欠驱动两足机器人控制策略及其应用研究
|
摘要
仿人机器人具有广阔的应用前景,一直以来受到各方面高度关注。经过近四十年发展,取得了辉煌成就,但就目前发展水平来看,还远未达到人类的期望,一个重要原因就是运动性能较差,主要存在速度低、能耗高等问题。欠驱动两足机器人是为了研究高速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,例如: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;需要通过时不变步态实现姿态可控等。但是,欠驱动机器人由于可以充分利用重力和惯性力,其步态具有高速、高效、动作自然等特点,为仿人机器人步态规划与运动控制提供了新的思路。
本文主要研究欠驱动两足机器人控制策略及其在仿人机器人上的应用问题,主要内容包括:
首先对欠驱动两足机器人的复杂控制系统模型进行研究,分别基于D-H坐标建立机器人运动学模型,基于Lagrange函数建立单脚支撑期的控制系统模型,基于角动量守恒建立状态切换模型,并对欠驱动步态的实现条件进行详细讨论,为后面的研究奠定基础。
为实现机器人姿态可控,开展了时不变步态规划和控制方法研究,提出了基于遗传算法的时不变步态规划策略:以状态变量为优化参数,以能耗最小为优化目标,以各种约束为限制条件,将步态规划问题转化为非线性规划问题,同时实现步态的规划和优化。基于复杂控制系统模型,机器人运动控制采用反馈线性化方法,因此对解耦矩阵的可逆条件进行了深入研究,并设计了有限时间稳定控制器。
稳定控制是欠驱动两足机器人控制最大的难点,也是本文研究的重点。由于机构特殊,现有的稳定判据并不能对其稳定性进行定义和判定。从Lyapunov稳定性理论出发,将机器人状态分为可行和不可行状态。在此基础上,对欠驱动两足机器人的稳定性进行定义,并提出了一种基于失衡度的稳定判据。失衡度是对机器人偏离平衡状态的一种定量评估,综合考虑了姿态和速度参数,满足稳定判据的基本性质。从失衡度收敛的角度出发,给出了欠驱动步态的稳定条件,并以平面欠驱动机器人为平台对欠驱动步态的特点展开研究。实验表明,欠驱动步态具备渐进稳定性,因此,虽然是一种离线规划步态,但是具有很强的鲁棒性和环境适应能力。
3D欠驱动两足机器人稳定控制是本研究的主要目标。3D欠驱动步态不稳定主要是由于侧向与前向运动周期不匹配。生物学和机器人学研究表明,两足步行通常以前向运动为主导,侧向辅助保持稳定。基于这一事实,本文提出了一种3D欠驱动步态稳定控制策略,通过控制步宽调整机器人侧向运动周期,实现侧向对前向周期的自适应跟踪,最终实现3D欠驱动步态的渐进稳定。实验表明,该策略对初始状态误差具有很强的鲁棒性,对地面环境具有一定的适应能力,可实现性较强。欠驱动两足机器人静态稳定站立十分困难,但其直立姿态是可控的,本文基于T-S模型和LQR控制设计直立姿态稳定控制器,实现了3D欠驱动两足机器人双脚支撑直立姿态的渐进稳定控制。实验表明,采用所提控制策略,稳定状态的吸引域明显扩大。
本文对欠驱动控制策略在仿人机器人上的应用问题展开研究。仿人机器人与欠驱动两足机器人的主要区别在于脚掌和踝关节力矩。利用主动欠驱动策略对支撑踝关节进行零力矩控制,仿人机器人可以实现高速的欠驱动步行。论文重点研究了支撑踝零力矩控制策略的实现方法,如何利用踝关节力矩提高步态稳定性和收敛速度,如何利用踝关节力矩控制步行速度等问题。机器人总是从立定状态开始行走,而最终回归于立定状态,因此论文探讨和解决了仿人机器人欠驱动步态起步和停止过程的控制问题,实现了仿人机器人欠驱动步态行走的全过程控制。实验表明,基于主动欠驱动控制策略,仿人机器人可以实现欠驱动步态,机器人的运动性能明显提高。
最后,总结本文所做工作,分析不足之处,并提出今后的研究重点。
For the humanoid robot’s potential application, related researches have aroused much attention since its appearance. In the past forty years, research on humanoid robot has acquired remarkable achievements and lots of research organizations built their prototypes to show and validate related results. But to the developmental level of humanoid technology, it achieves far from the expectation of human being. One of the critical reasons is that movement capability of current humanoid robots with huge mass is very poor, and the biped walking is slow and inefficient. So, underactuated biped robot is brought forward to research high speed and dynamic walking. The robot has no soles and touches ground with points, which brings great challenges to biped and humanoid stability control. For examples, 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. Therefore, the appearance of underactuated biped robot offers new methods for humanoid motion planning and control. The key of this dissertation covers the control strategy and application of underactuated biped robot, and its content as follows:
As the basis of research on underactuated biped robot control, the hybrid control system model has been built. Several models are built respectively: kinematics model by D-H reference frame, control system model of single-supporting by Lagrange function, and states-switching model by angular momentum conservation. Then, the realizable conditions of the underactuated gait are discussed in great detail.
The planning and control of the time-invariant gait of underactuated biped robot are researched. The gaits are planned and optimized by Genetic Algorithm, which takes the state variables as the optimized parameters, the minimum energy-expend as the optimized goal, the realizable conditions as the restriction, and then the problem of gait-planning is changed into a nonlinear-planning one. The gait is controlled by feedback linearization, so dynamic singularity states and finite-time stability controller are studied.
Stability is the principal goal of biped motion control and it is also the most important in this dissertation. The current stability criterion can not be used directly to estimate the stability of underactuated biped robot for its special configuration. Based on Lyapunov stability theory, states of the robot can be classified into two parts: viable and inviable. Then the stability of biped robot is defined and the Lose Balance Degree (LBD) is taken as the stability criterion of underactuated biped robot. LBD is used to evaluate the degree of current state to balance one and synthesizes the pose and speed of the robot. Stable conditions of underactuated gait are given based on LBD, and the characters of underactuated gait are validated based on planar biped robot. Underactuated gait has the characters of gradually stability, so time-invariant gait has strong robustness and adaptability although it is planned offline.
The stability control of 3D underactuated biped robot is the main goal of this dissertation. One of the critical conditions for stable biped walking is that the lateral motion should be in accordance with frontal one, where the frontal motion is the dominative part. Based on this fact, the stability control strategy of 3D underactuated gait is brought out which extends the planar one with step width adjustment to control the lateral walking cycle. By using this strategy, the lateral step cycle can be controlled to follow the frontal one and finally the stability of 3D underactuated gait is controlled. This strategy is robust to initial error and realizable for real robot. The stable still standing is very difficult for underactuated biped robot, but the posture is controllable. Then the stability controller based on T-S model and LQR controller has been designed to realize the asymptotic stability of double-support upright standing.
Using above proposed strategies, application on humanoid robot has been studied. The humanoid robot can be look on as an underactuated system by active underactuated method and high-speed dynamic walking can be realized by underactuated gait. Emphases of this part include: how to realize ankle Zero-Moment control, how to improve the stability and convergence speed and how to control the walking speed by the moment adjustment of supporting ankle. Bipedal walking always starts and ends with still standing, so the control of starting and stopping processes are studied and fully underactuated walking process for humanoid robots can be realized.
Finally, the main content of this dissertation is summarized and key points of future research are discussed.
本文主要研究欠驱动两足机器人控制策略及其在仿人机器人上的应用问题,主要内容包括:
首先对欠驱动两足机器人的复杂控制系统模型进行研究,分别基于D-H坐标建立机器人运动学模型,基于Lagrange函数建立单脚支撑期的控制系统模型,基于角动量守恒建立状态切换模型,并对欠驱动步态的实现条件进行详细讨论,为后面的研究奠定基础。
为实现机器人姿态可控,开展了时不变步态规划和控制方法研究,提出了基于遗传算法的时不变步态规划策略:以状态变量为优化参数,以能耗最小为优化目标,以各种约束为限制条件,将步态规划问题转化为非线性规划问题,同时实现步态的规划和优化。基于复杂控制系统模型,机器人运动控制采用反馈线性化方法,因此对解耦矩阵的可逆条件进行了深入研究,并设计了有限时间稳定控制器。
稳定控制是欠驱动两足机器人控制最大的难点,也是本文研究的重点。由于机构特殊,现有的稳定判据并不能对其稳定性进行定义和判定。从Lyapunov稳定性理论出发,将机器人状态分为可行和不可行状态。在此基础上,对欠驱动两足机器人的稳定性进行定义,并提出了一种基于失衡度的稳定判据。失衡度是对机器人偏离平衡状态的一种定量评估,综合考虑了姿态和速度参数,满足稳定判据的基本性质。从失衡度收敛的角度出发,给出了欠驱动步态的稳定条件,并以平面欠驱动机器人为平台对欠驱动步态的特点展开研究。实验表明,欠驱动步态具备渐进稳定性,因此,虽然是一种离线规划步态,但是具有很强的鲁棒性和环境适应能力。
3D欠驱动两足机器人稳定控制是本研究的主要目标。3D欠驱动步态不稳定主要是由于侧向与前向运动周期不匹配。生物学和机器人学研究表明,两足步行通常以前向运动为主导,侧向辅助保持稳定。基于这一事实,本文提出了一种3D欠驱动步态稳定控制策略,通过控制步宽调整机器人侧向运动周期,实现侧向对前向周期的自适应跟踪,最终实现3D欠驱动步态的渐进稳定。实验表明,该策略对初始状态误差具有很强的鲁棒性,对地面环境具有一定的适应能力,可实现性较强。欠驱动两足机器人静态稳定站立十分困难,但其直立姿态是可控的,本文基于T-S模型和LQR控制设计直立姿态稳定控制器,实现了3D欠驱动两足机器人双脚支撑直立姿态的渐进稳定控制。实验表明,采用所提控制策略,稳定状态的吸引域明显扩大。
本文对欠驱动控制策略在仿人机器人上的应用问题展开研究。仿人机器人与欠驱动两足机器人的主要区别在于脚掌和踝关节力矩。利用主动欠驱动策略对支撑踝关节进行零力矩控制,仿人机器人可以实现高速的欠驱动步行。论文重点研究了支撑踝零力矩控制策略的实现方法,如何利用踝关节力矩提高步态稳定性和收敛速度,如何利用踝关节力矩控制步行速度等问题。机器人总是从立定状态开始行走,而最终回归于立定状态,因此论文探讨和解决了仿人机器人欠驱动步态起步和停止过程的控制问题,实现了仿人机器人欠驱动步态行走的全过程控制。实验表明,基于主动欠驱动控制策略,仿人机器人可以实现欠驱动步态,机器人的运动性能明显提高。
最后,总结本文所做工作,分析不足之处,并提出今后的研究重点。
For the humanoid robot’s potential application, related researches have aroused much attention since its appearance. In the past forty years, research on humanoid robot has acquired remarkable achievements and lots of research organizations built their prototypes to show and validate related results. But to the developmental level of humanoid technology, it achieves far from the expectation of human being. One of the critical reasons is that movement capability of current humanoid robots with huge mass is very poor, and the biped walking is slow and inefficient. So, underactuated biped robot is brought forward to research high speed and dynamic walking. The robot has no soles and touches ground with points, which brings great challenges to biped and humanoid stability control. For examples, 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. Therefore, the appearance of underactuated biped robot offers new methods for humanoid motion planning and control. The key of this dissertation covers the control strategy and application of underactuated biped robot, and its content as follows:
As the basis of research on underactuated biped robot control, the hybrid control system model has been built. Several models are built respectively: kinematics model by D-H reference frame, control system model of single-supporting by Lagrange function, and states-switching model by angular momentum conservation. Then, the realizable conditions of the underactuated gait are discussed in great detail.
