerland. October 2002:2431-2436.
[23] Verrelst B, Yokoi K, Stasse O, et al. Mobility of humanoid robots: Stepping over large obstacles dynamically[C]. Proc. of the IEEE International Conference on Mechatronics and Automation. Luoyang, China. June 2006:1072-1079.
[24] Fujita M, Kuroki Y, Ishida T, et al. Autonomous behavior control architecture of entertainment humanoid robot SDR-4X[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Las vegas, USA. October 2003:960-967.
[25] Geppert L. Qrio, the robot that could[C]. IEEE spectrum. 2004, 41(5) :34-37.
[26] Nagasaka K, Kuroki Y, Suzuki, S, et al. Integrated motion control for walking, jumping and running on a small bipedal entertainment robot[C]. Proc. of the IEEE International Conference on Robotics and Automation. New Orleans, USA. April 2004:3189-3194.
[27] Espiau, B. BIP: A joint project for the development of an anthropomorphic biped robot[C].Proc. of the International Conference on Advanced Robotics. Monterey, USA. July 1997:267-272.
[28] Bessonnet G, Chesse S, Sardain P, Optimal gait synthesis of a seven-link planar biped[J]. International Journal of Robotics Research. 2004, 23(10):1059-1073.
[29] Bessonnet G, Seguin P, Sardain P, A parametric optimization approach to walking pattern synthesis[J]. International Journal of Robotics Research. 2005, 24(7):523-536.
[30] Sardain P, Rostami M, Thomas E, et al. Biped robots: Correlations betweens technological design and dynamic behavior[J]. Control Engineering Practice. 1999, 7(3):401-411.
[31] Loffler K, Gienger M, Pfeiffer F. Sensors and control concept of walking“Johnnie”[J]. International Journal of Robotics Research. 2003, 22(3):229-239.
[32] Nishiwaki K, Kagami S, Kuniyoshi Y, et al. Online generation of humanoid walking motion based on a fast generation method of motion pattern that follows desired ZMP[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Lausanne, Switzerland. October 2002. 2684-2689.
[33] Pratt J, Chew C M, Torres A, et al. Virtual mode control: an intuitive approach for bipedal locomotion[JC]. International Journal of Robotics Research. 2001, 20(2):129-143.
[34] Geng T, Porr B, Worgotter F. Fast biped walking with a sensor-driven neuronal controller and real-time online learning[J]. International Journal of Robotics Research. 2006, 25(3):243-259.
[35]刘志远.双足机器人动态行走研究[D].哈尔滨:哈尔滨工业大学,1991.
[36]纪军红. HIT-Ⅲ双足步行机器人步态规划研究[D].哈尔滨:哈尔滨工业大学,2000.
[37]竺长安.两足机器人系统分析、设计及运动控制[D].长沙:国防科技大学,1989.
[38]马宏绪.两足步行机器人动态步行研究[D].长沙:国防科技大学,1995.
[39]马宏绪,张彭,张良起.双足步行机器人动态步行姿态稳定性及姿态控制[J].机器人,1997,19(3):180-186.
[40]刘莉,汪劲松,陈恳,等. THBIP-Ⅰ拟人机器人研究进展[J].机器人,2002,24(3):262-267.
[41]赵建东,徐凯,付成龙,等.仿人机器人踝侧摆的自调节模糊非线性控制研究[J].机器人,2004,26(2):127-132..
[42]徐凯,陈恳,刘莉,等.基于六维力/力矩传感器和关节力矩的仿人机器人步态补偿算法[J].2006,28(2):213-218.
[43]石宗英.双足机器人步态规划与分散鲁棒跟踪控制研究[D].北京:清华大学,2005.
[44] Zhao M G, Liu L, Wang J S, et al. Control system design of THBIP-Ⅰhumanoid robot[C]. Proc. of the IEEE International Conference on Robotics and Automation. Washington, USA. May 2002:2253-2258.
[45] Wang G, Huang Q, Geng J H, et al. Cooperation of dynamic patterns and sensory reflex forhumanoid walking[C]. Proc. of the IEEE International Conference on Robotics and Automation. Taipei, Taiwan. September 2003:2472-2477.
[46] Yang J, Huang Q, Li J X, et al. Walking pattern generation for humanoid robot considering upper body motion[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Beijing, China. October, 2006:4441-4446.
[47]窦瑞军,马培荪,谢玲.两足机器人步态的参数化设计及优化[J].机械工程学报,2002,38(4):36-39.
[48]包志军.仿人型机器人的系统设计、步态规划及稳定性研究[D].上海:上海交通大学,2000.
[49] Jiang S, Cheng J S, Chen J P. Design of central pattern generator for humanoid robot walking based on multi-objective GA[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Takamatsu, Japan. October 2000:1930-1935.
[50]柯显信.仿人形机器人双足动态步行研究[D].上海:上海大学,1991.
[51]魏航信,刘明治,王淑艳,等.仿人型跑步机器人的运动学分析.中国机械工程,2006,17(13):1321-1324.
[52]陈贺.仿人机器人控制系统的研究与开发[D].天津:河北工业大学,2005.
[53]马锡琪.基于ZMP的双足步行机器人步态规划研究[D].西安:西北工业大学,2005.
[54] McGeer T. Passive dynamic walking[J]. International Journal of Robotics Research. 1990, 9(2):62-82.
[55] McGeer T. Passive walking with knees[C]. Proc. of the IEEE International Conference on Robotics and Automation. Cincinnati, USA. April 1990:1640-1645.
[56] McGeer T. Dynamics and control of bipedal locomotion[J]. Journal of Theoretical Biology. 1993, 166(3):277-314.
