腿式跳跃机器人运动规划与稳定性恢复研究
|
摘要
腿式跳跃机器人具有很强的移动性、灵活性和地形适应性,是移动机器人研究领域中的一个前沿应用课题,在家庭服务、医疗娱乐、星际探测、军事侦察、反恐救灾等领域有着极其广泛的应用前景。
腿式跳跃机器人是一个非线性、多变量、强耦合和变结构的复杂动力学系统,其驱动性能约束下的逾障规划和动态平衡问题的研究具有很大的挑战性。本文以不带弹性元件、完全电机驱动的多关节腿式跳跃机器人为研究对象,从提高机器人运动能力的角度,结合驱动约束条件,对腿式跳跃机器人的动力学建模、运动规划与优化、稳定性恢复控制等关键问题进行了研究,并通过仿真实验和机器人实体试验进行了验证。论文的主要工作如下:
(1)腿式机器人跳跃运动的特征量提取
基于生物的跳跃形态和人体跳跃运动捕捉试验,从生物力学、仿生学和机器人学的角度分析了影响跳跃运动的主要因素,采用起跳姿态、广义负载和上肢运动三个特征量刻画机器人的跳跃运动性能。
(2)腿式跳跃机器人的动力学建模
跳跃运动的腾空相参考基座是浮动基,具有动量矩守恒的非完整约束;站立相的参考基座是固定基,具有完整约束。针对变约束特性,采用Lagrange浮动基方法,推导了跳跃机器人的变约束动力学模型。
(3)腿式机器人的跳跃逾障运动规划
为提高机器人的地形适应能力,给出了基于模型综合与解耦策略的腿式机器人跳跃逾障运动规划方法。该方法先将腿式机器人的上身等效为一个具有惯量特性的刚体,根据跳跃姿态和障碍物,运用内在动力学,规划运动综合模型的跳跃逾障运动;接着基于等效刚体的COM可操作度,运用开环可操作度优化方法进行冗余度分解,规划冗余关节的运动。
(4)腿式机器人跳跃运动的特征量优化
视腿式跳跃机器人为持有末端载荷的冗余机械臂,从力与运动传递性能的角度,结合起跳动力学约束条件,给出了跳跃运动的特征量优化方法。该方法运用惯性匹配方向可操作度优化了跳跃运动的三个特征量,通过特征量的优化提高了跳跃性能。惯性匹配方向可操作度作为一种动力学评价指标,度量了机器人在跳跃任务下的跳跃高度。
(5)腿式跳跃机器人的稳定性恢复控制
基于驱动性能约束,给出了落地冲击力作用下的稳定性恢复控制方法。该方法运用ZMP可操作椭圆规划了跳跃步态,当机器人有足够的驱动能力进行自运动姿态调整时,采用ZMP平面映射法进行稳定性恢复;当机器人的驱动能力不足时,通过步态调整使机器人重获稳定。
(6)人体运动捕捉与机器人跳跃运动试验
为了验证本文所给出方法的有效性,分别构建了人体运动捕捉和机器人跳跃运动的试验平台。利用三维图像检测系统,通过人体跳跃运动的捕捉,分析了影响跳跃性能的主要特征因素;研制了两类跳跃机器人试验样机,分别验证了跳跃运动特征量优化方法的有效性,以及落地冲击下稳定性恢复控制策略的实用性。
本文有关跳跃机器人的动力学建模、运动规划、运动优化以及地面冲击力作用下的稳定性恢复控制方法,有助于提高机器人的灵活性和运动能力,拓展机器人的应用领域,在理论和应用上都具有一定的借鉴作用和参考价值。
In complex or nonstructure environment, legged jumping robots have a better mobility, dexterity and terrain suitability than wheeled or tracked robots. As an advanced topic in mobile robots, they have well application foreground in fields of house work, rehabilitation treatment, sports science, life entertainment, interstellar exploration and national defence.
Legged jumping robot is a multivariable, strongly coupled, nonlinear and varying structure dynamics system. Due to actuator constraints limitation, the ability of jumping over obstacles and dynamic stability are very challenging for control theory and motion planning. This dissertation concentrates on multi-joints legged jumping robot without elastic actuators. In order to improve versatility of jumping motion, some key problems related to dynamics modeling, motion planning, motion optimization and stability recovery are studied. Simulations and experiments have also been performed to test the methods presented in the dissertation. The discussed contents are listed as follows.
(1) Character parameters of jumping motion
From biology forms under literature datum and human jumping motion under motion capture experiment, three character parameters can be used to describe jumping robots related to biomechanics and robotics, and they are take-off postures, generalized load and upper limbs swing.
(2) Dynamics modeling of legged jumping robot
Legged jumping robot belongs to a variable constraint system because every phase has different constraint conditions. Stance phase has holonomic constraint, nevertheless flight phase has holonomic and non-holonomic constraints. The unified dynamics modelings of legged jumping robot including flight phase, stance phase and landing impact phase are achieved using Lagrange method based on floating basis.
(3) Motion planning of jumping over obstacles
Using the idea of motion synthesis and redundant DOFs decoupling, a motion planning method related jumping over obstacles is presented. Upper body is equivalent to a rigid body with inertia property. Based on internal dynamics and boundary conditions including jumping postures and obstacle’s size, a motion of jumping over obstacles is planned. Moreover, redundant DOFs are decoupled using open-manipulability optimization method based on COM manipulability of upper limb.
(4) Motion optimization for legged jumping robot
Legged jumping robot can be regarded as a redundant manipulator with a load at the end-effector. From the take-off dynamics and transfer performance between motion and force, inertia matching directional manipulability is used to optimize character parameters of jumping motion including take-off posture, generalized load and upper limbs swing. Inertia matching ellipsoid is an index of dynamic performance, and it measures the jumping height under jumping tasks.
(5) Stability recovery under landing impact
During landing impact phase, there is a large impact force. Aim at this landing impact, ZMP manipulability is introduced to plan jumping gaits based on actuator constraints limitation. Stability can be recovered by ZMP plane projection method within actuator performance, and it is only recovered through gait adjustment beyond actuator performance.
(6) Experiments of human motion capture and robot jumping motion
In order to verify the proposed methods, human motion capture and experiment platforms for jumping motion are constructed respectively. Main factors are obtained by analyzed motion of key points based on human motion capture system. Motion optimization and stability control strategy are tested under two jumping robots which one is run linked to a 3D platform and the other is an autonomous robot.
The main contributions of this dissertation consist in the improvement of mobility and jumping performance, motion planning and stability recovery control of legged robot. The presented methods are worth to be used for widening application fields and its reference value on the theory and application.