The planning and control of the time-invariant gait of underactuated biped robot are researched. The gaits are planned and optimized by Genetic Algorithm, which takes the state variables as the optimized parameters, the minimum energy-expend as the optimized goal, the realizable conditions as the restriction, and then the problem of gait-planning is changed into a nonlinear-planning one. The gait is controlled by feedback linearization, so dynamic singularity states and finite-time stability controller are studied.
Stability is the principal goal of biped motion control and it is also the most important in this dissertation. The current stability criterion can not be used directly to estimate the stability of underactuated biped robot for its special configuration. Based on Lyapunov stability theory, states of the robot can be classified into two parts: viable and inviable. Then the stability of biped robot is defined and the Lose Balance Degree (LBD) is taken as the stability criterion of underactuated biped robot. LBD is used to evaluate the degree of current state to balance one and synthesizes the pose and speed of the robot. Stable conditions of underactuated gait are given based on LBD, and the characters of underactuated gait are validated based on planar biped robot. Underactuated gait has the characters of gradually stability, so time-invariant gait has strong robustness and adaptability although it is planned offline.
The stability control of 3D underactuated biped robot is the main goal of this dissertation. One of the critical conditions for stable biped walking is that the lateral motion should be in accordance with frontal one, where the frontal motion is the dominative part. Based on this fact, the stability control strategy of 3D underactuated gait is brought out which extends the planar one with step width adjustment to control the lateral walking cycle. By using this strategy, the lateral step cycle can be controlled to follow the frontal one and finally the stability of 3D underactuated gait is controlled. This strategy is robust to initial error and realizable for real robot. The stable still standing is very difficult for underactuated biped robot, but the posture is controllable. Then the stability controller based on T-S model and LQR controller has been designed to realize the asymptotic stability of double-support upright standing.
Using above proposed strategies, application on humanoid robot has been studied. The humanoid robot can be look on as an underactuated system by active underactuated method and high-speed dynamic walking can be realized by underactuated gait. Emphases of this part include: how to realize ankle Zero-Moment control, how to improve the stability and convergence speed and how to control the walking speed by the moment adjustment of supporting ankle. Bipedal walking always starts and ends with still standing, so the control of starting and stopping processes are studied and fully underactuated walking process for humanoid robots can be realized.
Finally, the main content of this dissertation is summarized and key points of future research are discussed.
引文
[1] Yamaguchi, J. Kinoshita, N. Takanishi, et al. Development of a Biped Walking Robot Adapting to the Humans Living Floor. in Proceeding of IEEE International Conference on Robotics and Automation. 1996: p. 232-239.
[2] Hirai, K. Current and Future Perspective of Honda Humanoid Robot. in Proceedings of IEEE/RSJ Conference on Intelligent Robots and Systems. 1997: p. 500-508.
[3]谢涛,徐建峰,张永学,强文义,仿人机器人的研究历史、现状及展望.机器人, 2002. 24(4): p. 367-374.
[4] McGeer, T, Passive Dynamic Walking. International Journal of Robotics Research, 1990. 9(2): p. 62-82.
[5] McGeer, T., Dynamics and Control of Bipedal Locomotion. Journal of Theoretical Biology, 1993. 166(3): p. 277-314.
[6] Katic D., Vukobratovic, Survey of Intelligence Control Techniques for Humanoid Robots. Journal of Intelligent and Robotic Systems, 2003. 37: p. 117–141.
[7] Tanie, K. Humanoid Robot and its Application Possibility. in Proceeding of IEEE Conference on Robotics, Intelligent Systems and Signal Processing. 2003: p. 213-218.
[8] Kato, I. The Hydraulically Powerd Biped Walking Machine with High Carrying Capacity. in Proceeding of the International Symposium on Exteral Control of Human Extremities. 1972. Dubrovnik,Yugoslavia: p. 410-421.
[9] www.androidworld.com.
[10] Hirai K., Hirose M., Haikawa Y., Takenaka T.. The Development of Honda Humanoid Robot. in Proceddings of IEEE International Conference on Robotics and Automation. 1998: p. 1321-1326.
[11] Nakamura Y., Nakamura Y., Hirukawa H., et al., Humanoid Robot Simulator for the METI HRP Project. Robotics and Autonomous Systems, 2001. 37: p. 101-114.
[12] Hirukawa, H., Humanoid Robotics Platforms Developed in HRP. Robotics and Autonomous Systems, 2004. 48: p. 165-175.
[13] Kazuhiko AKACHI, Kenji KANEKO, Noriyuki KANEHIRA. Development of Humanoid Robot HRP-3P. in Proceedings of 2005 5th IEEE-RAS International Conference on Humanoid Robots. 2005: p. 50-55.
[14] Ishida. T, Kuroki.Y, Yamaguchi. J. Mechanical System of a Small Biped Entertainment Robot. in Proceedings. 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems. 2003: p. 1129-1134.
[15] Yoshihiro Kuroki, Masahiro Fujita, et al. A Small Biped Entertainment RobotExploring Attractive Applications. in IEEE International Conference on Robotics and Automation. 2003: p. 471-476.
[16] Nagasaka K., Kuroki Y. Integrated Motion Control for Walking, Jumping and Running on a Small Bipedal Entertainment Robot. in Proceedings of IEEE International Conference on Robotics and Automation. 2004: p. 3189-3914.
[17] Hirose M., Haikawa Y., Takenaka T., et al. Development of Humanoid Robot ASIMO. in Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2001: p. 1321-1326
[18] Gienger. M, Janben. H, Goerick. C. Exploiting Task Intervals for Whole Body Robot Control. in Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2006: p. 2484-2490.
[19] Chestnutt J., Lau M., Cheung G., et al. Footstep Planning for the Honda ASIMO Humanoid. in Proceedings of the 2005 IEEE International Conference on Robotics and Automation. 2005: p. 629-634.
[20] Nishio. A, Takahashi. K, Nenchev.D. Balance Control of a Humanoid Robot Based on the Reaction Null Space Method. in Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2006: p. 1996-2001.
[21] Yu Ogura; Aikawa, H.; Shimomura, K.; Kondo, H.; Morishima, A.; Hun-ok Lim; Takanishi, A. Development of a new humanoid robot WABIAN-2. in Proceedings 2006 IEEE International Conference on Robotics and Automation. 2006: p. 76-81.
[22] Kagami, S. Nishiwaki, K. Sugihara, T. et al. Design and Implementation of Software Research Platform for Humanoid Robotics: H6. in Proceeding of IEEE International Conference on Robotics and Automation. 2001: p. 2431-2436
[23] Ill-Woo Park, Jung-Yup Kim, Jungho Lee and Jun-Ho Oh. Mechanical Design of Humanoid Robot Platform KHR-3. in Proceedings of IEEE-RAS International Conference on Humanoid Robots. 2005: p. 321-326.
[24] Lohmeier, S. Loffler, K. Gienger, M. Ulbrich, H. Pfeiffer, F. Computer System and Control of Biped "Johnnie". in Proceeding of IEEE International Conference on Robotics and Automation. 2004: p. 4222-4227.
[25] Loffler, K. Gienger, M. Pfeiffer et al, Sensors and Control Concept of a Biped Robot. IEEE Transactions on Industrial Electronics, 2004. 51(5): p. 972-980.
[26] Wang G, Huang Qiang, Geng J H, et al. Coorperation of Dynamic Patterns and Sensory Reflex for Humanoid Robot. in Proceeding of IEEE International Conference on Robotics and Automation. 2003: p. 2472-2477.
[27] Yang J, Huang Qiang, et al. Walking Pattern Generation for Humanoid Robot Considering Upper Body Motion in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems 2006: p. 4441-4446.
[28] Mingguo Zhao, Li Liu, Jinsong Wang, et al. Control System Design of THBIP-IHumanoid Robot. in Proceedings of IEEE International Conference on Robotics and Automation. 2002: p. 2253-2258.
[29] Li Liu, Jinsong Wang, Ken Chen,el al. The Biped Humanoid Robot THBIP-I. in Proceedings of International Workshop on Bio-Robotics and Teleoperation 2001: p. 164-167.
[30] Jian Wang, Tao Sheng, Jianwen Wang, Hongxu Ma, System Overview of The Humanoid Robot Blackmann. WSEAS TRANSACTIONS on SYSTEMS, 2005. 4(7): p. 1070-1075.
[31] Vukobratovic M, Juricic D, Contribution to the Synthesis of Biped Gait. IEEE Transactions on Bio-Medical Engineering, 1969. 16(1): p. 1-6.
[32] Vukobratovic, M., Zero-Moment Point-Thirty Five Yeas of Its Life. International Jounal of Humanoid Robotics, 2004. 1(1): p. 157-173.
[33] Goswami, A., Postural Stability of Biped Robots and the Foot-Rotation Indicator (FRI) Point. International Journal of Robotics Research, 1999. 18(6): p. 523-533.