[57] Garcia M, Chatterjee A, Ruina A. Efficiency, speed, and scaling of two-dimensional passive-dynamic walking[J]. Dynamics and stability of systems. 2000, 15(2):75-99.
[58] Collins S, Wisse M, Ruina A. A three-dimensional passive-dynamic walking robot with two legs and knees[J]. International Journal of Robotics Research. 2001, 20(7):607-615.
[59] Goswami A, Espiau B, Keramane A. Limit cycles and their stability in a passive bipedal gait[C]. Proc. of the IEEE International Conference on Robotics and Automation. Minneapolis, USA. April 1996:246-251.
[60] Goswami A, Espiau B, Keramane A. Limit cycles in a passive compass gait biped and passivity-mimicking control laws[J]. Autonomous Robots. 1997, 4(3):273-286.
[61] Thuilot B, Goswami A, Espiau B. Bifurcation and chaos in a simple passive bipedal gait[C].Proc. of the IEEE International Conference on Robotics and Automation. Albuquerque,USA. April 1997:792-798.
[62] Goswami A, Thuilot B, Espiau B. A study of the passive gait of a compass-like biped robot: symmetry and chaos[J]. International Journal of Robotics Research. 1998, 17(12):1282-1301.
[63] Kuo, A. D. Stabilization of lateral motion in passive dynamic walking[J].International Journal of Robotics Research, 18 (9): 917-930.
[64] Alexander R M. Walking made simple[J]. Science. 2005, 308:58-59.
[65]付成龙,黄元林,王健美,等.半被动双足机器人的准开环控制[J].机器人,2009. 31(2):110-117,123.
[66]刘振泽,田彦涛,张佩杰,等.无动力双足步行机器人控制策略与算法[J].控制理论与应用,2009. 26(2):113-121.
[67] Pratt J, Dilworth P, Pratt G. Virtual model control of a bipedal walking robot[C]. Proceddings of IEEE International Conference on Robotics and Automation. 1997:193-1 98.
[68] Choi J H, Grizzle J W. Feedback control of an underactuated planar bipedal robot with impulsive foot action[J]Robotica,2005,23:567–580.
[69] Chevallereau C, Abba G, Aoustin Y, et al. RABBIT: A testbed for advanced control theory[J]. IEEE Control Systems Magazine. 2003, 23(5):57-79.
[70] Westervelt E R, Grizzle J W, Koditschek D E. Hybrid zero dynamics of planar biped walkers[J]. IEEE Transactions on Automatic Control, 2003, 48(1) :42-56.
[71] Shiriaev A, Perram J W, Canudas C. Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach[J]. IEEE Transactions on Automatic Control, 2005, 50(8):1164-1176.
[72]付成龙,陈恳,王健美,等.动态步行双足机器人THR-Ⅰ的设计与实现[J].机器人,2008,30(2):133-129.
[73]绳涛,程思微,王剑,等.欠驱动双足步行机器人动态步态规划方法研究[J].计算机工程与应用,2009,45(6):1-4,97.
[74] Q. J. Zhou, J. G Bai. An intelligent controller of novel design[C]. Proc of a Multi-National Instrumentation Conference, Part 1, Shanghai, China, 1983:137-149.
[75]李祖枢,涂亚庆.仿人智能控制[M].北京:国防工业出版社,2003.
[76] Vukobratovic M, Borovac B, Surla D, et al. Scientific fundamentals of robotics: biped locomotion[M]. New York: Springer, 1990.
[77]赵建东.仿人机器人行走误差自调整模糊控制研究[D].北京:清华大学,2004.
[78]徐凯.仿人机器人步态规划算法及其实现研究[D].北京:清华大学,2004.
[79] Kim JY, Park IW, Oh JH.Experimental realization of dynamic walking of the biped humanoid robot KHR-2 using zero moment point feedback and inertial measurement[J].AdvancedRobotics,2006,20(6):707-736.
[80]付成龙,陈恳.双足机器人稳定性与控制策略研究进展[J].高技术通讯,2006,16(3):319-324.
[81]尤书合,对影响跑速的因素分析辽宁体育科技,2007,29(4):93-94.
[82]蔡东红,张福友.对短跑摆动支撑技术生物力学的再认识[J].吉林体育学院学报,2008,24(5):59-60.
[83]张翠,周华,李卫平,等.优秀女子竞走运动员技术动作足底压力特征分析[J].山东体育学院学报,2008,24(5):40-43.
[84] Chevallereau C, Grizzle JW, Shih CL.Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot[J]. IEEE Transactions on Robotics,2009,25(1):37-50.
[85] Shing Long Shih,Grizzle,J W,Chevallereau,C.Asymptitically stable walking of a simple underactuated 3D bipedal robot[C]. Proceeding of IEEE International Conference on Robotics and Automation,2006:2766-2771.
[86] Westervelt, Eric R. Toward a coherent framework for the control of planar biped locomotion[D]. 2003. University of Michigan.
[87] Kaminka G A,Lima P U, Rojas R.The role of motion dynamics in the design,control and stability of bipedal and quadrupedal robots[C].RoboCup 2002,LNAI 2752.2003:206-223.
[88] Featherstone R,Orin D. Robot dynamics:equations and algorithm[C]. Proceedings of IEEE International Conference on Robotics and Automation. 2000:826-834.
[89] Hemami H, Wyman B. Rigid boay dynamics, constraints, and inverses[J]. Journal of Applied Mechanics.2007:74:47-56.
[90]刘才山,陈滨.多柔体系统碰撞动力学研究综述[J].力学进展, 2000,30(1):7-14.
[91]绳涛,王剑,马宏绪,等.欠驱动双足步行机器人运动控制与动力学仿真[J].系统仿真,2008,20(24):6745-6749,6753.