腿式跳跃机器人是一个非线性、多变量、强耦合和变结构的复杂动力学系统,其驱动性能约束下的逾障规划和动态平衡问题的研究具有很大的挑战性。本文以不带弹性元件、完全电机驱动的多关节腿式跳跃机器人为研究对象,从提高机器人运动能力的角度,结合驱动约束条件,对腿式跳跃机器人的动力学建模、运动规划与优化、稳定性恢复控制等关键问题进行了研究,并通过仿真实验和机器人实体试验进行了验证。论文的主要工作如下:
(1)腿式机器人跳跃运动的特征量提取
基于生物的跳跃形态和人体跳跃运动捕捉试验,从生物力学、仿生学和机器人学的角度分析了影响跳跃运动的主要因素,采用起跳姿态、广义负载和上肢运动三个特征量刻画机器人的跳跃运动性能。
(2)腿式跳跃机器人的动力学建模
跳跃运动的腾空相参考基座是浮动基,具有动量矩守恒的非完整约束;站立相的参考基座是固定基,具有完整约束。针对变约束特性,采用Lagrange浮动基方法,推导了跳跃机器人的变约束动力学模型。
(3)腿式机器人的跳跃逾障运动规划
为提高机器人的地形适应能力,给出了基于模型综合与解耦策略的腿式机器人跳跃逾障运动规划方法。该方法先将腿式机器人的上身等效为一个具有惯量特性的刚体,根据跳跃姿态和障碍物,运用内在动力学,规划运动综合模型的跳跃逾障运动;接着基于等效刚体的COM可操作度,运用开环可操作度优化方法进行冗余度分解,规划冗余关节的运动。
(4)腿式机器人跳跃运动的特征量优化
视腿式跳跃机器人为持有末端载荷的冗余机械臂,从力与运动传递性能的角度,结合起跳动力学约束条件,给出了跳跃运动的特征量优化方法。该方法运用惯性匹配方向可操作度优化了跳跃运动的三个特征量,通过特征量的优化提高了跳跃性能。惯性匹配方向可操作度作为一种动力学评价指标,度量了机器人在跳跃任务下的跳跃高度。
(5)腿式跳跃机器人的稳定性恢复控制
基于驱动性能约束,给出了落地冲击力作用下的稳定性恢复控制方法。该方法运用ZMP可操作椭圆规划了跳跃步态,当机器人有足够的驱动能力进行自运动姿态调整时,采用ZMP平面映射法进行稳定性恢复;当机器人的驱动能力不足时,通过步态调整使机器人重获稳定。
(6)人体运动捕捉与机器人跳跃运动试验
为了验证本文所给出方法的有效性,分别构建了人体运动捕捉和机器人跳跃运动的试验平台。利用三维图像检测系统,通过人体跳跃运动的捕捉,分析了影响跳跃性能的主要特征因素;研制了两类跳跃机器人试验样机,分别验证了跳跃运动特征量优化方法的有效性,以及落地冲击下稳定性恢复控制策略的实用性。
本文有关跳跃机器人的动力学建模、运动规划、运动优化以及地面冲击力作用下的稳定性恢复控制方法,有助于提高机器人的灵活性和运动能力,拓展机器人的应用领域,在理论和应用上都具有一定的借鉴作用和参考价值。
In complex or nonstructure environment, legged jumping robots have a better mobility, dexterity and terrain suitability than wheeled or tracked robots. As an advanced topic in mobile robots, they have well application foreground in fields of house work, rehabilitation treatment, sports science, life entertainment, interstellar exploration and national defence.
Legged jumping robot is a multivariable, strongly coupled, nonlinear and varying structure dynamics system. Due to actuator constraints limitation, the ability of jumping over obstacles and dynamic stability are very challenging for control theory and motion planning. This dissertation concentrates on multi-joints legged jumping robot without elastic actuators. In order to improve versatility of jumping motion, some key problems related to dynamics modeling, motion planning, motion optimization and stability recovery are studied. Simulations and experiments have also been performed to test the methods presented in the dissertation. The discussed contents are listed as follows.
(1) Character parameters of jumping motion
From biology forms under literature datum and human jumping motion under motion capture experiment, three character parameters can be used to describe jumping robots related to biomechanics and robotics, and they are take-off postures, generalized load and upper limbs swing.
(2) Dynamics modeling of legged jumping robot
Legged jumping robot belongs to a variable constraint system because every phase has different constraint conditions. Stance phase has holonomic constraint, nevertheless flight phase has holonomic and non-holonomic constraints. The unified dynamics modelings of legged jumping robot including flight phase, stance phase and landing impact phase are achieved using Lagrange method based on floating basis.
(3) Motion planning of jumping over obstacles
Using the idea of motion synthesis and redundant DOFs decoupling, a motion planning method related jumping over obstacles is presented. Upper body is equivalent to a rigid body with inertia property. Based on internal dynamics and boundary conditions including jumping postures and obstacle’s size, a motion of jumping over obstacles is planned. Moreover, redundant DOFs are decoupled using open-manipulability optimization method based on COM manipulability of upper limb.
(4) Motion optimization for legged jumping robot
Legged jumping robot can be regarded as a redundant manipulator with a load at the end-effector. From the take-off dynamics and transfer performance between motion and force, inertia matching directional manipulability is used to optimize character parameters of jumping motion including take-off posture, generalized load and upper limbs swing. Inertia matching ellipsoid is an index of dynamic performance, and it measures the jumping height under jumping tasks.
(5) Stability recovery under landing impact
During landing impact phase, there is a large impact force. Aim at this landing impact, ZMP manipulability is introduced to plan jumping gaits based on actuator constraints limitation. Stability can be recovered by ZMP plane projection method within actuator performance, and it is only recovered through gait adjustment beyond actuator performance.
(6) Experiments of human motion capture and robot jumping motion
In order to verify the proposed methods, human motion capture and experiment platforms for jumping motion are constructed respectively. Main factors are obtained by analyzed motion of key points based on human motion capture system. Motion optimization and stability control strategy are tested under two jumping robots which one is run linked to a 3D platform and the other is an autonomous robot.
The main contributions of this dissertation consist in the improvement of mobility and jumping performance, motion planning and stability recovery control of legged robot. The presented methods are worth to be used for widening application fields and its reference value on the theory and application.