[34] Takanishi A., Ishida M., Yamazaki Y., and Kato I.. The Realization of Dynamic Walking Robot WL-10RD. in Proceedings of International Conference on Advanced Robotics. 1985: p. 459-466.
[35] Hurmuzlu, Y., Dynamics of Bipedal Gait PartI: Objective Functions and the Contact Event of a Planar Five-Link Biped. Technical Report, 1998: p. 1-11.
[36] Hurmuzlu, Y., Dynamics of Bipedal Gait Part II: Stability Analysis of a Planar Five-Link Biped. Technical Report, 1998: p. 11-19.
[37] C.L.Shih, etc, The Dynamics and Control of a Biped Walking Robot with Seven Degrees of Freedom. ASME Journal of Dynamic Systems, Measurement and Control, 1996. 118: p. 683–690.
[38] Kajita S., Tani K.. Study of Dynamic Biped Locomotion on Rugged Terrain-Theory and Basic Experiment. in Proceeding of 5th Internatianal Conference On Advanced Robotics. 1991. Tokyo: p. 741-746.
[39] Huang Q., Yokoi K., Kajita S., el al, Planning Walking Patterns for A Biped Robot. IEEE Transactions on Robotics and Automation, 2001. 17(3): p. 280-289.
[40] Huang Q., Wang G., Li K.. A Sensory Reflexive Control for Humanoid Walking. in Proceedings of the 4th World Congress on Intelligent Control and Automation. 2002. Shanghai, P.R.China: p. 3256-3260.
[41] Huang Q., Kaneko K., Yokoi K, el al. Balance Control of a Biped Robot Combining Off-line Pattern with Real-time Modification. in Proceddings of IEEE International Conference on Robotics and Automation. 2000: p. 3346-3352.
[42] Park J. H., Chung H.. ZMP compensation by online trajectory generation for biped robots. in IEEE International Conference on Systems, Man, andCybernetics. 1999.
[43] Benbrahim H., Judy A. Franklin, Biped Dynamic Walking Using Reinforcement Learning. Robotics and Autonomous Systems, 1997(22): p. 283-302.
[44] Li Q., Takanishi A., Kato I.. Learning Control Compensative Trunk Motion for a Biped Walking Robot Based on ZMP Stability Criterion. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 1992: p. 597-603.
[45] Tsuchiya K., Aoi S., and Tsujita K.. Locomotion Control of a Biped Locomotion Robot using Nonlinear Oscillators. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2003: p. 1745-1750.
[46] Lim H.O., Kaneshima Y., and Takanishi A.. Online Walking Pattern Generation for Biped Humanoid Robot with Trunk. in Proceedings of IEEE International Conference on Robotics and Automation. 2002: p. 3111-3116.
[47] Nishiwaki K., Kagami S., Kuniyoshi Y., Inaba M., and Inoue H.. Online Generation of Humanoid Walking Motion based on a Fast Generation Method of Motion Pattern that Follows Desired ZMP. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2002: p. 2684-2689.
[48] Kajita, S., Kanehiro,F., Kaneko,K. The 3D Linear Inverted Pendulum Mode: A Simple Modeling for a Biped Walking Pattern Generation. in Proceedings of IEEE Conference on Intelligent Robots and Systems. 2001: p. 239-246.
[49] Kajita S., Kanehiro F., Kaneko K., et al. A Realtime Pattern Generator for Biped Walking. in Proceedings of IEEE International Conference on Robotics and Automation. 2002: p. 31-37.
[50] Lorch O., Seara J. F., Strobl K. H., et al. Perception Errors in Vision Guided Walking: Analysis, Modeling, and Filtering. in Proceeding of IEEE International Conference on Robotics and Automation. 2002: p. 2048-2053.
[51] Yagi M., Lumelsky V.. Biped Robot Locomotion in Scenes with Unknown Obstacles. in Proceddings of IEEE International Conference on Robotics and Automation. 1999 p. 375–380.
[52] Yagi M., Lumelsky V.. Synthesis of Turning Pattern Trajectories for a Biped Robot in a Scene with Obstacles. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2000: p. 1161–1166.
[53] Sugihara T., Nakamura Y.. A Fast Online Gait Planning with Boundary Condition Relaxation for Humanoid Robots. in Proceedings of IEEE International Conference on Robotics and Automation. 2005. Barcelona, Spain: p. 306-311.
[54] Tenreiro, Filipe M. J.A. Energy Analysis During Biped Walking. in Proceddings of IEEE International Conference on Robotics and Automation. 1999: p. 59-64.
[55]石宗英,徐文立,冯元琨,方海军,仿人型机器人动态步行控制方法.机器人, 2001. 23(6): p. 569-574.
[56] Jiro Doke, J. Maxwell Donelan , Arthur D. Kuo, Mechanics and Energetics of Swinging the Human Leg. The Journal of Experimental Biology, 2005. 208: p. 439-445.
[57] Westervelt, Eric R., Toward a Coherent Framework for the Control of Planar Biped Locomotion. 2003, University of Michigan.
[58] Y. Sugahara, Mikuriya, Y. Hashimoto, K. et al. Waling Control Method of Biped Locomotors on Inclined Plane. in Proceedings of IEEE International Conference on Robotics and Automation. 2005. Barcelona, Spain: p. 1989-1994.
[59] Yoshino, R., Stabilizing Control of High-Speed Walking Robot by Walking Pattren Regulator. Journal of the Robotics Society of Japan, 2000. 18(8): p. 1122-1132.
[60] Mariano Garcia, Andy Ruina, Michael Coleman. Some Results In Passive-Dynamic Walking. in Euromech Conference on Biology and Technology of Walking in Munich. 1998.
[61] Collins S. H., Wisse, M., Ruina A., A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees. The International Journal of Robotics Research, 2001. 20(7): p. 607-615.
[62] Garcia M., Chatterjee A., and Ruina A., Efficiency, Speed, and Scaling of Two Dimensional Passive-Dynamic Walking. Dynamics and Stability of Systems 2000. 15(3): p. 75–99.
[63] Goswami A., Espiau B., and Keramane A.. Limit Cycles and Their Stability in a Passive Bipedal Gait. in Proceeding of IEEE International Conference on Robotics and Automation. 1996: p. 246-251.
[64] Catherine E, , Active Control of Lateral Balance in Human Walking. Journal of Biomechanics, 2000. 33: p. 1433-1440.
[65] Maxwell J., et a, Mechanical and Metabolic Requirements for Active Lateral Stabilization in Human Walking. Journal of Biomechanics, 2004. 37: p. 827-835.
[66] Ruina, M. J. Coleman and A., An Uncontrolled Toy that Can Walk but Can not Stand Still. Physical Review Letters, 1998. 80: p. 3658-3661.
[67] Kuo, Arthur D., Stabilization of Lateral Motion in Passive Dynamic Walking. International Journal of Robotics Research September, 1999. 18(9): p. 917-930.
[68] Collins S., Ruina A., Tedrake R., and Wisse M., Efficient Bipedal Robots Based on Passive Dynamic Walkers. Science Magazine, 2005. 30(7): p. 1082-1085.
[69] Alexander, R.M Walking made simple. Science, 2005. 308: p. 58-59.
[70] Kuo, Arthur D., Harvesting energy by improving the economy of human walking. science, 2005. 309: p. 1686-1687.
[71] Pratt, J., Dilworth, P., Pratt, G. Virtual Model Control of a Bipedal Walking Robot. in Proceddings of IEEE International Conference on Robotics and Automation. 1997: p. 193-198
[72] Playter, R. R., Raibert, M. H. Generation of A Somersault by a 3D Biped Robot. in Proceeding of International Federation of Automatic Control. 1992.
[73] Chevallereau C., et al, RABBIT: A Test Bed for Advanced Control Theory. IEEE Control Systems Magazine, 2003. 8: p. 1-51.
[74] Morris B., Westervelt E.R. , Chevallereau C.. Achieving Bipedal Running with RABBIT: Six Steps toward Infinity. in Proceeding of Fast Motions in Biomechanics and Robotics Symposium. 2005: p. 277-297.
[75] Mike Stilman, Christopher G. Atkeson, et al. Dynamic Programming in Reduced Dimensional Spaces: Dynamic Planning For Robust Biped Locomotion. in Proceedings of IEEE International Conference on Robotics and Automation. 2005: p. 2399- 2404.
[76] Poramate Manoonpong, Tao Geng, Tomas Kulvicius, Bernd Porr, Adaptive, Fast Walking in a Biped Robot under Neuronal Control and Learning. PLoS Comput Biology. 7(3): p. e139.
[77]付成龙,陈恳,五杆四驱动平面双足机器人动态步态规划与非线性控制.机器人, 2006. 28(2): p. 206-212.
[78] Westervelt E.R., Grizzle J.W., and Koditschek D., Hybrid Zero Dynamics of Planar Biped Walkers. IEEE Transition. on Automatic Control, 2002. 48: p. 42-56.
[79] Sabourin, C, Bruneau, O, Robustness of the Dynamic Walk of a Biped Robot Subjected to Disturbing External Forces by Using CMAC Neural Networks. Robotics and Autonomous Systems, 2005. 23: p. 81-99.
[80] Sabourin, C, Bruneau, O, Buche, Control Strategy for the Robust Dynamic Walk of A Biped Robot. The International Journal of Robotics Research 2006. 29(9): p. 843-860.
[81] Hauser J., Chung C. C., Converse Lyapunov Functions for Exponentially Stable Periodic Orbits. Systems and Control Letters. 23(1): p. 27-34.
[82] Guobiao Song, Milos Zefran. Stabilization of Hybrid Periodic Orbits with Application to Bipedal Walking. in Proceeding of American Control Conference. 2006.
[83] Guobiao Song , Milos Zefran. Underactuated Dynamic Three-Dimensional Bipedal Walking. in Proceedings of IEEE International Conference on Robotics and Automation. 2006: p. 854 - 859.
[84] Masahiro D. , et al, Passive dynamic autonomous control of bipedal walking. Humanoid, 2004.
[85] Doi, Masahiro. 3D Dynamic Walking Based on the Inverted Pendulum Model With Two Degree of Underactuation. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2001: p. 4166-4171.
[86] Ching-Long Shih, Grizzle, J.W., Chevallereau, C. Asymptitically Stable Walking of a Simple Underactuated 3D Bipedal Robot. in Proceeding of IEEEInternational Conference on Robotics and Automation. 2006: p. 2766-2771.