[92] Westervelt ER,Buche G, Grizzle JW. Experimental validation of a framework for the design of controllers that induce stable walking in planar bipeds[J]. The International Journal of Robotics Research, 2004, 24(6):559-582.
[93] Grizzle J W, Hurst J, Morris B, Park H W, et al.MABEL,a new robotic bipedal walker and runner[C].American Control Conference, Saint Louis,MO,USA,2009:2030–2036.
[94] Hunt K H, Crossley F R E. Coefficient of restitution interpreted as damping in vibroimpact[J].ASME J. Appl. Mech,1975:440-445.
[95] Van De Velde F, De Baets P, Degrieck J. The friction force during stick-slip with velocity reversal. Wear,1998,216.
[96] Oden J, Martins J. A. C. Models and computation methods for dynamic friction phenomena[J]. Comput Methods Appl. 1985,52:527-634.
[97] Karnopp D. Computer simulation of stick-slip friction in mechanical dynamic systems[J]. ASME Journal of Dynamic Systems,Measurement and Control,1985:100-103.
[98] Antunes J F, Beaufils, B, Guilbaud B. Coulomb friction modeling in numerical simulation of vibrations and wear work rate of tube bundles[J]. Fluids Struct,1988,4:287-304.
[99]詹佩璇.神经生物学[M].台北:合记图书出版社,2004:121-141.
[100]付成龙.平面双足机器人的截面映射稳定性判据与应用[D].北京:清华大学,2006. 11.
[101] Chevallereau C, Grizzle J W, SHIH C L. Asymptotically stable walking of a five-link underactuated 3-D bipedal robot[J]. IEEE Transactions on Robotics,2009,25(1):37-50.
[102] Grizzle J W, Abba G. ,Plestan F. Asymptotically stable walking for biped robots: analysis via systems with impulse effects[J]. IEEE Transactions on Automatic Control, 2001,46(1):51-64.
[103] Plestan F, Grizzle J W, Westervelt E R, et al. Stable walking of a 7-DOF biped robot[J]. IEEE Transactions on Robotics and Automation,2003 19(4):653-668.
[104] Jorrdan K, Challis J H,Cusumano J P, et al. Stability and the time-dependent structure of gait variability in walking and running[J]. Human Movement Science,2009, 28(1):113-128.
[105]李祖枢,张华,温永玲,等.基于动觉智能图式的仿人智能控制[C].第五届全球智能控制与自动化大会论文集,杭州,2004:232-238.
[106]李祖枢,但远宏,温永玲.小车二级摆摆起倒立仿人智能控制控制器结构设计与关键参数探讨[C].中国人工智能协会第11届全国学术年会论文集,北京,2005:1203-1208.
[107]李祖枢,但远宏,温永玲,等.小车三级摆摆起倒立的仿人智能控制[J].华中科技大学学报(自然科学版),2004,32(增):38-41.
[108]李祖枢,王育新,谭智,等.小车二级摆系统的摆起倒立控制与实践[C].第五届全球智能控制与自动化大会论文集,杭州,2004:2360-2364.
[109]李祖枢,谭智,王育新,等.斜轨道上小车二级摆摆起倒立实时控制[C].第23届中国控制会议论文集,无锡,2004:1645-1649.
[110]古建功,李祖枢,张华.三关节体操机器人的动力学参数辨识[C].中国人工智能协会第11届全国学术年会,武汉,2005.
[111]青木纯一郎,南谷利和.步行与健康[M].李太默,译.济南:山东科学技术出版社,1987.
[112]刘振泽.欠驱动步行机器人运动学机理与控制策略研究[D].长春:吉林大学,2007.
[113] Huang Q,Yokoi K, Kajita S, et al. Planning walking patterns for a biped robot[J].IEEE Transactions on Robotics and Automation,2001,17(3):280-289.
[114] Collins S, Ruina A, Tedrake R, et al. Efficient bipedal robots based on passive dynamic walkers[J].Science, 2005,307(5712):1082-1085.
[115] Honda world:ASIMO[EB/OL].[2011.3.30]http://world.honda.com/ASIMO/.
[116] Collins SH, Ruina A. A bipedal walking robot with efficient and human-like gait[A].Proceedings of the IEEE Conference on Robotics and Automation[C]. Piscataway, NJ, USA: IEEE, 2005:1983-1988.
[117]毛勇,王家廞,贾培发,等.双足被动步行研究综述[J].机器人,2007,29(3):274-280.
[118]夏泽洋,陈恳,熊璟,等.仿人机器人运动规划研究进展[J].高技术通讯,2007,17(10): 1092-1099.
[119]廖晓昕.稳定性的数学理论及应用(第二版)[M].武汉:华中师范大学出版社,2001.
[120]张华.基于动觉智能图式的多级摆系统仿人智能运动控制[D].重庆:重庆大学,2006.
[121] Grizzle J W, Chevallereau C, Shih C L. HZD-based control of a five-link underactuated 3D bipedal robot[C].IEEE Conference on Decision and Control,Cancun,Mexico.2008, 5206-5213.
[122] Kane T R, Levinson, D A. Dynamics: theory and applications[M]. New York: McGraw-Hill Book Co. ,1985.
[123] Hale J, Hohl B, Hyon S H, et al. Highly precise dynamic simulation environment for humanoid robots[J]. Advanced Robotics, 2008, 22(10): 1075-1105.
[124] Reichenbach T. A dynamic simulator for humanoid robots[J]. Artificial Life and Robotics, 2009, 13(2): 561-565.
[125] Tang Q, Xiong R, Liu Y, et al. HumRoboSim: An autonomous humanoid robot simulation system[C]. Proceedings of the 2008 International Conference on Cyberworlds, Los Alamitos, CA, USA: IEEE, 2008: 537-542.