引文
[1]徐德,邹伟.室内移动式服务机器人的感知、定位与控制.北京:科学出版社, 2008
[2]罗庆生,韩宝玲.现代仿生机器人设计.北京:电子工业出版社, 2008
[3]许宏岩,付宜利,王树国,刘建国.仿生机器人的研究.机器人, 2004, 26(3): 283-288
[4]张秀丽,郑浩峻,陈恳,段广洪.机器人仿生学研究综述.机器人, 2002, 24(2): 188-192
[5]迟科祥,颜国正.仿生机器人的研究状况及其未来发展.机器人, 2001, 23(5): 476-480
[6] Regele R., Bott W., Levi P. Prorobot Predictions for the future development of humanoid robots. Autonome Mobile Systeme, 2003: 292-303
[7] Kovac M., Fuchs M., Guignard A., Zufferey J. C., Floreano D. A miniature 7g jumping robot, 2008: 373-378
[8]刘壮志,席文明,朱剑英,吴洪涛.弹跳式机器人研究.机器人, 2003, 25(6): 568-573
[9] Matsuoka K. A mechanical model of repetitive hopping movements. Biomechanisms, 1980, 5(2): 251-258
[10] Raibert M. H. Legged robots that balance. Cambridge, Mass.: MIT Press, 1986
[11] Papantoniou K. V. Electromechanical design for an electrically powered, activelybalanced one leg planar robot. IEEE/RSJ International Workshop on Intelligent Robots and Systems, 1991: 1553-1560
[12] Zeglin G., Brown B. Control of a bow leg hopping robot. IEEE International Conference on Robotics and Automation, 1998: 793-798
[13] Ahmadi M., Buehler M. The ARL monopod II running robot: Control and energetics. IEEE International Conference on Robotics and Automation, 1999: 1689-1694
[14] Lee W., Raibert M. Control of hoof rolling in an articulated leg. IEEE International Conference on Robotics and Automation, 1991: 1386-1391
[15] Zeglin G. J. Uniroo--a one legged dynamic hopping robot [Master Degree], Massachusetts Institute of Technology: Massachusetts Institute of Technology, 1991
[16] Hyon S. H., Mita T. Development of a biologically inspired hopping robot Kenken. IEEE International Conference on Robotics and Automation, 2002: 3984-3991
[17] Sung S., Youm Y. Landing Motion Control of Articulated Legged Robot. IEEE International Conference on Robotics and Automation, 2007: 3230-3236
[18] De Man H., Lefeber D., Vermeulen J. Design and control of a robot with one articulated leg for locomotion on irregular terrain. COURSES AND LECTURES-INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES, 1998: 417-424
[19] Berkemeier M. D., Desai K. V. Control of hopping height in legged robots using aneural-mechanical approach. IEEE International Conference on Robotics and Automation, 1999: 1695-1701
[20] Zhang W., Wang G., Chambers T., Simon W. E. Toward a folding-legged uniped that can learn to jump. IEEE International Conference on Systems, Man, and Cybernetics, 1997: 4315-4319
[21] Tajima R., Suga K. Motion having a Flight Phase: Experiments Involving a One-legged Robot. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2006: 1726-1731
[22] Lim B., Babic J., Park F. C. Optimal jumps for biarticular legged robots. IEEE International Conference on Robotics and Automation, 2008: 226-231
[23] Ishida T. Development of a small biped entertainment robot QRIO. International Symposium on Micro-Nanomechatronics and Human Science, 2004: 23-28
[24] Sakagami Y., Watanabe R., Aoyama C., Matsunaga S., Higaki N., Fujimura K., Ltd H., Saitama J. The intelligent ASIMO: System overview and integration. IEEE/RSJ International Conference on Intelligent Robots and System, 2002: 2478-2483
[25] Schiehlen W. Energy-optimal design of walking machines. Multibody System Dynamics, 2005, 13(1): 129-141
[26] Chevallereau C., Abba G., Aoustin Y., Plestan F., Westervelt E. R., Canudas-de-Wit C., Grizzle J. W. Rabbit: A testbed for advanced control theory. IEEE Control Systems Magazine, 2003, 23(5): 57-79
[27] Arsenic A. M. Developmental learning on a humanoid robot. IEEE International Joint Conference on Neural Networks, 2004: 3167-3172
[28] Dillmann R., Zollner R. D. Interactive and Cooperative Robot Assistants. Springer, 2006: 315-368
[29]杨煜普,耿涛,郭毓.一种新型翻转跳跃运动机器人的运动结构与轨迹规划.上海交通大学学报, 2003, 37(7): 1110-1113
[30]赵晓军,黄强,彭朝琴,张利格,李科杰.基于人体运动的仿人型机器人动作的运动学匹配.机器人, 2005, 27(4): 358-361
[31]刘壮志.弹跳机器人若干关键技术研究[博士论文],南京:南京航空航天大学, 2004
[32]何广平,谭晓兰,张向慧.双臂弹性单腿机器人的垂直跳跃控制.机械工程学报, 2007, 43(5): 44-49
[33]马利娥.仿袋鼠机器人跳跃运动机理的研究[硕士论文],西安:西北工业大学, 2005
[34]王淑艳.仿人型跑步机器人的稳定性条件及步态规划[硕士论文],西安:西安电子科技大学, 2006
[35]谢健.三连杆单杠体操机器人的智能控制方法研究[硕士论文],重庆:重庆大学, 2003
[36]邓宗全,岳明.球形机器人的发展概况综述.机器人技术与应用, 2006, (3): 27-31
[37]吉爱红,戴振东,周来水.仿生机器人的研究进展.机器人, 2005, 27(3): 284-288
[38]杨小传,胡海拉,王培聪,赵克强.单足弹跳机器人弹跳机构设计与弹跳动力学分析.厦门大学学报:自然科学版, 2006, 45(4): 504-508
[39] Kajita S., Nagasaki T., Kaneko K., Yokoi K., Tanie K. A hop towards running humanoid biped. IEEE International Conference on Robotics and Automation, 2004: 629-635
[40]魏航信,刘明治,王淑艳,赵丽琴.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
[41] Ikeda T., Iwatani Y., Suse K., Mita T. Analysis and design of running robots in touchdown phase. IEEE International Conference on Control Applications, 1999: 496-501
[42] Ohashi E., Ohnishi K. Hopping height control for hopping robots. Electrical Engineering in Japan, 2006, 155(1): 64-71
[43] Nunez V., Nadjar-Gauthier N. Control strategy for vertical jump of humanoid robots. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005: 2253-2258
[44] Ahmadi M., Buehler M. Stable control of a simulated one-legged running robot with hip and leg compliance. IEEE Transactions on Robotics and Automation, 1997, 13(1): 96-104
[45] Park J. H., Kwon O. Impedance control for running of biped robots. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2003: 944- 949
[46] Sato A., Buehler M. A planar hopping robot with one actuator: design, simulation, and experimental results. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004: 3540-3545
[47] Schwind W. J., Koditschek D. E. Approximating the stance map of a 2-dof monoped runner. Journal of Nonlinear Science, 2000, 10(5): 533-568
[48] Kawamura A., Sugio K., Suzuki K., Zhu C. Simulation study on one leg jumping for biped running. IEEE International Workshop on Advanced Motion Control, 2004: 433-438
[49]戈新生,刘延柱,魏宝刚.基于拟牛顿算法的自由下落猫的非完整运动规划.系统仿真学报, 2006, 18(5): 1123-1126
[50]王庆江.跳板跳水的数值分析与计算机仿真[硕士论文],南京:南京理工大学, 2002
[51] Albro J. V., Bobrow J. E. Optimal motion primitives for a 5 dof experimental hopper. IEEE International Conference on Robotics and Automation, 2001: 3630- 3635
