双足被动步行机器人性能分析及一种动力输入方法研究
|
摘要
最初的被动步行机器人是一种能在向下的斜坡上仅靠重力步行的纯被动步行机器人,后来在机器人的踝关节或髋关节处引入主动的驱动与控制,发展成为了可沿平地步行的半被动步行机器人。与传统的主动步行机器人相比,被动步行机器人具有步态自然、能量效率高等优点。被动步行的研究成果除可应用于双足机器人的研制外,还可应用于医疗康复设备和假肢的设计,以解决下肢残疾或截肢病人的康复问题。本文主要对双足被动步行机器人的性能进行了分析以及对一种半被动步行机器人的动力输入方法进行了研究。
首先介绍了所研制的考虑髋关节弹簧、髋关节阻尼以及腿质心前后偏移影响的二维双足无膝关节纯被动步行机器人样机,并建立了摆动过程动力学方程和碰撞过程动力学方程,利用数值软件MATLAB对动力学方程进行了仿真求解。采用Newton-Raphson迭代方法求出了稳定的不动点。分别采用在ADAMS软件中建立虚拟样机仿真和图像测量的方法验证了数值仿真的正确性。
研究了弹簧刚度、阻尼系数和质心偏移等参数对纯被动步行机器人抗干扰能力、步行速度、步行效率以及分岔特性的影响。使用无量纲步态敏感范数的倒数对机器人抗干扰能力进行评价。实验验证了弹簧刚度和质心偏移对机器人抗干扰能力的影响。在实验中,使机器人在各弹簧刚度参数下和质心偏移参数下沿斜坡向下行走100次,记录下行走到斜坡终点的次数作为抗干扰能力的度量。实验结果表明存在一个大小适中的弹簧刚度使机器人的抗干扰能力最大,存在一个较小的质心向后偏移使机器人的抗干扰能力最大。调整弹簧刚度和质心偏移的方法具有操作简单,提高抗干扰能力显著的优点。研究了弹簧刚度、阻尼系数和质心偏移对机器人抗干扰能力影响的作用机理。
提高抗干扰能力是被动步行机器人的一个研究热点,而多参数优化方法是提高抗干扰能力的一个非常有效的方法。以步态敏感范数的倒数值最大化为优化目标,使用遗传算法和模式搜索相结合的方法对弹簧刚度、质心偏移、轴向质心距离和转动惯量4个参数同时进行优化。获得稳定的不动点是求解步态敏感范数的前提。而采用Newton-Raphson迭代搜索不动点时,当所选初值偏离不动点较远时难以收敛,搜索时间和搜索成功与否都依赖于初始值的选取。因此使用BP神经网络对被动步行稳定不动点进行估算,并将估算值作为Newton-Raphson迭代的初值求解稳定不动点。参数变化较小时不动点的变化也较小,利用这一特点,在计算相邻两个样本的不动点以获取训练样本时,只使一个参数发生较小的变化,并将本次使用Newton-Raphson迭代搜索得到的稳定不动点作为下一样本使用Newton-Raphson迭代搜索不动点的初值。使用1000组随机产生的参数对所得神经网络进行测试,结果表明该方法不仅大幅提高了稳定不动点的搜索成功率,而且大幅缩短了搜索时间。将该方法应用于优化过程中稳定不动点的求解。首先利用遗传算法强大的全局优化能力进行优化,并将优化结果作为模式搜索的初值,利用模式搜索强大的局部搜索能力进行优化。通过与样机步态敏感范数的倒数值进行对比,验证了优化算法的有效性。
由于目前的半被动双足步行机器人所采用的控制方法大多较为复杂,因此由人类步行的生物力学研究得到启发,提出一种半被动双足步行机器人的动力输入方法,并定量分析了各参数对机器人性能的影响。由机器人摆动腿与地发生碰撞后开始于髋关节处施加方波力矩,作为动力输入。由于力矩在一个步行周期中没有做负功,该机器人具有与人类步行相似的高能量效率。该机器人能够实现沿上坡、下坡和平地步行。通过对机器人动力输入参数的适当调整,可以将原本摔倒的步态或分岔的步态控制到稳定的单周期步态上来,并且与纯被动步行机器人相比,半被动步行机器人可以在一个更大的斜坡角度范围以单周期步态稳定步行。
The first passive dynamic walker is a pure passive walker which can perform a stable walking motion down a slight slope powered only by gravity. Powered robots that can walk on a level floor by ankle push-off or hip actuation have also been built based on this concept. Compared with traditional walking robots, passive dynamic walkers have more natural-looking gait and higher energy efficiency. The research results can be used to the design of biped robots, medical rehabilitation devices and prosthetic legs to help rehabilitation for the amputees. The performance of a passive dynamic walker and a power input method for a quasi-passive dynamic walker is studied in this paper.