[126] Nakaoka S, Hattori S, Kanehiro F, et al. Constraint-based dynamics simulator for humanoid robots with shock absorbing mechanisms[C]. Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, NJ,USA: IEEE, 2007: 3641-3647.
[127]张,黄强,李光日.仿人机器人7DOF腿部的运动分析与仿真[J].微计算机信息, 2008, 24(5): 197-199.
[128] Chardonnet JR, Miossec S, Kheddar A, et al. Dynamic simulator for humanoids using constraint-based method with static friction[C]. Proceedings of 2006 IEEE International Conference on Robotics and Biomimetics. Piscataway, NJ, USA: IEEE, 2006: 1366-1371.
[129]孙毅军,余蕾斌,邱长伍,等.基于Java 3D的仿人型机器人三维仿真[J].上海交通大学学报,2007, 41(8): 1287-1291.
[130]甘志刚,肖南峰.仿人机器人三维实时仿真系统的研究与实现[J].系统仿真学报. 2007, 19(11) : 2444-2448,2518.
[131] Menegatti E, Silvestri G, Pagello E, et al. 3D models of humanoid soccer robot in USARsim and robotics studio simulators[J]. International Journal of Humanoid Robotics. 2008, 5(3):523–546.
[132] Greggio N, Menegatti E, Silvestri G, et al. Simulation of small humanoid robots for soccerdomain[J]. Journal of the Franklin Institute, 2009,346(5):500-519.
[133] Nakamura Y, Hirukawa H, Yamane K. et al. Humanoid Robot Simulator for the METI HRP Project[J]. Robotics and Autonomous Systems. 2001,37:101-114.
[134] Hirukawa H, Kanehiro F, Kajita S, et al. Experimental evaluation of the dynamic simulation of biped walking of humanoid robots[C]. Proceedings of 2003 IEEE International Conference on Robotics and Automation, Piscataway, NJ, USA: IEEE,2003: 1640-1645.
[135] Johnson MR, Demiris Y. An integrated rapid development environment for computer-aided robot design and simulation[C]. Proceedings of the 2003 International Conference on Mechatronics, Westminster, UK: Professional Engineering Publishing, 2003: 485-490.
[136] Smith R. Open Dynamics Engine v0. 5 User Guide[EB/OL].[2011.3.30]http://www. ode. org/ode-latest-userguide. html.
[137] Metta G, Sandini G, Vernon D, et al. The iCub humanoid robot: an open platform for research in embodied cognition[C]. Performance Metrics for Intelligent Systems Workshop, Gaithersburg, MD, USA: NIST Special Publication, 2008: 50-56.
[138] Friedmann M, Petersen K, Stryk OV. Tailored real-time simulation for teams of humanoid robots[C]. Lecture Notes in Computer Science-RoboCup 2007, Robot Soccer World Cup XI. Atlanta,USA: 2008:5001,425-432.
[139]梶田秀司.仿人机器人[M].管贻生,译.北京:清华大学出版社,2007.
[140] Byoung-Kuk Lee. Advanced low cost and high performance brushless DC motor drives for mass production [D]. Texas:Texas A&M University,2001:6-8.
[141]贺虎成,刘卫国,郎宝华.永磁无刷直流电动机非换相区间转矩特性研究[J].电气传动,2007, 37(10):33-38.
[142]王淑红,熊光煜.无刷直流电机换相转矩脉动减小及动态仿真[J].电机与控制学报,2008,12(2):169-173.
[143]李祖枢,张华,古建功,等. 3关节单杠体操机器人的动力学参数辨识[J].控制理论与应用,2008,25(2):242-246,252.
[2] Pratt J E. Exploiting Inherent robustness and natural dynamics in the control of bipedal walking robots[D]. USA: MIT, 2002.
[3] Hurmuzlu Y, Genot F, Brogliato B. Modeling, stability and control of biped robots—a general framework[J]. Automatica. 2004, 40(10):1647-1664.
[4] Hofmann A. Robust execution of bipedal walking tasks from biomechanical principles: [D]. USA: MIT, 2006.
[5] Vukobratovic M, Juricic D. Contribution to the synthesis of biped gait[J]. IEEE Transactions on Bio-Medical Engineering, 1969, 16(1) :1-6.
[6] Hemami H, Weimer F, Koozekanani S. Some aspects of the inverted pendulum problem for modeling of locomotion systems[J].. IEEE Transactions on Automatic and Control, 1973, 18(6):658-661.
[7] Kato I, Tsuiki H. The hydraulically powered biped walking machine with a high carrying capacity[C]. Proc. of the International Symposium on External Control of Human Extremities. Dubrovnik, Yugoslavia. September 1972:410-421.
[8] Lim H, Takanishi A. Biped walking robots created at Waseda University: WL and WABIAN family[J]. Phil. Trans. R. Soc. A, 2007, 365:49–64.
[9] Takanishi A, Ishida M, Yamazaki Y, et al. The realization of dynamic walking by the biped walking robot WL-10RD[C]. Proc. of the International Conference on Advanced Robotics. Tokyo, Japan. September 1985: 459-466.
[10] Yamaguchi J, Takanishi A. Development of a leg part of a humanoid robot—development of a biped walking robot adapting to the humans’normal living floor[J]. Autonomous Robots. 1997, 4(4):369-385.
[11] Yamaguchi J, Soga E, Inoue S, et al. Development of a bipedal humanoid robot control method of whole body cooperative dynamic biped walking[C]. Proc. of the IEEE International Conference on Robotics and Automation. Detroit, USA. April 1999:368-374.