[52] Yokozawa T., Hara S., Ishikawa M. Optimal control strategy for high jump based on complementarity modeling. IEEE Conference on Decision and Control, 2000: 3132-3137
[53] Takahashi T., Yamakita M., Hyon S. H. An optimization approach for underactuated running robot. International Joint Conference on SICE-ICASE, 2006: 3505-3510
[54] Fujimoto Y. Trajectory generation of biped running robot with minimum energy consumption. IEEE International Conference on Robotics and Automation, 2004: 3803-3808
[55] Bobrow J. E. Optimal robot plant planning using the minimum-time criterion. IEEE Journal of Robotics and Automation, 1988, 4(4): 443-450
[56] Levine W., Zajac F., Belzer M., Zomlefer M. Ankle controls that produce a maximal vertical jump when other joints are locked. IEEE Transactions on Automatic Control, 1983, 28(11): 1008-1016
[57] So B. R., Yi B. J., Oh S. R., Kim Y. S. Landing motion analysis of human-body model considering impact and ZMP condition. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004: 1972-1978
[58] Hyon S. H., Yokoyama N., Emura T. Back handspring robot: targetdynamics-based control. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004: 248-253
[59] Babic J., Omrcen D., Lenarcic J. Balance and control of human inspired jumping robot. Advances in Robot Kinematics: Mechanisms and Motion, 2006: 147-156
[60] Nagasaki T., Kajita S., Kaneko K., Yokoi K., Tanie K. A running experiment of humanoid biped. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004: 136-141
[61] Watabe T., Yamakita M., Mita T. Stabilization of 3 link acrobat robot in upright position. Proceedings of the 41st SICE Annual Conference, 2002: 2996-3001
[62]马勇占,方爱莲.对我国优秀跳远运动员起跳技术的运动学比较研究.中国体育科技, 2001, 37(2): 22-24
[63]王德平,任保莲.跳远起跳阶段摆动腿摆动的运动学特征及对起跳效果的影响.中国体育科技, 2000, 36(5): 24-25
[64] Higashimori M., Harada M., Yuya M., Ishii I., Kaneko M. Dimensional Analysis Based Design on Tracing Type Legged Robots. IEEE International Conference on Robotics and Automation, 2005: 3733-3738
[65] Hayashi R., Tsujio S. High-performance jumping movements by pendulum-type jumpingmachines. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2001: 722-727
[66] Sakka S., Yokoi K. Humanoid vertical jumping based on force feedback and inertial forces optimization. IEEE International Conference on Robotics and Automation, 2005: 3752-3757
[67] Chevallereau C., Sardain P. Design and actuation optimization of a 4 axes biped robot for walking and running. IEEE International Conference on Robotics and Automation, 2000: 3365-3370
[68] Yoshida Y., Kamano T., Yasuno T., Suzuki T., Harada H., Kataoka Y. Generation of suitable jumping motion pattern for hopping robot under genetic algorithm. TRANSACTIONS-INSTITUTE OF ELECTRICAL ENGINEERS OF JAPAN C, 2000, 120(10): 1365-1371
[69] Vermeulen J., Lefeber D., Verrelst B. Control of foot placement, forward velocity and body orientation of a one-legged hopping robot. Robotica, 2003, 21(1): 45-57
[70]齐晓慧.李雅普诺夫运动稳定性与平衡状态稳定性的关系.军械工程学院学报, 2002, 14(4): 35-38
[71] Vukobratovic M., Borovac B., Potkonjak V. ZMP: A review of some basic misunderstandings. International Journal of Humanoid Robotics, 2006, 3(2):153-175
[72] Vukobratovic M., Stepanenko J. Mathematical models of general anthropomorphic systems. Mathematical Biosciences, 1973, 17: 191-242
[73] Yamaguchi J., Soga E., Inoue S., Takanishi A. Development of a bipedal humanoid robot-control method of wholebody cooperative dynamic biped walking. IEEE International Conference on Robotics and Automation, 1999: 368-374
[74] Li Q., Takanishi A., Kato I. Learning control of compensative trunk motion for biped walking robot based on ZMP stability criterion. lEEE/RSJ International Conference on Intelligent Robots and Systems, 1992: 597-603
[75] Sugihara T., Nakamura Y., Inoue H. Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control. IEEE International Conference on Robotics and Automation, 2002: 1404-1409
[76] Goswami A. Postural stability of biped robots and the foot-rotation indicator (FRI) point. The International Journal of Robotics Research, 1999, 18(6): 523-533
[77] Popovic M. B., Goswami A., Herr H. Ground reference points in legged locomotion: Definitions, biological trajectories and control implications. The International Journal of Robotics Research, 2005, 24(12): 1013-1032
[78] Takhmar A. A., Alipour M., Moosavian K. MHS measure for postural stability monitoring and control of biped robots. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2008: 400-405
[79] Kang J. Y., Cochran J. E. Stability Criteria of Slosh Motion with Periodicity in a Spinning Spacecraft. Journal OF Guidance, Control, AND Dynamics, 2005, 28(3): 562-568
[80] Herr H., Popovic M. Angular momentum in human walking. Journal of Experimental Biology, 2008, 211(4): 467-481
[81] Li Z., Huang Q., Li K., Duan X. Stability criterion and pattern planning for humanoid running. IEEE International Conference on Robotics and Automation, 2004: 1059-1064
[82] Matsuno F., Saito K. Attitude control of a space robot with initial angular momentum. IEEE International Conference on Robotics and Automation, 2001: 1400-1405
[83] Ohashi E., Ohnishi K. Variable compliance control based on soft-landing trajectory for hopping robot. IEEE Conference on Industrial Electronics Society, 2004: 2253-2258
[84] Takemori F., Kitamura A. Soft landing approach for a reduced biped robot model. IEEE/ASME International Conference on Advanced Intelligent Mechatronics,2003: 753-758
[85]陈勇,陈东辉,佟金,陈秉聪.仿蝗虫机器人运动形态的三维动态仿真.农业机械学报, 2007, 38(9): 151-154
[86] Nagano A., Komura T., Fukashiro S. Optimal coordination of maximal-effort horizontal and vertical jump motions– a computer simulation study. BioMedical Engineering OnLine, 2007, 6(1): 20-28
[87] Vanrenterghem J., Lees A., Lenoir M., Aerts P., De Clercq D. Performing the vertical jump: movement adaptations for submaximal jumping. Human movement science, 2004, 22(6): 713-727
[88] Hara M., Shibayama A., Takeshita D., Fukashiro S. The effect of arm swing on lower extremities in vertical jumping. Journal of biomechanics, 2006, 39(13): 2503-2511