A 2D kneeless biped passive walking prototype with hip spring and offset of center of mass was proposed. The equations of motion of the swing phase and the impact phase were derived, respectively. The equations were solved with MATLAB software by numerical simulation. The stable fixed point was obtained by Newton-Raphson iteration. The numerical simulation is verified by virtual prototype simulation and experiment, respectively.
The effects of spring stiffness, damping coefficient and offset of center of mass on disturbance rejection, walking speed, walking efficiency and bifurcation characteristics were studied. Reciprocal of the gait sensitivity norm was used as a measure for disturbance rejection. The dimensionless mechanical cost of transport was used as a measure for walking efficiency. The effects of spring stiffness and offset of center of mass on disturbance rejection are verified by experiments. For experiments, we quantified disturbance rejection by observing 100 passive walking trials down a gentle slope of finite length and recording the fraction of trials which successfully walked to the end. The experiments show that an optimal spring stiffness and an optimal backward offset of center of mass for disturbance rejection exist. The method of adjusting spring stiffness and offset of center of mass has the advantages of easy to implement and improving disturbance rejection significantly. The reasons of the effects of spring stiffness, damping coefficient and offset of center of mass on disturbance rejection were investigated.
To improve disturbance rejection is a research focus of passive dynamic walker. Multi-parameter optimization is a very effective way to improve disturbance rejection. The genetic algorithm combined with pattern search method was used to find the maximum reciprocal of the gait sensitivity norm. Four optimal parameters were spring stiffness, offset of center of mass, axial displacement of center of mass and moment of inertia. Obtaining the stable fixed point is the premise of obtaining the gait sensitivity norm. Newton-Raphson method does not converge with improper initial values. The search time and successful search rate are dependent on the initial value. BP neural network was used to estimate the fixed point, and the estimated fixed point was taken as initial value for Newton-Raphson iteration to search the stable fixed point. Small variation of parameters leads to small variation of fixed points. When calculating fixed points of two successive samples, only one parameter had a small variation. The fixed point obtained with Newton-Raphson iteration was used as initial value for the next sample. 1000 groups of parameters were generated randomly to test the performance of the neural network. The results show that this method increases the successful search rate significantly and reduces the search time significantly. This method was used to obtain the stable fixed points for the optimization. The genetic algorithm was used for global optimization, then the optimal parameter was used as initial value for pattern search method to optimize locally. The effectiveness of the optimization is verified by comparing the optimal result with the prototype’s reciprocal of the gait sensitivity norm.
The present control methods for quasi-passive walkers are complex. Inspired by biomechanics in human walking, we presented a power input method for the quasi-passive walker and quantitatively studied the effects of parameters on the performance of the quasi-passive walker. After the impact between swing leg and ground, a square wave torque was applied at the hip as power input. Since the torque does not do negative work during the whole walking period, the walker has a high walking efficiency as human walking. The robot can walk up a slope, walk down a slope and walk on flat ground. The falling gait and bifurcation gait can be controlled to stable period-1 gait by properly adjusting power input parameters. The quasi-passive walker can walk with stable period-1 gait in a larger scope of slope angle compared with the pure passive walker.