[87] Tao Geng, Bernd Porr, Florentin Worgotter, Fast Biped Walking with A Sensor-driven Neuronal Controller and Real-time Online Learning. The International Journal of Robotics Research, 2006. 25(3): p. 243-259
[88] Matsubara T., Morimoto J., Jun Nakanishi, et al., Learning CPG-based Biped Locomotion with a Policy Gradient Method. Robotics and Autonomous Systems, 2006. 54: p. 911-920.
[89] Hongxu Ma, Jian Wan, et al. Synthesis of CPG Based Motion Control Methods for Humanoid Robots. in Proceedings of the 6th World Congress on Intelligent Control and Automation. 2006. Dalian,China: p. 8843-8847.
[90] Gunes, Atilim, Evolution of Central Pattern Generators for the Control of a Five-link Planar Bipedal Walking Mechanism. 2008.
[91] Alexander, R.McN.; Jayes, A.S., A Dynamic Similarity Hypothesis for the Gaits of Quadrupedal Mammals. Journal of Zoology (UK), 1983. 201(1): p. 135-152.
[92] Wisse M, van J Frankenhuyzen. Design and Construction of MIKE: a 2-D Autonomous Biped Based on Passive Dynamic Walking in Proceedings of the Second International Symposium on Adaptive Motion of Animals and Machines. 2003: p. 143-154.
[93] Elert, Glenn, Speed of the fastest human walking. The Physics Factbook, Available: http://hypertextbook.com/facts/2001/ConnieLau.shtml. Accessed 2008.
[94] Alexander, R., Walking and running. American Scientist, 1984. 72: p. 348–354.
[95] Westervelt E. R., Buche G., and Grizzle J. W., Experimental Validation of a Framework for the Design of Controllers that Induce Stable Walking in Planar Bipeds. The International Journal of Robotics Research, 2004. 23(6): p. 559-582
[96] Christine Chevallereau, Grizzle J.W., and Ching-Long Shih, Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot. IEEE Transactions on Robotics, 2008.
[97] Jerry E. Pratt , Russ Tedrake, Velocity Based Stability Margins for Fast Bipedal Walking. Lecture Notes in Control and Information Sciences, 2006. 340: p. 299-324.
[98] Hofmann A, , Robust Execution of Bipedal Walking Tasks From Biomechanical Principles. PhD Dissertation USA:MIT, 2006.
[99] Vukobratovic M, Borovac B, Surla D et al, Scienctific Fundamentals of Robotics: Biped Locomotion. New York: Springer, 1990.
[100] Shibata M., Natori T.. Impact Force Reduction for Biped Robot Based on Decoupling CoG Scheme. in Proceedings of IEEE International Conference on AMC. 2000: p. 612-617.
[101] Hurmuzlu Y., Genot F., Brogliato B., Modeling, Stability and Control of Biped Robots--A General Framework. Automatica, 2004. 40: p. 1647-1664.
[102] Mu, XiPing, Dynamics and Motion Regulation of a Five-Linked Biped Robot Walking in the Sagittal Plane, in Department of Mechanical and Manufacturing Engineering. 2004, The University of Manitoba.
[103] Kyosuke Ono, Rongqiang Liu, Optimal Biped Walking Locomotion Solved by Trajectory Planning Method. Transactions of the ASME, Journal of Dynamic Systems, Measurement, and Control, 2002. 124(4): p. 554-565
[104] Yagi M., Lumelsky V., Local On-line Planning in Biped Robot Locomotion Amongst Unknown Obstacles. Robotica, 2000. 18(4): p. 389-402.
[105] James Kuffner, Koichi Nishiwaki, Satoshi Kagami, Masayuki Inaba, and Hirochika Inoue. Motion Planning for Humanoid Robots. in Proceedings of 11th International Symposium of Robotics Research. 2003.
[106] Chevallereau, C., Time-Scaling Control of an Underactuated Biped Robot. IEEE Transactions on Robotics and Automation, 2003. 19(2): p. 362-368.
[107] Grizzle J.W., Christine Chevallereau, and Ching-Long Shih. HZD-Based Control of a Five-Link Underactuated 3D Bipedal Robot. in Proceeding of IEEE Conference on Decision and Control. 2008: p. 5206-5213.
[108] Wisse M., Schwab A. L., A 3D Passive Dynamic Biped with Yaw and Roll Compensation. Robotica, 2000. 19(3): p. 275-284.
[109] Hirabayashi, T. Ugurlu, B. Kawamura, A. Chi Zhu. Yaw Moment Compensation of Biped Fast Walking Using 3D Inverted Pendulum. in Proceedings of 10th IEEE International Workshop on Advanced Motion Control. 2008: p. 296-300.
[110] Ames AD, Gregg RD, et al. Towards the geometric reduction of controlled three-dimensional robotic bipedal walkers. in Proceeding of 3rd Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. 2006.
[111] Gregg, Aaron D. Ames and Robert D. Stably Extending Two-Dimensional Bipedal Walking to Three Dimensions. in Proceeding of American Control Conference. 2007: p. 2848-2854.
[112] Kaminka G.A., Lima P.U., and Rojas R.. The Role of Motion Dynamics in the Design, Control and Stability of Bipedal and Quadrupedal Robots. in RoboCup 2002, LNAI 2752. 2003: p. 206-223.
[113] Featherstone R., Orin D.. Robot Dynamics: Equations and Algorithm. in Proceddings of IEEE International Conference on Robotics and Automation. 2000: p. 826-834.
[114] Hemami H., Wyman B., Rigid Body Dynamics, Constraints, and Inverses. Journal of Applied Mechanics, 2007. 74: p. 47-56.
[115] Pal D. K., Ascher U. M., Kry P. G.. Forward Dynamics Algorithms for Multibody Chains and Contact. in Proceddings of IEEE International Conference on Robotics and Automation. 2000: p. 857-863.
[116] Goldsmith, W, ed. Impact, the Theory and Physical Behaviour of Colliding Solids. 1960, London Edward Arnold Publishers LTD.
[117] Hurmuzlu Y., Marghitu D. B., Rigid Body Collisions of Planar Kinematic Chains With Multiple Contact Points. International Journal of Robotics Research, 1994. 13(1): p. 82-92.
[118] Zhe Tang, Changjiu Zhou, Zenqi Sun. Trajectory Planning for Smooth Transition of a Biped Robot. in Proceedings of IEEE International Conference on Robotics & Automation. 2003: p. 2455-2460.
[119] Canudas-de-Wit, Carlos, On the Concept of Virtual Constraints as a Tool for Walking Robot Control and Balancing. Annual Reviews in Control, 2004: p. 1-10.
[120] Westervelt E. R., Grizzle J. W., et al, Hybrid Zero Dynamics of Planar Biped Walkers. IEEE Transactions on Automatic Control, 2003. 48(1): p. 42-56.
[121] Hlland, J.H., Adaptation in Nature and Artificial System. MIT Press, 1992.
[122] Goldberg E., D, Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, 1989.
[123]飞思科技产品研发中心, MATLAB6.5辅助优化计算与设计, 2003:电子工业出版社.
[124] Roussel L., Canudas C., Goswami A.. Generation of Energy Optimal Complete Gait Cycles for Biped Robots. in Proceedings of IEEE International Conference on Robotics and Automation. 1998: p. 2036-2041.
[125] Chevallereau C., Formalsky A., and Perrin B.. Low Energy Cost Reference Trajectories for a Biped Robot. in Proceedings of IEEE International Conference on Robotics and Automation. 1998: p. 1398-1404.
[126] Fujimoto, Y. Trajectory Generation of Biped Running Robot with Minimum Energy Consumption. in Proceedings of IEEE International Conference on Robotics and Automation. 2004: p. 3803-3808.
[127]何广平,陆震,王凤翔,欠驱动机器人的动力学耦合奇异研究.航空学报, 2005. 26(12): p. 240-245.
[128]丁希仑,战强,解玉文,自由漂浮的空间机器人系统的动力学奇异特性分析及其运动规划.航空学报, 2001. 22(5): p. 474-477.
[129] Farrell, E.R. Westervelt B. Morris K. D., Analysis Results and Tools for the Control of Planar Bipedal Gaits Using Hybrid Zero Dynamics. Auton Robot, 2007(23): p. 131-145.
[130]谭道盛,温启愚,矩阵的任意分块求逆及其应用.四川大学学报(自然科学版), 1999. 36(1): p. 34-37.
[131] Sanjay P. Bhat , Dennis S. Bernstein. Finite-Time Stability of Homogeneous Systems. in Proceedings of American Control Conference. 1997: p. 2513-2514.
[132] YANG, Shuanghe YU,Zi M A,Xiaohui, Nonsmooth Finite-Time Control of Uncertain Second-Order Nonlinear Systems. Journal ofControl Theory andApplications, 2007. 5(2): p. 171-176.
[133] Bhat S P, Bernstein D, Finite-Time Stability of Continuous Autonomous Systems. SLAM Journal on Controla nd Optimi zation, 2000. 38(3): p. 751-766.
[134] Bhat S P, Bernstein DS, Continuous Finite-Time Stabilization of the Translational and Rotational Double Integrator. IEEE Transations on Automatic Control, 1998. 43(5): p. 678-682.
[135] Kajita S, Kanehiro F, Kaneko K, et al. Biped Walking Pattern Generation by Using Preview Control of Zero-Moment Point. in Proceeding of the IEEE International Conference on Robotics and Automation. 2003: p. 1620-1626.
[136] Kim J., et al. Real-time ZMP Compensation Method using Null Motion for Mobile Manipulators. in Proceedings of IEEE International Conference on Robotics and Automation 2002: p. 1967-1972.
[137] Choi Y., You B., Oh S.. On the Stability of Indirect ZMP Controller for Biped Robot Systems. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2004: p. 1966-1971.
[138] Ikemata Y., Sano A., Fujirioto H.. Analysis of Stable Limit Cycle in Passive Walking. in SICE Annual Conference. 2003: p. 117-122.
[139] Hiskens, Ian A. Stability of Hybrid System Limit Cycles: Application to the Compass Gait Biped Robot. in Proceeding of The 40th lEEE Conference on Decision and Contml. 2001: p. 774-779.
[140] Rubensson M., Lennartsson B., Pettersson S.. Convergence to Limit Cycles in Hybrid Systems. in 8th International Federation of Automatic Control Symposium on Large Scale Systems. 1998: p. 704-709.