[89]郭权,柴全义.影响男排运动员单脚起跳效果的主要因素.上海体育学院学报, 2003, (2): 28-32
[90]张军.试析影响跳高高度的力学因素.哈尔滨体育学院学报, 2000, 18(64): 31-33
[91]裘琴儿.影响跳远成绩的若干关联因素分析.浙江体育科学, 2000, 22(3): 62-64
[92]靳小雨.影响弹跳高度的动力学指标和运动技术因素分析.山东体育科技, 2002, 24(4): 5-7
[93]葛文杰.仿袋鼠跳跃机器人运动学及动力学研究[博士论文],西安:西北工业大学, 2006
[94]刘卫民.对发展纵跳能力的训练探讨.田径, 2005, (2): 5-7
[95]王进.论“髋”在短跑,跳跃中的作用与训练.南京体育学院学报:社会科学版, 2002, 16(2): 79-81
[96]刘延柱.跳跃运动的定性理论.力学学报, 1994, 26(4): 477-482
[97]张毅.单面约束系统动力学研究进展.力学与实践, 2000, 22(4): 8-11
[98]郭安萍,洪嘉振.柔性多体系统接触碰撞子结构动力学模型.中国科学: E辑, 2002, 32(6): 765-770
[99]梁斌,刘良栋,李庚田.空间机器人的动力学等价机械臂.自动化学报, 1998, 24(6): 761-767
[100] Kajita S., Nagasaki T., Yokoi K., Kaneko K., Tanie K. Running pattern generation for a humanoid robot. IEEE International Conference on Robotics and Automation, 2002: 2755-2761
[101] Papadopoulos E., Cherouvim N. On increasing energy autonomy for a one-legged hopping robot. IEEE International Conference on Robotics and Automation, 2004: 4645- 4650
[102]邹慧君,蓝光辉.机构学研究现状,发展趋势和应用前景.机械工程学报, 1999, 35(5): 1-4
[103]刘安心,杨廷力.连续法在机构运动综合中的应用.机械设计, 1995, 12(7): 7-9
[104]付成龙,陈恳.双足机器人稳定性与控制策略研究进展.高技术通讯, 2006, 16(3): 319-324
[105]谢黎明,查富生,李国慧.快速运动过程中双足机器人重心稳定的自适应模糊控制.机床与液压, 2004, (9): 65-67
[106]石斌,王安麟,赵群飞.基于过程ZMP的双足步行机器椅步态规划.机械设计, 2007, 24(10): 11-14
[107]吴瑞珉,刘廷荣.冗余度机器人操作机运动学及其设计的研究.机器人, 1996, 18(1): 55-64
[108]陆震.冗余自由度机器人原理及应用.北京:机械工业出版社, 2007
[109] Siciliano B. Kinematic control of redundant robot manipulators: A tutorial. Journal of Intelligent and Robotic Systems, 1990, 3(3): 201-212
[110]陈力,戈新生.冗余度空间机械臂的动力学与优化控制.上海交通大学学报, 1997, 31(1): 27-31
[111]李鲁亚,张启先.基于运动可优化度的冗余自由度机器人运动学实时控制研究.机械工程学报, 1994, 30(6): 93-100
[112] Kircanski M. Kinematic isotropy and optimal kinematic design of planar manipulators and a 3-DOF spatial manipulator. The International Journal of Robotics Research, 1996, 15(1): 61-77
[113]丑武胜,吴忠.冗余机械臂运动奇异性分析.机械工程学报, 2000, 36(9): 33-36
[114] Ding H., Chan S. P. A real-time planning algorithm for obstacle avoidance of redundant robots. Journal of Intelligent and Robotic Systems, 1996, 16(3): 229-243
[115] Ahuactzin J. M., Gupta K., Mazer E. Manipulation planning for redundant robots: a practical approach. The International Journal of Robotics Research, 1998, 17(7): 731-747
[116] Van den Doel K., Pai D. K. Redundancy and non-linearity measures for robot manipulators, 1994: 1873-1880
[117]熊有伦,丁汉,刘恩沦.机器人学.北京:机械工业出版社, 1992
[118] Yoshikawa T. Manipulability of robotic mechanisms. The International Journal ofRobotics Research, 1985, 4(2): 3-9
[119]张磊.一类对称矩阵的逆特征值问题.高等学校计算数学学报, 1990, 12(1): 65-72
[120] Duarte F. B. M., Machado J. A. T. Chaos dynamics in the trajectory control of redundant manipulators. IEEE International Conference on Robotics and Automation, 2000: 4109-4109
[121]曾清红,卢德唐.基于移动最小二乘法的曲线曲面拟合.工程图学学报, 2004, 25(1): 84-89
[122] Seereeram S., Wen J. T. A global approach to path planning for redundant manipulators. IEEE transactions on robotics and automation, 1995, 11(1): 152-160
[123]葛文杰,沈允文,黄杰,李向阳.仿袋鼠机器人跳跃过程中的能量变化分析.机械科学与技术(西安), 2007, 26(6): 677-680
[124] Najib S. M., Yusoh S., Yamashita S., Kokubo N., Nomura Y. A study of a jumping one-leg robot with two degrees of freedom. Artificial Life and Robotics, 2009, 13(2): 442-446
[125] Ohnishi K., Ohashi E. Motion control in the support phase for a one-legged hopping robot. IEEE International Workshop on Advanced Motion Control, 2004: 259-262
[126] Sakka S., Sian N. E., Yokoi K. Motion Pattern for the Landing Phase of a Vertical Jump for Humanoid Robots. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2006: 5477-5483
[127] Wen J. T. Y., Wilfinger L. S. Kinematic manipulability of general constrained rigid multibody systems. IEEE Transactions on Robotics and Automation, 1999, 15(3): 558-567
[128] Chiacchio P. A new dynamic manipulability ellipsoid for redundant manipulators. Robotica, 2001, 18(4): 381-387
[129] Walker I. D. Impact configurations and measures for kinematically redundant andmultiple armed robot systems. IEEE Transactions on Robotics and Automation, 1994, 10(5): 670-683
[130]李健,李剑锋.基于可操作度的单冗余度机器人容错性指标.北京航空航天大学学报, 2002, 28(1): 54-57
[131]赵京,缪萍.冗余度机械臂关节运动和末端运动的同步容错规划.机械工程学报, 2003, 39(3): 53-57
[132]赵永生,杜永辉.步行机动力学操作性的研究及机构参数的优化.光学精密工程, 1998, 6(1): 75-80
[133]陈安军,许佩霞,李国梁.双臂机器人机构速度方向可操作性研究.南京理工大学学报, 2005, 29(2): 202-205
[134] Kurazume R., Hasegawa T. A New Index of Serial-Link Manipulator Performance Combining Dynamic Manipulability and Manipulating Force Ellisoids. IEEE Transactions on Robotics, 2006, 22(5): 1022-1028
[135]陈安军.仿袋鼠跳跃机器人运动和力传递性能研究.机械科学与技术(西安), 2008, 27(7): 971-975
[136]刘迎春,余跃庆,姜春福.机器人可操作性研究进展.机械设计与研究, 2003, 19(4): 34-37
[137] Chen D. Z., Tsai L. W. The generalized principle of inertia match for geared roboticmechanisms. IEEE International Conference on Robotics and Automation, 1991: 1282-1287
[138]马宏绪,张彭.两足步行机器人研究.高技术通讯, 1995, 5(9): 17-20
[139] Vukobratovic M., Borovac B. Zero-moment point-thirty five years of its life. International Journal of Humanoid Robotics, 2004, 1(1): 157-173
[140] Yin C., Albers A., Ottnad J., Haussler P. Stability maintenance of a humanoid robot under disturbance with fictitious zero-moment point (FZMP). IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005: 3149-3156
[141] Collins J. J., Luca C. J. Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Experimental Brain Research, 1993, 95(2): 308-318
[142] Kudoh S., Komura T., Ikeuchi K. Stepping motion for a humanlike character to maintain balance against large perturbations. IEEE Int. Conf. Robotics and Automation, 2006: 2561-2567
[143] Vanel O., Gorce P. Adaptive criteria for biped dynamic stability under externalperturbations. IEEE/RSJ International Conference on Intelligent Robots and Systems, 1996: 192-199
[144]殷晨波,周庆敏,徐海涵,杨敏.拟人机器人抗干扰行走稳定性分析.控制与决策, 2006, 21(6): 619-624
[145]李斌,刘金国,谈大龙.可重构模块机器人倾翻稳定性研究.机器人, 2005, 27(3): 241-246
[146] Naksuk N., Lee C. S. G. Zero moment point manipulability ellipsoid. IEEE International Conference on Robotics and Automation, 2006: 1970-1975
[147] Kondak K., Hommel G. Control and online computation of stable movement for biped robots. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2003:874-879