[12] Furusho J, Moritsuka H, Masubuchi M. Low order modeling of biped locomotion system using local feedback[J]. Transactions of the Society of Japan Instrument and Control Engineers. 1981, 17(5):596-601.
[13] Furusho J, Masubuchi M. Control of a dynamical biped locomotion system for steadywalking[J]. Journal of Dynamic Systems, Measurement, and Control. 1986, 108(6):111-118.
[14] Furusho J, Sano A. Sensor-based control of a nine-link biped[J]. International Journal of Robotics Research, 1990, 9(2):83-98.
[15] Furusho J, Masubuchi M. A theoretically motivated reduced order model for the control of dynamic biped locomotion[J]. Journal of Dynamic Systems, Measurement, and Control. 1987, 109(6):155-163.
[16] Zheng Y F, Hemami H. Impact effect of biped contact with the environment[J]. IEEE Transactions on Systems, Man, and Cybernetics. 1984, 14(3):437-443.
[17] Zheng Y F, Fred R S. Design and motion control of practical biped robots[J]. International Journal of Robotics and Automation. 1988, 3(2):70-77.
[18] Zheng Y F, Shen J. Gait Synthesis for the SD-2 biped robot to climb sloping surface[J]. IEEE Transactions on Robotics and Automation. 1990, 6(1):86-96.
[19] Kajita S, Tani K, Kobayashi A. Dynamic walk control of a biped robot along the potential energy conserving orbit[C]. Proc. of the International Workshop on Intelligent Robots and Systems, 1990:789-794.
[20] Kajita S, Tani K. Experimental study of biped dynamic walking[J]. IEEE Control Systems Magazine. 1996, 16(1):13-19.
[21] Sakagami Y, Watanabe R, Aoyama C, et al. The intelligent ASIMO: System overview and integration[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Lausanne, Switzerland. October 2002:2478-2483.
[22] Kaneko K, Kanehiro F, Kajita S, et al. Design of prototype humanoid robotics platform for HRP[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Lausanne, Switzerland. October 2002:2431-2436.
[23] Verrelst B, Yokoi K, Stasse O, et al. Mobility of humanoid robots: Stepping over large obstacles dynamically[C]. Proc. of the IEEE International Conference on Mechatronics and Automation. Luoyang, China. June 2006:1072-1079.
[24] Fujita M, Kuroki Y, Ishida T, et al. Autonomous behavior control architecture of entertainment humanoid robot SDR-4X[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Las vegas, USA. October 2003:960-967.
[25] Geppert L. Qrio, the robot that could[C]. IEEE spectrum. 2004, 41(5) :34-37.
[26] Nagasaka K, Kuroki Y, Suzuki, S, et al. Integrated motion control for walking, jumping and running on a small bipedal entertainment robot[C]. Proc. of the IEEE International Conference on Robotics and Automation. New Orleans, USA. April 2004:3189-3194.
[27] Espiau, B. BIP: A joint project for the development of an anthropomorphic biped robot[C].Proc. of the International Conference on Advanced Robotics. Monterey, USA. July 1997:267-272.
[28] Bessonnet G, Chesse S, Sardain P, Optimal gait synthesis of a seven-link planar biped[J]. International Journal of Robotics Research. 2004, 23(10):1059-1073.
[29] Bessonnet G, Seguin P, Sardain P, A parametric optimization approach to walking pattern synthesis[J]. International Journal of Robotics Research. 2005, 24(7):523-536.
[30] Sardain P, Rostami M, Thomas E, et al. Biped robots: Correlations betweens technological design and dynamic behavior[J]. Control Engineering Practice. 1999, 7(3):401-411.
[31] Loffler K, Gienger M, Pfeiffer F. Sensors and control concept of walking“Johnnie”[J]. International Journal of Robotics Research. 2003, 22(3):229-239.
[32] Nishiwaki K, Kagami S, Kuniyoshi Y, et al. Online generation of humanoid walking motion based on a fast generation method of motion pattern that follows desired ZMP[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Lausanne, Switzerland. October 2002. 2684-2689.
[33] Pratt J, Chew C M, Torres A, et al. Virtual mode control: an intuitive approach for bipedal locomotion[JC]. International Journal of Robotics Research. 2001, 20(2):129-143.
[34] Geng T, Porr B, Worgotter F. Fast biped walking with a sensor-driven neuronal controller and real-time online learning[J]. International Journal of Robotics Research. 2006, 25(3):243-259.
[35]刘志远.双足机器人动态行走研究[D].哈尔滨:哈尔滨工业大学,1991.
[36]纪军红. HIT-Ⅲ双足步行机器人步态规划研究[D].哈尔滨:哈尔滨工业大学,2000.
[37]竺长安.两足机器人系统分析、设计及运动控制[D].长沙:国防科技大学,1989.
[38]马宏绪.两足步行机器人动态步行研究[D].长沙:国防科技大学,1995.
[39]马宏绪,张彭,张良起.双足步行机器人动态步行姿态稳定性及姿态控制[J].机器人,1997,19(3):180-186.
[40]刘莉,汪劲松,陈恳,等. THBIP-Ⅰ拟人机器人研究进展[J].机器人,2002,24(3):262-267.
[41]赵建东,徐凯,付成龙,等.仿人机器人踝侧摆的自调节模糊非线性控制研究[J].机器人,2004,26(2):127-132..
[42]徐凯,陈恳,刘莉,等.基于六维力/力矩传感器和关节力矩的仿人机器人步态补偿算法[J].2006,28(2):213-218.
[43]石宗英.双足机器人步态规划与分散鲁棒跟踪控制研究[D].北京:清华大学,2005.