[141] Goswami A., Espiau B., Keramane A., Limit Cycles in a Passive Compass Gait Biped and Passivity-Mimicking Control Laws. Journal of Autonomous Robots, 1997. 4(3): p. 273-286.
[142] Marko Popovic, Amy Englehart. Angular Momentum Primitives for Human Walking: Biomechanics and Control. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2004: p. 1685-1691.
[143] Herr H, Popovic M Angular Momentum in Human Walking. Journal of Experimental Biology, 2008. 211(4): p. 467-481.
[144] Marko B. Popovic, Hugh Herr, Ground Reference Points in Legged Locomotion: Definitions, Biological Trajectories and Control Implications. Mobile Robots Towards New Applications, 2006: p. 784-810.
[145] Popovic, M., Hofmann, A. and Herr, H. Zero spin angular momentum control: definition and applicability. in Proceedings of the IEEE-RAS/RSJ International Conference on Humanoid Robots. 2004: p. 478- 493
[146] Goswami A., Kallem V.. Rate of Change of Angular Momentum and Balance Maintenace of Biped Robots. in Proceedings of IEEE International Conference on Robotics and Automation. 2004: p. 3785-3790.
[147] Shuuji KAJITA, Fumio KANEHIRO, Kenji KANEKO. Resolved MomentumControl: Humanoid Motion Planning based on the Linear and Angular Momentum. in Proceedings of the 2003 IEEE/RSJ Intl. Conference on Intelligent Robots and Systems. 2003: p. 1644-1650.
[148] Zhaohui LI, Qiang HUANG, Kejie LI, et al. Stability Criterion and Pattern Planning for Humanoid Running. in Proceedings of IEEE International Conference on Robotics & Automation. 2004: p. 1059-1064.
[149] Yuichi Morita, Kouhei Ohnishi. Attitude Control of Hopping Robot Using Angular Momentum. 2003: p. 173-178.
[150] Pierre-Brice, WIEBER. On the Stability of Walking Systems. in In Proceedings of the International Workshop on Humanoid and Human Friendly Robots. 2002.
[151] Dempster, W.T, Gaughran, G, Properties of Body Segments Based on Size and Weight. American Journal of Anatomy, 1965.
[152] Jesse W. Grizzle, Gabriel Abba, Franck Plestan, Asymptotically Stable Walking for Biped Robots:Analysis via Systems with Impulse Effects. IEEE Transactions on Automatic Control, 2001. 46(1): p. 51-64.
[153] Westervelt E. R., Grizzle J. W., and Kodistschek D. E. Switching and PI Control of Walking Motions of Planar Biped Walkers. IEEE Transactions on Automatic Control, 2003. 48(2): p. 308-312.
[154]吴剑,李建设,人体行走时步态的生物力学研究进展.中国运动医学杂志, 2002. 21(3): p. 305-307.
[155] Maxwell J. Donelan, Rodger Kram , Arthur D. Kuo, Mechanical and Metabolic Determinants of the Preferred Step Width in Human Walking. The Royal Society, 2001: p. 1985-1992.
[156] Isidori, A., Nonlinear Conbvl Systems. 1989, New York: Springer-Verlag.
[157] ]TanakaK, SanoM, Fuzzy Stability Criterion of a Class of Nonlinear Systems. Information Science, 1993. 70(1): p. 3-26.
[158] TanakaK, Sugeno M, Stability Analysis and Design of Fuzzy Control System. Fuzzy Sets and System, 1992. 45(2): p. 135-196.
[159] Takagi T, Sugeno M, Fuzzy Identification of Systems and Its Application to Modeling and Control. IEEE Transtions on Systems, Man and Cybernetics, 1985. 15(1): p. 116-132.
[160] Tanaka, K. and Kosali, T, Design of a Stable Fuzzy Controller for an Articulated Vehicle. IEEE transactions on Systems, Man, and Cybernetics, 1997. 27(3): p. 552-558.
[161] Yoshida H., Inoue K., Arai T., Mae Y.. Mobile Manipulation of Humanoid Robots -Optimal Posture for Generating Large Force based on Statics. in Proceedings of IEEE International Conference on Robotics and Automation. 2002: p. 2271-2276.
[162] Harada K., Kajita S., et al. Real-Time Planning of Humanoid Robot's Gait for Force Controlled Manipulation. in Proceedings of IEEE InternationalConference on Robotics and Automation. 2004: p. 616-622.
[163] Naoto Kawauchi, Shigetoshi Shiotani, Hiroyuki Kanazawa, et al. A Plant Maintenance Humanoid Robot System. in Proceedings of IEEE International Conference on Robotics & Automation. 2003: p. 2973-2978.
[164] Bryan Adams, Cynthia Breazeal, Rodney A, et al, Humanoid Robots: A New Kind of Tool. Intelligent Systems and their Applications, 2000. 15(4): p. 25-31.
[165] Jun Ho Choi, J.W. Grizzle, Planar Bipedal Walking with Anthropomorphic Foot Action. IEEE Transection on Robotics, 2005.
[166] Choi JH, Grizzle JW. Planar Bipedal Walking with Foot Rotation. in Proceedings of American Control Conference. 2005: p. 4909- 4916
[167] Chenglong FU , Ken CHEN, Jing XIONG, Leon XU, Stability and Control of Dynamic Walking for a Five-Link Planar Biped Robot with Feet. Journal of Control Theory and Applications, 2007. 5(2): p. 113–120.
[168] Keon Young Yi, Yuan F Zheng, Biped Locomotion by Reduced Ankle Power. Autonomous Robots, 1997. 4: p. 307–314.
[169] Leardini, Alberto, Geometry and Mechanics of Human Ankle Complex and Ankle Prosthesis Design. Clinical Biomechanics, 2001. 16: p. 706-709.
[170]绳涛,仿人机器人力信息反馈控制方法研究, in机电工程与自动化学院. 2004,国防科学技术大学:长沙.
[171] Arimoto S, Miyazaki F. Stability and Robustness of PID Feedback Control for Robot Manipulator of Sensory Capability. in Proceeding of First Int. Symposium: Robotics Research. 1983: p. 783~799.
[172] James Kuffner, Koichi Nishiwaki, Satoshi Kagami. Self-Collision Detection and Prevention for Humanoid Robots. in Proceddings of IEEE International Conference on Robotics and Automation. 2002: p. 2265-2270.
[173] Kei Okada, Masayuki Inaba, Hirochika Inoue. Real-time and Precise Self Collision Detection System for Humanoid Robots. in Proceedings of IEEE International Conference on Robotics and Automation. 2005: p. 1072-1077.
[174] Atsuo Kawamura, Chi Zhu. The Development of Biped Robot MARI-3 for Fast Walking and Running. in Proceedings of IEEE-RAS International Conference on Humanoid Robots. 2006: p. 599-604.
[175] Sang-Ho Hyon, Takashi Emura. Aerial Posture Control for 3D Biped Running Using Compensator around Yaw Axis in Proceedings of the 2003 IEEE International Conference on Robotics & Automation. 2003: p. 57-62.
[176] Ueda Jun, Shirae Kenji, Oda Shingo, et al, Moment Compensation for Fast Dynamic Walking of Humanoids based on Human Athletes Pelvis Rotation. Journal of the Robotics Society of Japan, 2005. 23(4): p. 457-465.
[2] Hirai, K. Current and Future Perspective of Honda Humanoid Robot. in Proceedings of IEEE/RSJ Conference on Intelligent Robots and Systems. 1997: p. 500-508.
[3]谢涛,徐建峰,张永学,强文义,仿人机器人的研究历史、现状及展望.机器人, 2002. 24(4): p. 367-374.
[4] McGeer, T, Passive Dynamic Walking. International Journal of Robotics Research, 1990. 9(2): p. 62-82.
[5] McGeer, T., Dynamics and Control of Bipedal Locomotion. Journal of Theoretical Biology, 1993. 166(3): p. 277-314.
[6] Katic D., Vukobratovic, Survey of Intelligence Control Techniques for Humanoid Robots. Journal of Intelligent and Robotic Systems, 2003. 37: p. 117–141.
[7] Tanie, K. Humanoid Robot and its Application Possibility. in Proceeding of IEEE Conference on Robotics, Intelligent Systems and Signal Processing. 2003: p. 213-218.
[8] Kato, I. The Hydraulically Powerd Biped Walking Machine with High Carrying Capacity. in Proceeding of the International Symposium on Exteral Control of Human Extremities. 1972. Dubrovnik,Yugoslavia: p. 410-421.
[9] www.androidworld.com.
[10] Hirai K., Hirose M., Haikawa Y., Takenaka T.. The Development of Honda Humanoid Robot. in Proceddings of IEEE International Conference on Robotics and Automation. 1998: p. 1321-1326.
[11] Nakamura Y., Nakamura Y., Hirukawa H., et al., Humanoid Robot Simulator for the METI HRP Project. Robotics and Autonomous Systems, 2001. 37: p. 101-114.
[12] Hirukawa, H., Humanoid Robotics Platforms Developed in HRP. Robotics and Autonomous Systems, 2004. 48: p. 165-175.
[13] Kazuhiko AKACHI, Kenji KANEKO, Noriyuki KANEHIRA. Development of Humanoid Robot HRP-3P. in Proceedings of 2005 5th IEEE-RAS International Conference on Humanoid Robots. 2005: p. 50-55.
[14] Ishida. T, Kuroki.Y, Yamaguchi. J. Mechanical System of a Small Biped Entertainment Robot. in Proceedings. 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems. 2003: p. 1129-1134.
[15] Yoshihiro Kuroki, Masahiro Fujita, et al. A Small Biped Entertainment RobotExploring Attractive Applications. in IEEE International Conference on Robotics and Automation. 2003: p. 471-476.
[16] Nagasaka K., Kuroki Y. Integrated Motion Control for Walking, Jumping and Running on a Small Bipedal Entertainment Robot. in Proceedings of IEEE International Conference on Robotics and Automation. 2004: p. 3189-3914.
[17] Hirose M., Haikawa Y., Takenaka T., et al. Development of Humanoid Robot ASIMO. in Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2001: p. 1321-1326
[18] Gienger. M, Janben. H, Goerick. C. Exploiting Task Intervals for Whole Body Robot Control. in Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2006: p. 2484-2490.
[19] Chestnutt J., Lau M., Cheung G., et al. Footstep Planning for the Honda ASIMO Humanoid. in Proceedings of the 2005 IEEE International Conference on Robotics and Automation. 2005: p. 629-634.