[148]马颂德,张正友.计算机视觉.北京:科学出版社, 1998
[2]罗庆生,韩宝玲.现代仿生机器人设计.北京:电子工业出版社, 2008
[3]许宏岩,付宜利,王树国,刘建国.仿生机器人的研究.机器人, 2004, 26(3): 283-288
[4]张秀丽,郑浩峻,陈恳,段广洪.机器人仿生学研究综述.机器人, 2002, 24(2): 188-192
[5]迟科祥,颜国正.仿生机器人的研究状况及其未来发展.机器人, 2001, 23(5): 476-480
[6] Regele R., Bott W., Levi P. Prorobot Predictions for the future development of humanoid robots. Autonome Mobile Systeme, 2003: 292-303
[7] Kovac M., Fuchs M., Guignard A., Zufferey J. C., Floreano D. A miniature 7g jumping robot, 2008: 373-378
[8]刘壮志,席文明,朱剑英,吴洪涛.弹跳式机器人研究.机器人, 2003, 25(6): 568-573
[9] Matsuoka K. A mechanical model of repetitive hopping movements. Biomechanisms, 1980, 5(2): 251-258
[10] Raibert M. H. Legged robots that balance. Cambridge, Mass.: MIT Press, 1986
[11] Papantoniou K. V. Electromechanical design for an electrically powered, activelybalanced one leg planar robot. IEEE/RSJ International Workshop on Intelligent Robots and Systems, 1991: 1553-1560
[12] Zeglin G., Brown B. Control of a bow leg hopping robot. IEEE International Conference on Robotics and Automation, 1998: 793-798
[13] Ahmadi M., Buehler M. The ARL monopod II running robot: Control and energetics. IEEE International Conference on Robotics and Automation, 1999: 1689-1694
[14] Lee W., Raibert M. Control of hoof rolling in an articulated leg. IEEE International Conference on Robotics and Automation, 1991: 1386-1391
[15] Zeglin G. J. Uniroo--a one legged dynamic hopping robot [Master Degree], Massachusetts Institute of Technology: Massachusetts Institute of Technology, 1991
[16] Hyon S. H., Mita T. Development of a biologically inspired hopping robot Kenken. IEEE International Conference on Robotics and Automation, 2002: 3984-3991
[17] Sung S., Youm Y. Landing Motion Control of Articulated Legged Robot. IEEE International Conference on Robotics and Automation, 2007: 3230-3236
[18] De Man H., Lefeber D., Vermeulen J. Design and control of a robot with one articulated leg for locomotion on irregular terrain. COURSES AND LECTURES-INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES, 1998: 417-424
[19] Berkemeier M. D., Desai K. V. Control of hopping height in legged robots using aneural-mechanical approach. IEEE International Conference on Robotics and Automation, 1999: 1695-1701
[20] Zhang W., Wang G., Chambers T., Simon W. E. Toward a folding-legged uniped that can learn to jump. IEEE International Conference on Systems, Man, and Cybernetics, 1997: 4315-4319
[21] Tajima R., Suga K. Motion having a Flight Phase: Experiments Involving a One-legged Robot. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2006: 1726-1731
[22] Lim B., Babic J., Park F. C. Optimal jumps for biarticular legged robots. IEEE International Conference on Robotics and Automation, 2008: 226-231
[23] Ishida T. Development of a small biped entertainment robot QRIO. International Symposium on Micro-Nanomechatronics and Human Science, 2004: 23-28
[24] Sakagami Y., Watanabe R., Aoyama C., Matsunaga S., Higaki N., Fujimura K., Ltd H., Saitama J. The intelligent ASIMO: System overview and integration. IEEE/RSJ International Conference on Intelligent Robots and System, 2002: 2478-2483
[25] Schiehlen W. Energy-optimal design of walking machines. Multibody System Dynamics, 2005, 13(1): 129-141
[26] Chevallereau C., Abba G., Aoustin Y., Plestan F., Westervelt E. R., Canudas-de-Wit C., Grizzle J. W. Rabbit: A testbed for advanced control theory. IEEE Control Systems Magazine, 2003, 23(5): 57-79
[27] Arsenic A. M. Developmental learning on a humanoid robot. IEEE International Joint Conference on Neural Networks, 2004: 3167-3172
[28] Dillmann R., Zollner R. D. Interactive and Cooperative Robot Assistants. Springer, 2006: 315-368
[29]杨煜普,耿涛,郭毓.一种新型翻转跳跃运动机器人的运动结构与轨迹规划.上海交通大学学报, 2003, 37(7): 1110-1113
[30]赵晓军,黄强,彭朝琴,张利格,李科杰.基于人体运动的仿人型机器人动作的运动学匹配.机器人, 2005, 27(4): 358-361
[31]刘壮志.弹跳机器人若干关键技术研究[博士论文],南京:南京航空航天大学, 2004
[32]何广平,谭晓兰,张向慧.双臂弹性单腿机器人的垂直跳跃控制.机械工程学报, 2007, 43(5): 44-49
[33]马利娥.仿袋鼠机器人跳跃运动机理的研究[硕士论文],西安:西北工业大学, 2005
[34]王淑艳.仿人型跑步机器人的稳定性条件及步态规划[硕士论文],西安:西安电子科技大学, 2006
[35]谢健.三连杆单杠体操机器人的智能控制方法研究[硕士论文],重庆:重庆大学, 2003
[36]邓宗全,岳明.球形机器人的发展概况综述.机器人技术与应用, 2006, (3): 27-31
[37]吉爱红,戴振东,周来水.仿生机器人的研究进展.机器人, 2005, 27(3): 284-288
[38]杨小传,胡海拉,王培聪,赵克强.单足弹跳机器人弹跳机构设计与弹跳动力学分析.厦门大学学报:自然科学版, 2006, 45(4): 504-508
[39] Kajita S., Nagasaki T., Kaneko K., Yokoi K., Tanie K. A hop towards running humanoid biped. IEEE International Conference on Robotics and Automation, 2004: 629-635
[40]魏航信,刘明治,王淑艳,赵丽琴.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
[41] Ikeda T., Iwatani Y., Suse K., Mita T. Analysis and design of running robots in touchdown phase. IEEE International Conference on Control Applications, 1999: 496-501
[42] Ohashi E., Ohnishi K. Hopping height control for hopping robots. Electrical Engineering in Japan, 2006, 155(1): 64-71
[43] Nunez V., Nadjar-Gauthier N. Control strategy for vertical jump of humanoid robots. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005: 2253-2258
[44] Ahmadi M., Buehler M. Stable control of a simulated one-legged running robot with hip and leg compliance. IEEE Transactions on Robotics and Automation, 1997, 13(1): 96-104
[45] Park J. H., Kwon O. Impedance control for running of biped robots. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2003: 944- 949
[46] Sato A., Buehler M. A planar hopping robot with one actuator: design, simulation, and experimental results. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004: 3540-3545
[47] Schwind W. J., Koditschek D. E. Approximating the stance map of a 2-dof monoped runner. Journal of Nonlinear Science, 2000, 10(5): 533-568
[48] Kawamura A., Sugio K., Suzuki K., Zhu C. Simulation study on one leg jumping for biped running. IEEE International Workshop on Advanced Motion Control, 2004: 433-438
[49]戈新生,刘延柱,魏宝刚.基于拟牛顿算法的自由下落猫的非完整运动规划.系统仿真学报, 2006, 18(5): 1123-1126
[50]王庆江.跳板跳水的数值分析与计算机仿真[硕士论文],南京:南京理工大学, 2002
[51] Albro J. V., Bobrow J. E. Optimal motion primitives for a 5 dof experimental hopper. IEEE International Conference on Robotics and Automation, 2001: 3630- 3635