首先介绍了所研制的考虑髋关节弹簧、髋关节阻尼以及腿质心前后偏移影响的二维双足无膝关节纯被动步行机器人样机,并建立了摆动过程动力学方程和碰撞过程动力学方程,利用数值软件MATLAB对动力学方程进行了仿真求解。采用Newton-Raphson迭代方法求出了稳定的不动点。分别采用在ADAMS软件中建立虚拟样机仿真和图像测量的方法验证了数值仿真的正确性。
研究了弹簧刚度、阻尼系数和质心偏移等参数对纯被动步行机器人抗干扰能力、步行速度、步行效率以及分岔特性的影响。使用无量纲步态敏感范数的倒数对机器人抗干扰能力进行评价。实验验证了弹簧刚度和质心偏移对机器人抗干扰能力的影响。在实验中,使机器人在各弹簧刚度参数下和质心偏移参数下沿斜坡向下行走100次,记录下行走到斜坡终点的次数作为抗干扰能力的度量。实验结果表明存在一个大小适中的弹簧刚度使机器人的抗干扰能力最大,存在一个较小的质心向后偏移使机器人的抗干扰能力最大。调整弹簧刚度和质心偏移的方法具有操作简单,提高抗干扰能力显著的优点。研究了弹簧刚度、阻尼系数和质心偏移对机器人抗干扰能力影响的作用机理。
提高抗干扰能力是被动步行机器人的一个研究热点,而多参数优化方法是提高抗干扰能力的一个非常有效的方法。以步态敏感范数的倒数值最大化为优化目标,使用遗传算法和模式搜索相结合的方法对弹簧刚度、质心偏移、轴向质心距离和转动惯量4个参数同时进行优化。获得稳定的不动点是求解步态敏感范数的前提。而采用Newton-Raphson迭代搜索不动点时,当所选初值偏离不动点较远时难以收敛,搜索时间和搜索成功与否都依赖于初始值的选取。因此使用BP神经网络对被动步行稳定不动点进行估算,并将估算值作为Newton-Raphson迭代的初值求解稳定不动点。参数变化较小时不动点的变化也较小,利用这一特点,在计算相邻两个样本的不动点以获取训练样本时,只使一个参数发生较小的变化,并将本次使用Newton-Raphson迭代搜索得到的稳定不动点作为下一样本使用Newton-Raphson迭代搜索不动点的初值。使用1000组随机产生的参数对所得神经网络进行测试,结果表明该方法不仅大幅提高了稳定不动点的搜索成功率,而且大幅缩短了搜索时间。将该方法应用于优化过程中稳定不动点的求解。首先利用遗传算法强大的全局优化能力进行优化,并将优化结果作为模式搜索的初值,利用模式搜索强大的局部搜索能力进行优化。通过与样机步态敏感范数的倒数值进行对比,验证了优化算法的有效性。
由于目前的半被动双足步行机器人所采用的控制方法大多较为复杂,因此由人类步行的生物力学研究得到启发,提出一种半被动双足步行机器人的动力输入方法,并定量分析了各参数对机器人性能的影响。由机器人摆动腿与地发生碰撞后开始于髋关节处施加方波力矩,作为动力输入。由于力矩在一个步行周期中没有做负功,该机器人具有与人类步行相似的高能量效率。该机器人能够实现沿上坡、下坡和平地步行。通过对机器人动力输入参数的适当调整,可以将原本摔倒的步态或分岔的步态控制到稳定的单周期步态上来,并且与纯被动步行机器人相比,半被动步行机器人可以在一个更大的斜坡角度范围以单周期步态稳定步行。
The first passive dynamic walker is a pure passive walker which can perform a stable walking motion down a slight slope powered only by gravity. Powered robots that can walk on a level floor by ankle push-off or hip actuation have also been built based on this concept. Compared with traditional walking robots, passive dynamic walkers have more natural-looking gait and higher energy efficiency. The research results can be used to the design of biped robots, medical rehabilitation devices and prosthetic legs to help rehabilitation for the amputees. The performance of a passive dynamic walker and a power input method for a quasi-passive dynamic walker is studied in this paper.
A 2D kneeless biped passive walking prototype with hip spring and offset of center of mass was proposed. The equations of motion of the swing phase and the impact phase were derived, respectively. The equations were solved with MATLAB software by numerical simulation. The stable fixed point was obtained by Newton-Raphson iteration. The numerical simulation is verified by virtual prototype simulation and experiment, respectively.
The effects of spring stiffness, damping coefficient and offset of center of mass on disturbance rejection, walking speed, walking efficiency and bifurcation characteristics were studied. Reciprocal of the gait sensitivity norm was used as a measure for disturbance rejection. The dimensionless mechanical cost of transport was used as a measure for walking efficiency. The effects of spring stiffness and offset of center of mass on disturbance rejection are verified by experiments. For experiments, we quantified disturbance rejection by observing 100 passive walking trials down a gentle slope of finite length and recording the fraction of trials which successfully walked to the end. The experiments show that an optimal spring stiffness and an optimal backward offset of center of mass for disturbance rejection exist. The method of adjusting spring stiffness and offset of center of mass has the advantages of easy to implement and improving disturbance rejection significantly. The reasons of the effects of spring stiffness, damping coefficient and offset of center of mass on disturbance rejection were investigated.