[20] Nishio. A, Takahashi. K, Nenchev.D. Balance Control of a Humanoid Robot Based on the Reaction Null Space Method. in Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2006: p. 1996-2001.
[21] Yu Ogura; Aikawa, H.; Shimomura, K.; Kondo, H.; Morishima, A.; Hun-ok Lim; Takanishi, A. Development of a new humanoid robot WABIAN-2. in Proceedings 2006 IEEE International Conference on Robotics and Automation. 2006: p. 76-81.
[22] Kagami, S. Nishiwaki, K. Sugihara, T. et al. Design and Implementation of Software Research Platform for Humanoid Robotics: H6. in Proceeding of IEEE International Conference on Robotics and Automation. 2001: p. 2431-2436
[23] Ill-Woo Park, Jung-Yup Kim, Jungho Lee and Jun-Ho Oh. Mechanical Design of Humanoid Robot Platform KHR-3. in Proceedings of IEEE-RAS International Conference on Humanoid Robots. 2005: p. 321-326.
[24] Lohmeier, S. Loffler, K. Gienger, M. Ulbrich, H. Pfeiffer, F. Computer System and Control of Biped "Johnnie". in Proceeding of IEEE International Conference on Robotics and Automation. 2004: p. 4222-4227.
[25] Loffler, K. Gienger, M. Pfeiffer et al, Sensors and Control Concept of a Biped Robot. IEEE Transactions on Industrial Electronics, 2004. 51(5): p. 972-980.
[26] Wang G, Huang Qiang, Geng J H, et al. Coorperation of Dynamic Patterns and Sensory Reflex for Humanoid Robot. in Proceeding of IEEE International Conference on Robotics and Automation. 2003: p. 2472-2477.
[27] Yang J, Huang Qiang, et al. Walking Pattern Generation for Humanoid Robot Considering Upper Body Motion in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems 2006: p. 4441-4446.
[28] Mingguo Zhao, Li Liu, Jinsong Wang, et al. Control System Design of THBIP-IHumanoid Robot. in Proceedings of IEEE International Conference on Robotics and Automation. 2002: p. 2253-2258.
[29] Li Liu, Jinsong Wang, Ken Chen,el al. The Biped Humanoid Robot THBIP-I. in Proceedings of International Workshop on Bio-Robotics and Teleoperation 2001: p. 164-167.
[30] Jian Wang, Tao Sheng, Jianwen Wang, Hongxu Ma, System Overview of The Humanoid Robot Blackmann. WSEAS TRANSACTIONS on SYSTEMS, 2005. 4(7): p. 1070-1075.
[31] Vukobratovic M, Juricic D, Contribution to the Synthesis of Biped Gait. IEEE Transactions on Bio-Medical Engineering, 1969. 16(1): p. 1-6.
[32] Vukobratovic, M., Zero-Moment Point-Thirty Five Yeas of Its Life. International Jounal of Humanoid Robotics, 2004. 1(1): p. 157-173.
[33] Goswami, A., Postural Stability of Biped Robots and the Foot-Rotation Indicator (FRI) Point. International Journal of Robotics Research, 1999. 18(6): p. 523-533.
[34] Takanishi A., Ishida M., Yamazaki Y., and Kato I.. The Realization of Dynamic Walking Robot WL-10RD. in Proceedings of International Conference on Advanced Robotics. 1985: p. 459-466.
[35] Hurmuzlu, Y., Dynamics of Bipedal Gait PartI: Objective Functions and the Contact Event of a Planar Five-Link Biped. Technical Report, 1998: p. 1-11.
[36] Hurmuzlu, Y., Dynamics of Bipedal Gait Part II: Stability Analysis of a Planar Five-Link Biped. Technical Report, 1998: p. 11-19.
[37] C.L.Shih, etc, The Dynamics and Control of a Biped Walking Robot with Seven Degrees of Freedom. ASME Journal of Dynamic Systems, Measurement and Control, 1996. 118: p. 683–690.
[38] Kajita S., Tani K.. Study of Dynamic Biped Locomotion on Rugged Terrain-Theory and Basic Experiment. in Proceeding of 5th Internatianal Conference On Advanced Robotics. 1991. Tokyo: p. 741-746.
[39] Huang Q., Yokoi K., Kajita S., el al, Planning Walking Patterns for A Biped Robot. IEEE Transactions on Robotics and Automation, 2001. 17(3): p. 280-289.
[40] Huang Q., Wang G., Li K.. A Sensory Reflexive Control for Humanoid Walking. in Proceedings of the 4th World Congress on Intelligent Control and Automation. 2002. Shanghai, P.R.China: p. 3256-3260.
[41] Huang Q., Kaneko K., Yokoi K, el al. Balance Control of a Biped Robot Combining Off-line Pattern with Real-time Modification. in Proceddings of IEEE International Conference on Robotics and Automation. 2000: p. 3346-3352.
[42] Park J. H., Chung H.. ZMP compensation by online trajectory generation for biped robots. in IEEE International Conference on Systems, Man, andCybernetics. 1999.
[43] Benbrahim H., Judy A. Franklin, Biped Dynamic Walking Using Reinforcement Learning. Robotics and Autonomous Systems, 1997(22): p. 283-302.
[44] Li Q., Takanishi A., Kato I.. Learning Control Compensative Trunk Motion for a Biped Walking Robot Based on ZMP Stability Criterion. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 1992: p. 597-603.
[45] Tsuchiya K., Aoi S., and Tsujita K.. Locomotion Control of a Biped Locomotion Robot using Nonlinear Oscillators. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2003: p. 1745-1750.
[46] Lim H.O., Kaneshima Y., and Takanishi A.. Online Walking Pattern Generation for Biped Humanoid Robot with Trunk. in Proceedings of IEEE International Conference on Robotics and Automation. 2002: p. 3111-3116.
[47] Nishiwaki K., Kagami S., Kuniyoshi Y., Inaba M., and Inoue H.. Online Generation of Humanoid Walking Motion based on a Fast Generation Method of Motion Pattern that Follows Desired ZMP. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2002: p. 2684-2689.
[48] Kajita, S., Kanehiro,F., Kaneko,K. The 3D Linear Inverted Pendulum Mode: A Simple Modeling for a Biped Walking Pattern Generation. in Proceedings of IEEE Conference on Intelligent Robots and Systems. 2001: p. 239-246.
[49] Kajita S., Kanehiro F., Kaneko K., et al. A Realtime Pattern Generator for Biped Walking. in Proceedings of IEEE International Conference on Robotics and Automation. 2002: p. 31-37.
[50] Lorch O., Seara J. F., Strobl K. H., et al. Perception Errors in Vision Guided Walking: Analysis, Modeling, and Filtering. in Proceeding of IEEE International Conference on Robotics and Automation. 2002: p. 2048-2053.
[51] Yagi M., Lumelsky V.. Biped Robot Locomotion in Scenes with Unknown Obstacles. in Proceddings of IEEE International Conference on Robotics and Automation. 1999 p. 375–380.
[52] Yagi M., Lumelsky V.. Synthesis of Turning Pattern Trajectories for a Biped Robot in a Scene with Obstacles. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2000: p. 1161–1166.
[53] Sugihara T., Nakamura Y.. A Fast Online Gait Planning with Boundary Condition Relaxation for Humanoid Robots. in Proceedings of IEEE International Conference on Robotics and Automation. 2005. Barcelona, Spain: p. 306-311.
[54] Tenreiro, Filipe M. J.A. Energy Analysis During Biped Walking. in Proceddings of IEEE International Conference on Robotics and Automation. 1999: p. 59-64.
[55]石宗英,徐文立,冯元琨,方海军,仿人型机器人动态步行控制方法.机器人, 2001. 23(6): p. 569-574.
[56] Jiro Doke, J. Maxwell Donelan , Arthur D. Kuo, Mechanics and Energetics of Swinging the Human Leg. The Journal of Experimental Biology, 2005. 208: p. 439-445.
[57] Westervelt, Eric R., Toward a Coherent Framework for the Control of Planar Biped Locomotion. 2003, University of Michigan.
[58] Y. Sugahara, Mikuriya, Y. Hashimoto, K. et al. Waling Control Method of Biped Locomotors on Inclined Plane. in Proceedings of IEEE International Conference on Robotics and Automation. 2005. Barcelona, Spain: p. 1989-1994.
[59] Yoshino, R., Stabilizing Control of High-Speed Walking Robot by Walking Pattren Regulator. Journal of the Robotics Society of Japan, 2000. 18(8): p. 1122-1132.
[60] Mariano Garcia, Andy Ruina, Michael Coleman. Some Results In Passive-Dynamic Walking. in Euromech Conference on Biology and Technology of Walking in Munich. 1998.
[61] Collins S. H., Wisse, M., Ruina A., A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees. The International Journal of Robotics Research, 2001. 20(7): p. 607-615.
[62] Garcia M., Chatterjee A., and Ruina A., Efficiency, Speed, and Scaling of Two Dimensional Passive-Dynamic Walking. Dynamics and Stability of Systems 2000. 15(3): p. 75–99.
[63] Goswami A., Espiau B., and Keramane A.. Limit Cycles and Their Stability in a Passive Bipedal Gait. in Proceeding of IEEE International Conference on Robotics and Automation. 1996: p. 246-251.
[64] Catherine E, , Active Control of Lateral Balance in Human Walking. Journal of Biomechanics, 2000. 33: p. 1433-1440.
[65] Maxwell J., et a, Mechanical and Metabolic Requirements for Active Lateral Stabilization in Human Walking. Journal of Biomechanics, 2004. 37: p. 827-835.
[66] Ruina, M. J. Coleman and A., An Uncontrolled Toy that Can Walk but Can not Stand Still. Physical Review Letters, 1998. 80: p. 3658-3661.
[67] Kuo, Arthur D., Stabilization of Lateral Motion in Passive Dynamic Walking. International Journal of Robotics Research September, 1999. 18(9): p. 917-930.
[68] Collins S., Ruina A., Tedrake R., and Wisse M., Efficient Bipedal Robots Based on Passive Dynamic Walkers. Science Magazine, 2005. 30(7): p. 1082-1085.
[69] Alexander, R.M Walking made simple. Science, 2005. 308: p. 58-59.
[70] Kuo, Arthur D., Harvesting energy by improving the economy of human walking. science, 2005. 309: p. 1686-1687.