[44] Zhao M G, Liu L, Wang J S, et al. Control system design of THBIP-Ⅰhumanoid robot[C]. Proc. of the IEEE International Conference on Robotics and Automation. Washington, USA. May 2002:2253-2258.
[45] Wang G, Huang Q, Geng J H, et al. Cooperation of dynamic patterns and sensory reflex forhumanoid walking[C]. Proc. of the IEEE International Conference on Robotics and Automation. Taipei, Taiwan. September 2003:2472-2477.
[46] Yang J, Huang Q, Li J X, et al. Walking pattern generation for humanoid robot considering upper body motion[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Beijing, China. October, 2006:4441-4446.
[47]窦瑞军,马培荪,谢玲.两足机器人步态的参数化设计及优化[J].机械工程学报,2002,38(4):36-39.
[48]包志军.仿人型机器人的系统设计、步态规划及稳定性研究[D].上海:上海交通大学,2000.
[49] Jiang S, Cheng J S, Chen J P. Design of central pattern generator for humanoid robot walking based on multi-objective GA[C]. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Takamatsu, Japan. October 2000:1930-1935.
[50]柯显信.仿人形机器人双足动态步行研究[D].上海:上海大学,1991.
[51]魏航信,刘明治,王淑艳,等.仿人型跑步机器人的运动学分析.中国机械工程,2006,17(13):1321-1324.
[52]陈贺.仿人机器人控制系统的研究与开发[D].天津:河北工业大学,2005.
[53]马锡琪.基于ZMP的双足步行机器人步态规划研究[D].西安:西北工业大学,2005.
[54] McGeer T. Passive dynamic walking[J]. International Journal of Robotics Research. 1990, 9(2):62-82.
[55] McGeer T. Passive walking with knees[C]. Proc. of the IEEE International Conference on Robotics and Automation. Cincinnati, USA. April 1990:1640-1645.
[56] McGeer T. Dynamics and control of bipedal locomotion[J]. Journal of Theoretical Biology. 1993, 166(3):277-314.
[57] Garcia M, Chatterjee A, Ruina A. Efficiency, speed, and scaling of two-dimensional passive-dynamic walking[J]. Dynamics and stability of systems. 2000, 15(2):75-99.
[58] Collins S, Wisse M, Ruina A. A three-dimensional passive-dynamic walking robot with two legs and knees[J]. International Journal of Robotics Research. 2001, 20(7):607-615.
[59] Goswami A, Espiau B, Keramane A. Limit cycles and their stability in a passive bipedal gait[C]. Proc. of the IEEE International Conference on Robotics and Automation. Minneapolis, USA. April 1996:246-251.
[60] Goswami A, Espiau B, Keramane A. Limit cycles in a passive compass gait biped and passivity-mimicking control laws[J]. Autonomous Robots. 1997, 4(3):273-286.
[61] Thuilot B, Goswami A, Espiau B. Bifurcation and chaos in a simple passive bipedal gait[C].Proc. of the IEEE International Conference on Robotics and Automation. Albuquerque,USA. April 1997:792-798.
[62] Goswami A, Thuilot B, Espiau B. A study of the passive gait of a compass-like biped robot: symmetry and chaos[J]. International Journal of Robotics Research. 1998, 17(12):1282-1301.
[63] Kuo, A. D. Stabilization of lateral motion in passive dynamic walking[J].International Journal of Robotics Research, 18 (9): 917-930.
[64] Alexander R M. Walking made simple[J]. Science. 2005, 308:58-59.
[65]付成龙,黄元林,王健美,等.半被动双足机器人的准开环控制[J].机器人,2009. 31(2):110-117,123.
[66]刘振泽,田彦涛,张佩杰,等.无动力双足步行机器人控制策略与算法[J].控制理论与应用,2009. 26(2):113-121.
[67] Pratt J, Dilworth P, Pratt G. Virtual model control of a bipedal walking robot[C]. Proceddings of IEEE International Conference on Robotics and Automation. 1997:193-1 98.
[68] Choi J H, Grizzle J W. Feedback control of an underactuated planar bipedal robot with impulsive foot action[J]Robotica,2005,23:567–580.
[69] Chevallereau C, Abba G, Aoustin Y, et al. RABBIT: A testbed for advanced control theory[J]. IEEE Control Systems Magazine. 2003, 23(5):57-79.
[70] Westervelt E R, Grizzle J W, Koditschek D E. Hybrid zero dynamics of planar biped walkers[J]. IEEE Transactions on Automatic Control, 2003, 48(1) :42-56.
[71] Shiriaev A, Perram J W, Canudas C. Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach[J]. IEEE Transactions on Automatic Control, 2005, 50(8):1164-1176.
[72]付成龙,陈恳,王健美,等.动态步行双足机器人THR-Ⅰ的设计与实现[J].机器人,2008,30(2):133-129.
[73]绳涛,程思微,王剑,等.欠驱动双足步行机器人动态步态规划方法研究[J].计算机工程与应用,2009,45(6):1-4,97.
[74] Q. J. Zhou, J. G Bai. An intelligent controller of novel design[C]. Proc of a Multi-National Instrumentation Conference, Part 1, Shanghai, China, 1983:137-149.
[75]李祖枢,涂亚庆.仿人智能控制[M].北京:国防工业出版社,2003.
[76] Vukobratovic M, Borovac B, Surla D, et al. Scientific fundamentals of robotics: biped locomotion[M]. New York: Springer, 1990.
[77]赵建东.仿人机器人行走误差自调整模糊控制研究[D].北京:清华大学,2004.
[78]徐凯.仿人机器人步态规划算法及其实现研究[D].北京:清华大学,2004.