To improve disturbance rejection is a research focus of passive dynamic walker. Multi-parameter optimization is a very effective way to improve disturbance rejection. The genetic algorithm combined with pattern search method was used to find the maximum reciprocal of the gait sensitivity norm. Four optimal parameters were spring stiffness, offset of center of mass, axial displacement of center of mass and moment of inertia. Obtaining the stable fixed point is the premise of obtaining the gait sensitivity norm. Newton-Raphson method does not converge with improper initial values. The search time and successful search rate are dependent on the initial value. BP neural network was used to estimate the fixed point, and the estimated fixed point was taken as initial value for Newton-Raphson iteration to search the stable fixed point. Small variation of parameters leads to small variation of fixed points. When calculating fixed points of two successive samples, only one parameter had a small variation. The fixed point obtained with Newton-Raphson iteration was used as initial value for the next sample. 1000 groups of parameters were generated randomly to test the performance of the neural network. The results show that this method increases the successful search rate significantly and reduces the search time significantly. This method was used to obtain the stable fixed points for the optimization. The genetic algorithm was used for global optimization, then the optimal parameter was used as initial value for pattern search method to optimize locally. The effectiveness of the optimization is verified by comparing the optimal result with the prototype’s reciprocal of the gait sensitivity norm.
The present control methods for quasi-passive walkers are complex. Inspired by biomechanics in human walking, we presented a power input method for the quasi-passive walker and quantitatively studied the effects of parameters on the performance of the quasi-passive walker. After the impact between swing leg and ground, a square wave torque was applied at the hip as power input. Since the torque does not do negative work during the whole walking period, the walker has a high walking efficiency as human walking. The robot can walk up a slope, walk down a slope and walk on flat ground. The falling gait and bifurcation gait can be controlled to stable period-1 gait by properly adjusting power input parameters. The quasi-passive walker can walk with stable period-1 gait in a larger scope of slope angle compared with the pure passive walker.
引文
1谭定忠,王叶兰,王启明,曹日起.弹跳式机器人的发展现状.机械工程师. 2005,(10):30~31
2 Y. Sakagami, R. Watanabe, C. Aoyama, S. Matsunaga, N. Higaki, K. Fujimura. The Intelligent Asimo: System Overview and Integration. 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, 2002:2478~2483
3 M. Vukobratovic, B. Borovac. Zero-Moment Point-Thirty Five Years of Its Life. Int J Hum Robot. 2004,1(1):157~173
4毛勇.半被动双足机器人的设计与再励学习控制.清华大学博士论文. 2007:2
5 S. Collins, A. Ruina, R. Tedrake, M. Wisse. Efficient Bipedal Robots Based on Passive-Dynamic Walkers. Science. 2005,307(5712):1082~1085
6张秀丽,郑浩峻.机器人仿生学研究综述.机器人. 2002,24(2):188~192
7柳宁.双足被动行走器动力学仿真与实验研究.清华大学博士论文. 2009:3,82,67~68
8 R. M. Alexander. Walking Made Simple. Science. 2005,308(5718):58~59
9 R. Pfeifer, M. Lungarella, F. Iida. Self-Organization, Embodiment, and Biologically Inspired Robotics. Science. 2007,318(5853):1088~1093
10 M. Srinivasan, A. Ruina. Computer Optimization of a Minimal Biped Model Discovers Walking and Running. Nature. 2006,439(7072):72~75
11张更林,金宝士,张宇光.人体下肢假肢发展概况.佳木斯大学学报(自然科学版). 2002,20(03):336~342
12 T. McGeer. Passive Walking with Knees. Proceedings of the 1990 IEEE International Conference on Robotics and Automation, Cincinnati, OH, USA, 1990:1640~1645
13 T. McGeer. Passive Dynamic Walking. International Journal of Robotics Research. 1990,9(2):62~82
14 T. McGeer. Passive Dynamic Biped Catalogue. The 2nd International Symposium on Experimental Robotics II, Springer-Verlag, 1991:465~490
15 S. Mochon, T. A. McMahon. Ballistic Walking: An Improved Model. Mathematical Biosciences. 1980,52(3-4):241~260
16 J. V. Basmajian, Tuttle. Emg of Locomotion in Gorilla and Man. Plenum Press, 1973
17 M. Wisse, J. van Frankenhuyzen. Design and Construction of Mike; a 2-DAutonomous Biped Based on Passive Dynamic Walking. International Symposium on Adaptive Motion of Animals and Machines (AMAM), Kyoto, JAPAN, 2003:143~154