[71] Pratt, J., Dilworth, P., Pratt, G. Virtual Model Control of a Bipedal Walking Robot. in Proceddings of IEEE International Conference on Robotics and Automation. 1997: p. 193-198
[72] Playter, R. R., Raibert, M. H. Generation of A Somersault by a 3D Biped Robot. in Proceeding of International Federation of Automatic Control. 1992.
[73] Chevallereau C., et al, RABBIT: A Test Bed for Advanced Control Theory. IEEE Control Systems Magazine, 2003. 8: p. 1-51.
[74] Morris B., Westervelt E.R. , Chevallereau C.. Achieving Bipedal Running with RABBIT: Six Steps toward Infinity. in Proceeding of Fast Motions in Biomechanics and Robotics Symposium. 2005: p. 277-297.
[75] Mike Stilman, Christopher G. Atkeson, et al. Dynamic Programming in Reduced Dimensional Spaces: Dynamic Planning For Robust Biped Locomotion. in Proceedings of IEEE International Conference on Robotics and Automation. 2005: p. 2399- 2404.
[76] Poramate Manoonpong, Tao Geng, Tomas Kulvicius, Bernd Porr, Adaptive, Fast Walking in a Biped Robot under Neuronal Control and Learning. PLoS Comput Biology. 7(3): p. e139.
[77]付成龙,陈恳,五杆四驱动平面双足机器人动态步态规划与非线性控制.机器人, 2006. 28(2): p. 206-212.
[78] Westervelt E.R., Grizzle J.W., and Koditschek D., Hybrid Zero Dynamics of Planar Biped Walkers. IEEE Transition. on Automatic Control, 2002. 48: p. 42-56.
[79] Sabourin, C, Bruneau, O, Robustness of the Dynamic Walk of a Biped Robot Subjected to Disturbing External Forces by Using CMAC Neural Networks. Robotics and Autonomous Systems, 2005. 23: p. 81-99.
[80] Sabourin, C, Bruneau, O, Buche, Control Strategy for the Robust Dynamic Walk of A Biped Robot. The International Journal of Robotics Research 2006. 29(9): p. 843-860.
[81] Hauser J., Chung C. C., Converse Lyapunov Functions for Exponentially Stable Periodic Orbits. Systems and Control Letters. 23(1): p. 27-34.
[82] Guobiao Song, Milos Zefran. Stabilization of Hybrid Periodic Orbits with Application to Bipedal Walking. in Proceeding of American Control Conference. 2006.
[83] Guobiao Song , Milos Zefran. Underactuated Dynamic Three-Dimensional Bipedal Walking. in Proceedings of IEEE International Conference on Robotics and Automation. 2006: p. 854 - 859.
[84] Masahiro D. , et al, Passive dynamic autonomous control of bipedal walking. Humanoid, 2004.
[85] Doi, Masahiro. 3D Dynamic Walking Based on the Inverted Pendulum Model With Two Degree of Underactuation. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2001: p. 4166-4171.
[86] Ching-Long Shih, Grizzle, J.W., Chevallereau, C. Asymptitically Stable Walking of a Simple Underactuated 3D Bipedal Robot. in Proceeding of IEEEInternational Conference on Robotics and Automation. 2006: p. 2766-2771.
[87] Tao Geng, Bernd Porr, Florentin Worgotter, Fast Biped Walking with A Sensor-driven Neuronal Controller and Real-time Online Learning. The International Journal of Robotics Research, 2006. 25(3): p. 243-259
[88] Matsubara T., Morimoto J., Jun Nakanishi, et al., Learning CPG-based Biped Locomotion with a Policy Gradient Method. Robotics and Autonomous Systems, 2006. 54: p. 911-920.
[89] Hongxu Ma, Jian Wan, et al. Synthesis of CPG Based Motion Control Methods for Humanoid Robots. in Proceedings of the 6th World Congress on Intelligent Control and Automation. 2006. Dalian,China: p. 8843-8847.
[90] Gunes, Atilim, Evolution of Central Pattern Generators for the Control of a Five-link Planar Bipedal Walking Mechanism. 2008.
[91] Alexander, R.McN.; Jayes, A.S., A Dynamic Similarity Hypothesis for the Gaits of Quadrupedal Mammals. Journal of Zoology (UK), 1983. 201(1): p. 135-152.
[92] Wisse M, van J Frankenhuyzen. Design and Construction of MIKE: a 2-D Autonomous Biped Based on Passive Dynamic Walking in Proceedings of the Second International Symposium on Adaptive Motion of Animals and Machines. 2003: p. 143-154.
[93] Elert, Glenn, Speed of the fastest human walking. The Physics Factbook, Available: http://hypertextbook.com/facts/2001/ConnieLau.shtml. Accessed 2008.
[94] Alexander, R., Walking and running. American Scientist, 1984. 72: p. 348–354.
[95] Westervelt E. R., Buche G., and Grizzle J. W., Experimental Validation of a Framework for the Design of Controllers that Induce Stable Walking in Planar Bipeds. The International Journal of Robotics Research, 2004. 23(6): p. 559-582
[96] Christine Chevallereau, Grizzle J.W., and Ching-Long Shih, Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot. IEEE Transactions on Robotics, 2008.
[97] Jerry E. Pratt , Russ Tedrake, Velocity Based Stability Margins for Fast Bipedal Walking. Lecture Notes in Control and Information Sciences, 2006. 340: p. 299-324.
[98] Hofmann A, , Robust Execution of Bipedal Walking Tasks From Biomechanical Principles. PhD Dissertation USA:MIT, 2006.
[99] Vukobratovic M, Borovac B, Surla D et al, Scienctific Fundamentals of Robotics: Biped Locomotion. New York: Springer, 1990.
[100] Shibata M., Natori T.. Impact Force Reduction for Biped Robot Based on Decoupling CoG Scheme. in Proceedings of IEEE International Conference on AMC. 2000: p. 612-617.
[101] Hurmuzlu Y., Genot F., Brogliato B., Modeling, Stability and Control of Biped Robots--A General Framework. Automatica, 2004. 40: p. 1647-1664.
[102] Mu, XiPing, Dynamics and Motion Regulation of a Five-Linked Biped Robot Walking in the Sagittal Plane, in Department of Mechanical and Manufacturing Engineering. 2004, The University of Manitoba.
[103] Kyosuke Ono, Rongqiang Liu, Optimal Biped Walking Locomotion Solved by Trajectory Planning Method. Transactions of the ASME, Journal of Dynamic Systems, Measurement, and Control, 2002. 124(4): p. 554-565
[104] Yagi M., Lumelsky V., Local On-line Planning in Biped Robot Locomotion Amongst Unknown Obstacles. Robotica, 2000. 18(4): p. 389-402.
[105] James Kuffner, Koichi Nishiwaki, Satoshi Kagami, Masayuki Inaba, and Hirochika Inoue. Motion Planning for Humanoid Robots. in Proceedings of 11th International Symposium of Robotics Research. 2003.
[106] Chevallereau, C., Time-Scaling Control of an Underactuated Biped Robot. IEEE Transactions on Robotics and Automation, 2003. 19(2): p. 362-368.
[107] Grizzle J.W., Christine Chevallereau, and Ching-Long Shih. HZD-Based Control of a Five-Link Underactuated 3D Bipedal Robot. in Proceeding of IEEE Conference on Decision and Control. 2008: p. 5206-5213.
[108] Wisse M., Schwab A. L., A 3D Passive Dynamic Biped with Yaw and Roll Compensation. Robotica, 2000. 19(3): p. 275-284.
[109] Hirabayashi, T. Ugurlu, B. Kawamura, A. Chi Zhu. Yaw Moment Compensation of Biped Fast Walking Using 3D Inverted Pendulum. in Proceedings of 10th IEEE International Workshop on Advanced Motion Control. 2008: p. 296-300.
[110] Ames AD, Gregg RD, et al. Towards the geometric reduction of controlled three-dimensional robotic bipedal walkers. in Proceeding of 3rd Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. 2006.
[111] Gregg, Aaron D. Ames and Robert D. Stably Extending Two-Dimensional Bipedal Walking to Three Dimensions. in Proceeding of American Control Conference. 2007: p. 2848-2854.
[112] Kaminka G.A., Lima P.U., and Rojas R.. The Role of Motion Dynamics in the Design, Control and Stability of Bipedal and Quadrupedal Robots. in RoboCup 2002, LNAI 2752. 2003: p. 206-223.
[113] Featherstone R., Orin D.. Robot Dynamics: Equations and Algorithm. in Proceddings of IEEE International Conference on Robotics and Automation. 2000: p. 826-834.
[114] Hemami H., Wyman B., Rigid Body Dynamics, Constraints, and Inverses. Journal of Applied Mechanics, 2007. 74: p. 47-56.
[115] Pal D. K., Ascher U. M., Kry P. G.. Forward Dynamics Algorithms for Multibody Chains and Contact. in Proceddings of IEEE International Conference on Robotics and Automation. 2000: p. 857-863.
[116] Goldsmith, W, ed. Impact, the Theory and Physical Behaviour of Colliding Solids. 1960, London Edward Arnold Publishers LTD.
[117] Hurmuzlu Y., Marghitu D. B., Rigid Body Collisions of Planar Kinematic Chains With Multiple Contact Points. International Journal of Robotics Research, 1994. 13(1): p. 82-92.
[118] Zhe Tang, Changjiu Zhou, Zenqi Sun. Trajectory Planning for Smooth Transition of a Biped Robot. in Proceedings of IEEE International Conference on Robotics & Automation. 2003: p. 2455-2460.
[119] Canudas-de-Wit, Carlos, On the Concept of Virtual Constraints as a Tool for Walking Robot Control and Balancing. Annual Reviews in Control, 2004: p. 1-10.
[120] Westervelt E. R., Grizzle J. W., et al, Hybrid Zero Dynamics of Planar Biped Walkers. IEEE Transactions on Automatic Control, 2003. 48(1): p. 42-56.
[121] Hlland, J.H., Adaptation in Nature and Artificial System. MIT Press, 1992.
[122] Goldberg E., D, Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, 1989.
[123]飞思科技产品研发中心, MATLAB6.5辅助优化计算与设计, 2003:电子工业出版社.
[124] Roussel L., Canudas C., Goswami A.. Generation of Energy Optimal Complete Gait Cycles for Biped Robots. in Proceedings of IEEE International Conference on Robotics and Automation. 1998: p. 2036-2041.