[79] Kim JY, Park IW, Oh JH.Experimental realization of dynamic walking of the biped humanoid robot KHR-2 using zero moment point feedback and inertial measurement[J].AdvancedRobotics,2006,20(6):707-736.
[80]付成龙,陈恳.双足机器人稳定性与控制策略研究进展[J].高技术通讯,2006,16(3):319-324.
[81]尤书合,对影响跑速的因素分析辽宁体育科技,2007,29(4):93-94.
[82]蔡东红,张福友.对短跑摆动支撑技术生物力学的再认识[J].吉林体育学院学报,2008,24(5):59-60.
[83]张翠,周华,李卫平,等.优秀女子竞走运动员技术动作足底压力特征分析[J].山东体育学院学报,2008,24(5):40-43.
[84] Chevallereau C, Grizzle JW, Shih CL.Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot[J]. IEEE Transactions on Robotics,2009,25(1):37-50.
[85] Shing Long Shih,Grizzle,J W,Chevallereau,C.Asymptitically stable walking of a simple underactuated 3D bipedal robot[C]. Proceeding of IEEE International Conference on Robotics and Automation,2006:2766-2771.
[86] Westervelt, Eric R. Toward a coherent framework for the control of planar biped locomotion[D]. 2003. University of Michigan.
[87] Kaminka G A,Lima P U, Rojas R.The role of motion dynamics in the design,control and stability of bipedal and quadrupedal robots[C].RoboCup 2002,LNAI 2752.2003:206-223.
[88] Featherstone R,Orin D. Robot dynamics:equations and algorithm[C]. Proceedings of IEEE International Conference on Robotics and Automation. 2000:826-834.
[89] Hemami H, Wyman B. Rigid boay dynamics, constraints, and inverses[J]. Journal of Applied Mechanics.2007:74:47-56.
[90]刘才山,陈滨.多柔体系统碰撞动力学研究综述[J].力学进展, 2000,30(1):7-14.
[91]绳涛,王剑,马宏绪,等.欠驱动双足步行机器人运动控制与动力学仿真[J].系统仿真,2008,20(24):6745-6749,6753.
[92] Westervelt ER,Buche G, Grizzle JW. Experimental validation of a framework for the design of controllers that induce stable walking in planar bipeds[J]. The International Journal of Robotics Research, 2004, 24(6):559-582.
[93] Grizzle J W, Hurst J, Morris B, Park H W, et al.MABEL,a new robotic bipedal walker and runner[C].American Control Conference, Saint Louis,MO,USA,2009:2030–2036.
[94] Hunt K H, Crossley F R E. Coefficient of restitution interpreted as damping in vibroimpact[J].ASME J. Appl. Mech,1975:440-445.
[95] Van De Velde F, De Baets P, Degrieck J. The friction force during stick-slip with velocity reversal. Wear,1998,216.
[96] Oden J, Martins J. A. C. Models and computation methods for dynamic friction phenomena[J]. Comput Methods Appl. 1985,52:527-634.
[97] Karnopp D. Computer simulation of stick-slip friction in mechanical dynamic systems[J]. ASME Journal of Dynamic Systems,Measurement and Control,1985:100-103.
[98] Antunes J F, Beaufils, B, Guilbaud B. Coulomb friction modeling in numerical simulation of vibrations and wear work rate of tube bundles[J]. Fluids Struct,1988,4:287-304.
[99]詹佩璇.神经生物学[M].台北:合记图书出版社,2004:121-141.
[100]付成龙.平面双足机器人的截面映射稳定性判据与应用[D].北京:清华大学,2006. 11.
[101] Chevallereau C, Grizzle J W, SHIH C L. Asymptotically stable walking of a five-link underactuated 3-D bipedal robot[J]. IEEE Transactions on Robotics,2009,25(1):37-50.
[102] Grizzle J W, Abba G. ,Plestan F. Asymptotically stable walking for biped robots: analysis via systems with impulse effects[J]. IEEE Transactions on Automatic Control, 2001,46(1):51-64.
[103] Plestan F, Grizzle J W, Westervelt E R, et al. Stable walking of a 7-DOF biped robot[J]. IEEE Transactions on Robotics and Automation,2003 19(4):653-668.
[104] Jorrdan K, Challis J H,Cusumano J P, et al. Stability and the time-dependent structure of gait variability in walking and running[J]. Human Movement Science,2009, 28(1):113-128.
[105]李祖枢,张华,温永玲,等.基于动觉智能图式的仿人智能控制[C].第五届全球智能控制与自动化大会论文集,杭州,2004:232-238.
[106]李祖枢,但远宏,温永玲.小车二级摆摆起倒立仿人智能控制控制器结构设计与关键参数探讨[C].中国人工智能协会第11届全国学术年会论文集,北京,2005:1203-1208.
[107]李祖枢,但远宏,温永玲,等.小车三级摆摆起倒立的仿人智能控制[J].华中科技大学学报(自然科学版),2004,32(增):38-41.
[108]李祖枢,王育新,谭智,等.小车二级摆系统的摆起倒立控制与实践[C].第五届全球智能控制与自动化大会论文集,杭州,2004:2360-2364.
[109]李祖枢,谭智,王育新,等.斜轨道上小车二级摆摆起倒立实时控制[C].第23届中国控制会议论文集,无锡,2004:1645-1649.
[110]古建功,李祖枢,张华.三关节体操机器人的动力学参数辨识[C].中国人工智能协会第11届全国学术年会,武汉,2005.
[111]青木纯一郎,南谷利和.步行与健康[M].李太默,译.济南:山东科学技术出版社,1987.
[112]刘振泽.欠驱动步行机器人运动学机理与控制策略研究[D].长春:吉林大学,2007.