[52] Yokozawa T., Hara S., Ishikawa M. Optimal control strategy for high jump based on complementarity modeling. IEEE Conference on Decision and Control, 2000: 3132-3137
[53] Takahashi T., Yamakita M., Hyon S. H. An optimization approach for underactuated running robot. International Joint Conference on SICE-ICASE, 2006: 3505-3510
[54] Fujimoto Y. Trajectory generation of biped running robot with minimum energy consumption. IEEE International Conference on Robotics and Automation, 2004: 3803-3808
[55] Bobrow J. E. Optimal robot plant planning using the minimum-time criterion. IEEE Journal of Robotics and Automation, 1988, 4(4): 443-450
[56] Levine W., Zajac F., Belzer M., Zomlefer M. Ankle controls that produce a maximal vertical jump when other joints are locked. IEEE Transactions on Automatic Control, 1983, 28(11): 1008-1016
[57] So B. R., Yi B. J., Oh S. R., Kim Y. S. Landing motion analysis of human-body model considering impact and ZMP condition. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004: 1972-1978
[58] Hyon S. H., Yokoyama N., Emura T. Back handspring robot: targetdynamics-based control. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004: 248-253
[59] Babic J., Omrcen D., Lenarcic J. Balance and control of human inspired jumping robot. Advances in Robot Kinematics: Mechanisms and Motion, 2006: 147-156
[60] Nagasaki T., Kajita S., Kaneko K., Yokoi K., Tanie K. A running experiment of humanoid biped. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004: 136-141
[61] Watabe T., Yamakita M., Mita T. Stabilization of 3 link acrobat robot in upright position. Proceedings of the 41st SICE Annual Conference, 2002: 2996-3001
[62]马勇占,方爱莲.对我国优秀跳远运动员起跳技术的运动学比较研究.中国体育科技, 2001, 37(2): 22-24
[63]王德平,任保莲.跳远起跳阶段摆动腿摆动的运动学特征及对起跳效果的影响.中国体育科技, 2000, 36(5): 24-25
[64] Higashimori M., Harada M., Yuya M., Ishii I., Kaneko M. Dimensional Analysis Based Design on Tracing Type Legged Robots. IEEE International Conference on Robotics and Automation, 2005: 3733-3738
[65] Hayashi R., Tsujio S. High-performance jumping movements by pendulum-type jumpingmachines. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2001: 722-727
[66] Sakka S., Yokoi K. Humanoid vertical jumping based on force feedback and inertial forces optimization. IEEE International Conference on Robotics and Automation, 2005: 3752-3757
[67] Chevallereau C., Sardain P. Design and actuation optimization of a 4 axes biped robot for walking and running. IEEE International Conference on Robotics and Automation, 2000: 3365-3370
[68] Yoshida Y., Kamano T., Yasuno T., Suzuki T., Harada H., Kataoka Y. Generation of suitable jumping motion pattern for hopping robot under genetic algorithm. TRANSACTIONS-INSTITUTE OF ELECTRICAL ENGINEERS OF JAPAN C, 2000, 120(10): 1365-1371
[69] Vermeulen J., Lefeber D., Verrelst B. Control of foot placement, forward velocity and body orientation of a one-legged hopping robot. Robotica, 2003, 21(1): 45-57
[70]齐晓慧.李雅普诺夫运动稳定性与平衡状态稳定性的关系.军械工程学院学报, 2002, 14(4): 35-38
[71] Vukobratovic M., Borovac B., Potkonjak V. ZMP: A review of some basic misunderstandings. International Journal of Humanoid Robotics, 2006, 3(2):153-175
[72] Vukobratovic M., Stepanenko J. Mathematical models of general anthropomorphic systems. Mathematical Biosciences, 1973, 17: 191-242
[73] Yamaguchi J., Soga E., Inoue S., Takanishi A. Development of a bipedal humanoid robot-control method of wholebody cooperative dynamic biped walking. IEEE International Conference on Robotics and Automation, 1999: 368-374
[74] Li Q., Takanishi A., Kato I. Learning control of compensative trunk motion for biped walking robot based on ZMP stability criterion. lEEE/RSJ International Conference on Intelligent Robots and Systems, 1992: 597-603
[75] Sugihara T., Nakamura Y., Inoue H. Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control. IEEE International Conference on Robotics and Automation, 2002: 1404-1409
[76] Goswami A. Postural stability of biped robots and the foot-rotation indicator (FRI) point. The International Journal of Robotics Research, 1999, 18(6): 523-533
[77] Popovic M. B., Goswami A., Herr H. Ground reference points in legged locomotion: Definitions, biological trajectories and control implications. The International Journal of Robotics Research, 2005, 24(12): 1013-1032
[78] Takhmar A. A., Alipour M., Moosavian K. MHS measure for postural stability monitoring and control of biped robots. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2008: 400-405
[79] Kang J. Y., Cochran J. E. Stability Criteria of Slosh Motion with Periodicity in a Spinning Spacecraft. Journal OF Guidance, Control, AND Dynamics, 2005, 28(3): 562-568
[80] Herr H., Popovic M. Angular momentum in human walking. Journal of Experimental Biology, 2008, 211(4): 467-481
[81] Li Z., Huang Q., Li K., Duan X. Stability criterion and pattern planning for humanoid running. IEEE International Conference on Robotics and Automation, 2004: 1059-1064
[82] Matsuno F., Saito K. Attitude control of a space robot with initial angular momentum. IEEE International Conference on Robotics and Automation, 2001: 1400-1405
[83] Ohashi E., Ohnishi K. Variable compliance control based on soft-landing trajectory for hopping robot. IEEE Conference on Industrial Electronics Society, 2004: 2253-2258
[84] Takemori F., Kitamura A. Soft landing approach for a reduced biped robot model. IEEE/ASME International Conference on Advanced Intelligent Mechatronics,2003: 753-758
[85]陈勇,陈东辉,佟金,陈秉聪.仿蝗虫机器人运动形态的三维动态仿真.农业机械学报, 2007, 38(9): 151-154
[86] Nagano A., Komura T., Fukashiro S. Optimal coordination of maximal-effort horizontal and vertical jump motions– a computer simulation study. BioMedical Engineering OnLine, 2007, 6(1): 20-28
[87] Vanrenterghem J., Lees A., Lenoir M., Aerts P., De Clercq D. Performing the vertical jump: movement adaptations for submaximal jumping. Human movement science, 2004, 22(6): 713-727
[88] Hara M., Shibayama A., Takeshita D., Fukashiro S. The effect of arm swing on lower extremities in vertical jumping. Journal of biomechanics, 2006, 39(13): 2503-2511
[89]郭权,柴全义.影响男排运动员单脚起跳效果的主要因素.上海体育学院学报, 2003, (2): 28-32