[125] Chevallereau C., Formalsky A., and Perrin B.. Low Energy Cost Reference Trajectories for a Biped Robot. in Proceedings of IEEE International Conference on Robotics and Automation. 1998: p. 1398-1404.
[126] Fujimoto, Y. Trajectory Generation of Biped Running Robot with Minimum Energy Consumption. in Proceedings of IEEE International Conference on Robotics and Automation. 2004: p. 3803-3808.
[127]何广平,陆震,王凤翔,欠驱动机器人的动力学耦合奇异研究.航空学报, 2005. 26(12): p. 240-245.
[128]丁希仑,战强,解玉文,自由漂浮的空间机器人系统的动力学奇异特性分析及其运动规划.航空学报, 2001. 22(5): p. 474-477.
[129] Farrell, E.R. Westervelt B. Morris K. D., Analysis Results and Tools for the Control of Planar Bipedal Gaits Using Hybrid Zero Dynamics. Auton Robot, 2007(23): p. 131-145.
[130]谭道盛,温启愚,矩阵的任意分块求逆及其应用.四川大学学报(自然科学版), 1999. 36(1): p. 34-37.
[131] Sanjay P. Bhat , Dennis S. Bernstein. Finite-Time Stability of Homogeneous Systems. in Proceedings of American Control Conference. 1997: p. 2513-2514.
[132] YANG, Shuanghe YU,Zi M A,Xiaohui, Nonsmooth Finite-Time Control of Uncertain Second-Order Nonlinear Systems. Journal ofControl Theory andApplications, 2007. 5(2): p. 171-176.
[133] Bhat S P, Bernstein D, Finite-Time Stability of Continuous Autonomous Systems. SLAM Journal on Controla nd Optimi zation, 2000. 38(3): p. 751-766.
[134] Bhat S P, Bernstein DS, Continuous Finite-Time Stabilization of the Translational and Rotational Double Integrator. IEEE Transations on Automatic Control, 1998. 43(5): p. 678-682.
[135] Kajita S, Kanehiro F, Kaneko K, et al. Biped Walking Pattern Generation by Using Preview Control of Zero-Moment Point. in Proceeding of the IEEE International Conference on Robotics and Automation. 2003: p. 1620-1626.
[136] Kim J., et al. Real-time ZMP Compensation Method using Null Motion for Mobile Manipulators. in Proceedings of IEEE International Conference on Robotics and Automation 2002: p. 1967-1972.
[137] Choi Y., You B., Oh S.. On the Stability of Indirect ZMP Controller for Biped Robot Systems. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2004: p. 1966-1971.
[138] Ikemata Y., Sano A., Fujirioto H.. Analysis of Stable Limit Cycle in Passive Walking. in SICE Annual Conference. 2003: p. 117-122.
[139] Hiskens, Ian A. Stability of Hybrid System Limit Cycles: Application to the Compass Gait Biped Robot. in Proceeding of The 40th lEEE Conference on Decision and Contml. 2001: p. 774-779.
[140] Rubensson M., Lennartsson B., Pettersson S.. Convergence to Limit Cycles in Hybrid Systems. in 8th International Federation of Automatic Control Symposium on Large Scale Systems. 1998: p. 704-709.
[141] Goswami A., Espiau B., Keramane A., Limit Cycles in a Passive Compass Gait Biped and Passivity-Mimicking Control Laws. Journal of Autonomous Robots, 1997. 4(3): p. 273-286.
[142] Marko Popovic, Amy Englehart. Angular Momentum Primitives for Human Walking: Biomechanics and Control. in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2004: p. 1685-1691.
[143] Herr H, Popovic M Angular Momentum in Human Walking. Journal of Experimental Biology, 2008. 211(4): p. 467-481.
[144] Marko B. Popovic, Hugh Herr, Ground Reference Points in Legged Locomotion: Definitions, Biological Trajectories and Control Implications. Mobile Robots Towards New Applications, 2006: p. 784-810.
[145] Popovic, M., Hofmann, A. and Herr, H. Zero spin angular momentum control: definition and applicability. in Proceedings of the IEEE-RAS/RSJ International Conference on Humanoid Robots. 2004: p. 478- 493
[146] Goswami A., Kallem V.. Rate of Change of Angular Momentum and Balance Maintenace of Biped Robots. in Proceedings of IEEE International Conference on Robotics and Automation. 2004: p. 3785-3790.
[147] Shuuji KAJITA, Fumio KANEHIRO, Kenji KANEKO. Resolved MomentumControl: Humanoid Motion Planning based on the Linear and Angular Momentum. in Proceedings of the 2003 IEEE/RSJ Intl. Conference on Intelligent Robots and Systems. 2003: p. 1644-1650.
[148] Zhaohui LI, Qiang HUANG, Kejie LI, et al. Stability Criterion and Pattern Planning for Humanoid Running. in Proceedings of IEEE International Conference on Robotics & Automation. 2004: p. 1059-1064.
[149] Yuichi Morita, Kouhei Ohnishi. Attitude Control of Hopping Robot Using Angular Momentum. 2003: p. 173-178.
[150] Pierre-Brice, WIEBER. On the Stability of Walking Systems. in In Proceedings of the International Workshop on Humanoid and Human Friendly Robots. 2002.
[151] Dempster, W.T, Gaughran, G, Properties of Body Segments Based on Size and Weight. American Journal of Anatomy, 1965.
[152] Jesse W. Grizzle, Gabriel Abba, Franck Plestan, Asymptotically Stable Walking for Biped Robots:Analysis via Systems with Impulse Effects. IEEE Transactions on Automatic Control, 2001. 46(1): p. 51-64.
[153] Westervelt E. R., Grizzle J. W., and Kodistschek D. E. Switching and PI Control of Walking Motions of Planar Biped Walkers. IEEE Transactions on Automatic Control, 2003. 48(2): p. 308-312.
[154]吴剑,李建设,人体行走时步态的生物力学研究进展.中国运动医学杂志, 2002. 21(3): p. 305-307.
[155] Maxwell J. Donelan, Rodger Kram , Arthur D. Kuo, Mechanical and Metabolic Determinants of the Preferred Step Width in Human Walking. The Royal Society, 2001: p. 1985-1992.
[156] Isidori, A., Nonlinear Conbvl Systems. 1989, New York: Springer-Verlag.
[157] ]TanakaK, SanoM, Fuzzy Stability Criterion of a Class of Nonlinear Systems. Information Science, 1993. 70(1): p. 3-26.
[158] TanakaK, Sugeno M, Stability Analysis and Design of Fuzzy Control System. Fuzzy Sets and System, 1992. 45(2): p. 135-196.
[159] Takagi T, Sugeno M, Fuzzy Identification of Systems and Its Application to Modeling and Control. IEEE Transtions on Systems, Man and Cybernetics, 1985. 15(1): p. 116-132.
[160] Tanaka, K. and Kosali, T, Design of a Stable Fuzzy Controller for an Articulated Vehicle. IEEE transactions on Systems, Man, and Cybernetics, 1997. 27(3): p. 552-558.
[161] Yoshida H., Inoue K., Arai T., Mae Y.. Mobile Manipulation of Humanoid Robots -Optimal Posture for Generating Large Force based on Statics. in Proceedings of IEEE International Conference on Robotics and Automation. 2002: p. 2271-2276.
[162] Harada K., Kajita S., et al. Real-Time Planning of Humanoid Robot's Gait for Force Controlled Manipulation. in Proceedings of IEEE InternationalConference on Robotics and Automation. 2004: p. 616-622.
[163] Naoto Kawauchi, Shigetoshi Shiotani, Hiroyuki Kanazawa, et al. A Plant Maintenance Humanoid Robot System. in Proceedings of IEEE International Conference on Robotics & Automation. 2003: p. 2973-2978.
[164] Bryan Adams, Cynthia Breazeal, Rodney A, et al, Humanoid Robots: A New Kind of Tool. Intelligent Systems and their Applications, 2000. 15(4): p. 25-31.
[165] Jun Ho Choi, J.W. Grizzle, Planar Bipedal Walking with Anthropomorphic Foot Action. IEEE Transection on Robotics, 2005.
[166] Choi JH, Grizzle JW. Planar Bipedal Walking with Foot Rotation. in Proceedings of American Control Conference. 2005: p. 4909- 4916
[167] Chenglong FU , Ken CHEN, Jing XIONG, Leon XU, Stability and Control of Dynamic Walking for a Five-Link Planar Biped Robot with Feet. Journal of Control Theory and Applications, 2007. 5(2): p. 113–120.
[168] Keon Young Yi, Yuan F Zheng, Biped Locomotion by Reduced Ankle Power. Autonomous Robots, 1997. 4: p. 307–314.
[169] Leardini, Alberto, Geometry and Mechanics of Human Ankle Complex and Ankle Prosthesis Design. Clinical Biomechanics, 2001. 16: p. 706-709.
[170]绳涛,仿人机器人力信息反馈控制方法研究, in机电工程与自动化学院. 2004,国防科学技术大学:长沙.
[171] Arimoto S, Miyazaki F. Stability and Robustness of PID Feedback Control for Robot Manipulator of Sensory Capability. in Proceeding of First Int. Symposium: Robotics Research. 1983: p. 783~799.
[172] James Kuffner, Koichi Nishiwaki, Satoshi Kagami. Self-Collision Detection and Prevention for Humanoid Robots. in Proceddings of IEEE International Conference on Robotics and Automation. 2002: p. 2265-2270.
[173] Kei Okada, Masayuki Inaba, Hirochika Inoue. Real-time and Precise Self Collision Detection System for Humanoid Robots. in Proceedings of IEEE International Conference on Robotics and Automation. 2005: p. 1072-1077.
[174] Atsuo Kawamura, Chi Zhu. The Development of Biped Robot MARI-3 for Fast Walking and Running. in Proceedings of IEEE-RAS International Conference on Humanoid Robots. 2006: p. 599-604.
[175] Sang-Ho Hyon, Takashi Emura. Aerial Posture Control for 3D Biped Running Using Compensator around Yaw Axis in Proceedings of the 2003 IEEE International Conference on Robotics & Automation. 2003: p. 57-62.
[176] Ueda Jun, Shirae Kenji, Oda Shingo, et al, Moment Compensation for Fast Dynamic Walking of Humanoids based on Human Athletes Pelvis Rotation. Journal of the Robotics Society of Japan, 2005. 23(4): p. 457-465.