[113] Huang Q,Yokoi K, Kajita S, et al. Planning walking patterns for a biped robot[J].IEEE Transactions on Robotics and Automation,2001,17(3):280-289.
[114] Collins S, Ruina A, Tedrake R, et al. Efficient bipedal robots based on passive dynamic walkers[J].Science, 2005,307(5712):1082-1085.
[115] Honda world:ASIMO[EB/OL].[2011.3.30]http://world.honda.com/ASIMO/.
[116] Collins SH, Ruina A. A bipedal walking robot with efficient and human-like gait[A].Proceedings of the IEEE Conference on Robotics and Automation[C]. Piscataway, NJ, USA: IEEE, 2005:1983-1988.
[117]毛勇,王家廞,贾培发,等.双足被动步行研究综述[J].机器人,2007,29(3):274-280.
[118]夏泽洋,陈恳,熊璟,等.仿人机器人运动规划研究进展[J].高技术通讯,2007,17(10): 1092-1099.
[119]廖晓昕.稳定性的数学理论及应用(第二版)[M].武汉:华中师范大学出版社,2001.
[120]张华.基于动觉智能图式的多级摆系统仿人智能运动控制[D].重庆:重庆大学,2006.
[121] Grizzle J W, Chevallereau C, Shih C L. HZD-based control of a five-link underactuated 3D bipedal robot[C].IEEE Conference on Decision and Control,Cancun,Mexico.2008, 5206-5213.
[122] Kane T R, Levinson, D A. Dynamics: theory and applications[M]. New York: McGraw-Hill Book Co. ,1985.
[123] Hale J, Hohl B, Hyon S H, et al. Highly precise dynamic simulation environment for humanoid robots[J]. Advanced Robotics, 2008, 22(10): 1075-1105.
[124] Reichenbach T. A dynamic simulator for humanoid robots[J]. Artificial Life and Robotics, 2009, 13(2): 561-565.
[125] Tang Q, Xiong R, Liu Y, et al. HumRoboSim: An autonomous humanoid robot simulation system[C]. Proceedings of the 2008 International Conference on Cyberworlds, Los Alamitos, CA, USA: IEEE, 2008: 537-542.
[126] Nakaoka S, Hattori S, Kanehiro F, et al. Constraint-based dynamics simulator for humanoid robots with shock absorbing mechanisms[C]. Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, NJ,USA: IEEE, 2007: 3641-3647.
[127]张,黄强,李光日.仿人机器人7DOF腿部的运动分析与仿真[J].微计算机信息, 2008, 24(5): 197-199.
[128] Chardonnet JR, Miossec S, Kheddar A, et al. Dynamic simulator for humanoids using constraint-based method with static friction[C]. Proceedings of 2006 IEEE International Conference on Robotics and Biomimetics. Piscataway, NJ, USA: IEEE, 2006: 1366-1371.
[129]孙毅军,余蕾斌,邱长伍,等.基于Java 3D的仿人型机器人三维仿真[J].上海交通大学学报,2007, 41(8): 1287-1291.
[130]甘志刚,肖南峰.仿人机器人三维实时仿真系统的研究与实现[J].系统仿真学报. 2007, 19(11) : 2444-2448,2518.
[131] Menegatti E, Silvestri G, Pagello E, et al. 3D models of humanoid soccer robot in USARsim and robotics studio simulators[J]. International Journal of Humanoid Robotics. 2008, 5(3):523–546.
[132] Greggio N, Menegatti E, Silvestri G, et al. Simulation of small humanoid robots for soccerdomain[J]. Journal of the Franklin Institute, 2009,346(5):500-519.
[133] Nakamura Y, Hirukawa H, Yamane K. et al. Humanoid Robot Simulator for the METI HRP Project[J]. Robotics and Autonomous Systems. 2001,37:101-114.
[134] Hirukawa H, Kanehiro F, Kajita S, et al. Experimental evaluation of the dynamic simulation of biped walking of humanoid robots[C]. Proceedings of 2003 IEEE International Conference on Robotics and Automation, Piscataway, NJ, USA: IEEE,2003: 1640-1645.
[135] Johnson MR, Demiris Y. An integrated rapid development environment for computer-aided robot design and simulation[C]. Proceedings of the 2003 International Conference on Mechatronics, Westminster, UK: Professional Engineering Publishing, 2003: 485-490.
[136] Smith R. Open Dynamics Engine v0. 5 User Guide[EB/OL].[2011.3.30]http://www. ode. org/ode-latest-userguide. html.
[137] Metta G, Sandini G, Vernon D, et al. The iCub humanoid robot: an open platform for research in embodied cognition[C]. Performance Metrics for Intelligent Systems Workshop, Gaithersburg, MD, USA: NIST Special Publication, 2008: 50-56.
[138] Friedmann M, Petersen K, Stryk OV. Tailored real-time simulation for teams of humanoid robots[C]. Lecture Notes in Computer Science-RoboCup 2007, Robot Soccer World Cup XI. Atlanta,USA: 2008:5001,425-432.
[139]梶田秀司.仿人机器人[M].管贻生,译.北京:清华大学出版社,2007.
[140] Byoung-Kuk Lee. Advanced low cost and high performance brushless DC motor drives for mass production [D]. Texas:Texas A&M University,2001:6-8.
[141]贺虎成,刘卫国,郎宝华.永磁无刷直流电动机非换相区间转矩特性研究[J].电气传动,2007, 37(10):33-38.
[142]王淑红,熊光煜.无刷直流电机换相转矩脉动减小及动态仿真[J].电机与控制学报,2008,12(2):169-173.
[143]李祖枢,张华,古建功,等. 3关节单杠体操机器人的动力学参数辨识[J].控制理论与应用,2008,25(2):242-246,252.