[90]张军.试析影响跳高高度的力学因素.哈尔滨体育学院学报, 2000, 18(64): 31-33
[91]裘琴儿.影响跳远成绩的若干关联因素分析.浙江体育科学, 2000, 22(3): 62-64
[92]靳小雨.影响弹跳高度的动力学指标和运动技术因素分析.山东体育科技, 2002, 24(4): 5-7
[93]葛文杰.仿袋鼠跳跃机器人运动学及动力学研究[博士论文],西安:西北工业大学, 2006
[94]刘卫民.对发展纵跳能力的训练探讨.田径, 2005, (2): 5-7
[95]王进.论“髋”在短跑,跳跃中的作用与训练.南京体育学院学报:社会科学版, 2002, 16(2): 79-81
[96]刘延柱.跳跃运动的定性理论.力学学报, 1994, 26(4): 477-482
[97]张毅.单面约束系统动力学研究进展.力学与实践, 2000, 22(4): 8-11
[98]郭安萍,洪嘉振.柔性多体系统接触碰撞子结构动力学模型.中国科学: E辑, 2002, 32(6): 765-770
[99]梁斌,刘良栋,李庚田.空间机器人的动力学等价机械臂.自动化学报, 1998, 24(6): 761-767
[100] Kajita S., Nagasaki T., Yokoi K., Kaneko K., Tanie K. Running pattern generation for a humanoid robot. IEEE International Conference on Robotics and Automation, 2002: 2755-2761
[101] Papadopoulos E., Cherouvim N. On increasing energy autonomy for a one-legged hopping robot. IEEE International Conference on Robotics and Automation, 2004: 4645- 4650
[102]邹慧君,蓝光辉.机构学研究现状,发展趋势和应用前景.机械工程学报, 1999, 35(5): 1-4
[103]刘安心,杨廷力.连续法在机构运动综合中的应用.机械设计, 1995, 12(7): 7-9
[104]付成龙,陈恳.双足机器人稳定性与控制策略研究进展.高技术通讯, 2006, 16(3): 319-324
[105]谢黎明,查富生,李国慧.快速运动过程中双足机器人重心稳定的自适应模糊控制.机床与液压, 2004, (9): 65-67
[106]石斌,王安麟,赵群飞.基于过程ZMP的双足步行机器椅步态规划.机械设计, 2007, 24(10): 11-14
[107]吴瑞珉,刘廷荣.冗余度机器人操作机运动学及其设计的研究.机器人, 1996, 18(1): 55-64
[108]陆震.冗余自由度机器人原理及应用.北京:机械工业出版社, 2007
[109] Siciliano B. Kinematic control of redundant robot manipulators: A tutorial. Journal of Intelligent and Robotic Systems, 1990, 3(3): 201-212
[110]陈力,戈新生.冗余度空间机械臂的动力学与优化控制.上海交通大学学报, 1997, 31(1): 27-31
[111]李鲁亚,张启先.基于运动可优化度的冗余自由度机器人运动学实时控制研究.机械工程学报, 1994, 30(6): 93-100
[112] Kircanski M. Kinematic isotropy and optimal kinematic design of planar manipulators and a 3-DOF spatial manipulator. The International Journal of Robotics Research, 1996, 15(1): 61-77
[113]丑武胜,吴忠.冗余机械臂运动奇异性分析.机械工程学报, 2000, 36(9): 33-36
[114] Ding H., Chan S. P. A real-time planning algorithm for obstacle avoidance of redundant robots. Journal of Intelligent and Robotic Systems, 1996, 16(3): 229-243
[115] Ahuactzin J. M., Gupta K., Mazer E. Manipulation planning for redundant robots: a practical approach. The International Journal of Robotics Research, 1998, 17(7): 731-747
[116] Van den Doel K., Pai D. K. Redundancy and non-linearity measures for robot manipulators, 1994: 1873-1880
[117]熊有伦,丁汉,刘恩沦.机器人学.北京:机械工业出版社, 1992
[118] Yoshikawa T. Manipulability of robotic mechanisms. The International Journal ofRobotics Research, 1985, 4(2): 3-9
[119]张磊.一类对称矩阵的逆特征值问题.高等学校计算数学学报, 1990, 12(1): 65-72
[120] Duarte F. B. M., Machado J. A. T. Chaos dynamics in the trajectory control of redundant manipulators. IEEE International Conference on Robotics and Automation, 2000: 4109-4109
[121]曾清红,卢德唐.基于移动最小二乘法的曲线曲面拟合.工程图学学报, 2004, 25(1): 84-89
[122] Seereeram S., Wen J. T. A global approach to path planning for redundant manipulators. IEEE transactions on robotics and automation, 1995, 11(1): 152-160
[123]葛文杰,沈允文,黄杰,李向阳.仿袋鼠机器人跳跃过程中的能量变化分析.机械科学与技术(西安), 2007, 26(6): 677-680
[124] Najib S. M., Yusoh S., Yamashita S., Kokubo N., Nomura Y. A study of a jumping one-leg robot with two degrees of freedom. Artificial Life and Robotics, 2009, 13(2): 442-446
[125] Ohnishi K., Ohashi E. Motion control in the support phase for a one-legged hopping robot. IEEE International Workshop on Advanced Motion Control, 2004: 259-262
[126] Sakka S., Sian N. E., Yokoi K. Motion Pattern for the Landing Phase of a Vertical Jump for Humanoid Robots. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2006: 5477-5483
[127] Wen J. T. Y., Wilfinger L. S. Kinematic manipulability of general constrained rigid multibody systems. IEEE Transactions on Robotics and Automation, 1999, 15(3): 558-567
[128] Chiacchio P. A new dynamic manipulability ellipsoid for redundant manipulators. Robotica, 2001, 18(4): 381-387
[129] Walker I. D. Impact configurations and measures for kinematically redundant andmultiple armed robot systems. IEEE Transactions on Robotics and Automation, 1994, 10(5): 670-683
[130]李健,李剑锋.基于可操作度的单冗余度机器人容错性指标.北京航空航天大学学报, 2002, 28(1): 54-57
[131]赵京,缪萍.冗余度机械臂关节运动和末端运动的同步容错规划.机械工程学报, 2003, 39(3): 53-57
[132]赵永生,杜永辉.步行机动力学操作性的研究及机构参数的优化.光学精密工程, 1998, 6(1): 75-80
[133]陈安军,许佩霞,李国梁.双臂机器人机构速度方向可操作性研究.南京理工大学学报, 2005, 29(2): 202-205
[134] Kurazume R., Hasegawa T. A New Index of Serial-Link Manipulator Performance Combining Dynamic Manipulability and Manipulating Force Ellisoids. IEEE Transactions on Robotics, 2006, 22(5): 1022-1028
[135]陈安军.仿袋鼠跳跃机器人运动和力传递性能研究.机械科学与技术(西安), 2008, 27(7): 971-975
[136]刘迎春,余跃庆,姜春福.机器人可操作性研究进展.机械设计与研究, 2003, 19(4): 34-37
[137] Chen D. Z., Tsai L. W. The generalized principle of inertia match for geared roboticmechanisms. IEEE International Conference on Robotics and Automation, 1991: 1282-1287
[138]马宏绪,张彭.两足步行机器人研究.高技术通讯, 1995, 5(9): 17-20
[139] Vukobratovic M., Borovac B. Zero-moment point-thirty five years of its life. International Journal of Humanoid Robotics, 2004, 1(1): 157-173
[140] Yin C., Albers A., Ottnad J., Haussler P. Stability maintenance of a humanoid robot under disturbance with fictitious zero-moment point (FZMP). IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005: 3149-3156
[141] Collins J. J., Luca C. J. Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Experimental Brain Research, 1993, 95(2): 308-318
[142] Kudoh S., Komura T., Ikeuchi K. Stepping motion for a humanlike character to maintain balance against large perturbations. IEEE Int. Conf. Robotics and Automation, 2006: 2561-2567
[143] Vanel O., Gorce P. Adaptive criteria for biped dynamic stability under externalperturbations. IEEE/RSJ International Conference on Intelligent Robots and Systems, 1996: 192-199
[144]殷晨波,周庆敏,徐海涵,杨敏.拟人机器人抗干扰行走稳定性分析.控制与决策, 2006, 21(6): 619-624
[145]李斌,刘金国,谈大龙.可重构模块机器人倾翻稳定性研究.机器人, 2005, 27(3): 241-246
[146] Naksuk N., Lee C. S. G. Zero moment point manipulability ellipsoid. IEEE International Conference on Robotics and Automation, 2006: 1970-1975
[147] Kondak K., Hommel G. Control and online computation of stable movement for biped robots. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2003:874-879
[148]马颂德,张正友.计算机视觉.北京:科学出版社, 1998