18 N. Liu, J. F. Li, T. S. Wang. Passive Walker That Can Walk Down Steps: Simulations and Experiments. Acta Mechanica Sinica. 2008,24(5):569~573
19 A. L. Schwab, M. Wisse. Basin of Attraction of the Simplest Walking Model. Proceedings of the ASME Design Engineering Technical Conference, Pittsburgh, PA, United States, 2001:531~539
20 R. Tedrake, T. W. Zhang, M.-F. Fong, H. S. Seung. Actuating a Simple 3d Passive Dynamic Walker. 2004 IEEE International Conference on Robotics and Automation New Orleans, LA, United States, 2004:4656~4661
21 R. Tedrake, T. W. Zhang, H. S. Seung. Stochastic Policy Gradient Reinforcement Learning on a Simple 3d Biped. 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Sendai, Japan, 2004:2849~2854
22 N. Liu, J. F. Li, T. S. Wang. The Effects of Parameter Variation on the Gaits of Passive Walking Models: Simulations and Experiments. Robotica. 2009,27:511~528
23 S. H. Collins, M. Wisse, A. Ruina. A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees. International Journal of Robotics Research. 2001,20(7):607~615
24 S. H. Collins, A. Ruina. A Bipedal Walking Robot with Efficient and Human-Like Gait. 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, 2005:1983~1988
25 M. Wisse, A. L. Schwab, R. Q. van der Linde, F. C. T. van der Helm. How to Keep from Falling Forward: Elementary Swing Leg Action for Passive Dynamic Walkers. Ieee Transactions on Robotics. 2005,21(3):393~401
26 M. Wisse, D. G. E. Hobbelen, A. L. Schwab. Adding an Upper Body to Passive Dynamic Walking Robots by Means of a Bisecting Hip Mechanism. Ieee Transactions on Robotics. 2007,23(1):112~123
27 M. Wisse, G. Feliksdal, J. van Frankenhuyzen, B. Moyer. Passive-Based Walking Robot - Denise, a Simple, Efficient, and Lightweight Biped. Ieee Robot Autom Mag. 2007,14(2):52~62
28 M. Wisse, A. L. Schwab. Skateboards, Bicycles, and Three-Dimensional Biped Walking Machines: Velocity-Dependent Stability by Means of Lean-to-Yaw Coupling. International Journal of Robotics Research. 2005,24(6):417~429
29 J. E. Pratt, B. T. Krupp. Series Elastic Actuators for Legged Robots. Proceedings of SPIE - The International Society for Optical Engineering, Orlando, FL, Unitedstates, 2004:135~144
30 G. A. Pratt, M. M. Williamson. Series Elastic Actuators. IEEE International Conference on Intelligent Robots and Systems, Pittsburgh, PA, USA, 1995:399~406
31 D. G. E. Hobbelen, M. Wisse. Swing-Leg Retraction for Limit Cycle Walkers Improves Disturbance Rejection. IEEE Transactions on Robotics. 2008,24(2):377~389
32 D. W. Robinson, J. E. Pratt, D. J. Paluska, G. A. Pratt. Series Elastic Actuator Development for a Biomimetic Walking Robot. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM. 1999:561~568
33 J. E. Pratt, G. A. Pratt. Exploiting Natural Dynamics in the Control of a Three-Dimensional Bipedal Walking Simulation. Proceedings of the 2nd International Conference on Climbing and Walking Robots, Clawar 99, 1999:797~807
34 D. Hobbelen, T. De Boer, M. Wisse. System Overview of Bipedal Robots Flame and Tulip: Tailor-Made for Limit Cycle Walking. 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, Nice, France, 2008:2486~2491
35 D. G. E. Hobbelen, M. Wisse. Ankle Actuation for Limit Cycle Walkers. International Journal of Robotics Research. 2008,27(6):709~735
36 M. Wisse, D. G. E. Hobbelen, R. J. J. Rotteveel, S. O. Anderson, G. J. Zeglin. Ankle Springs Instead of Arc-Shaped Feet for Passive Dynamic Walkers. Proceedings of the 2006 6th IEEE-RAS International Conference on Humanoid Robots, HUMANOIDS, Genoa, Italy, 2006:110~116
37 D. G. E. Hobbelen, M. Wisse. Controlling the Walking Speed in Limit Cycle Walking. International Journal of Robotics Research. 2008,27(9):989~1005
38 T. Geng, B. Porr, F. Worgotter. Fast Biped Walking with a Sensor-Driven Neuronal Controller and Real-Time Online Learning. International Journal of Robotics Research. 2006,25(3):243~259
39 J. Morimoto, G. Zeglin, C. G. Atkeson. Minimax Differential Dynamic Programming: Application to a Biped Walking Robot. 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, October 27, 2003 - October 31, 2003, Las Vegas, NV, United states, 2003:1927~1932
40 S. O. Anderson, M. Wisse, C. G. Atkeson, J. K. Hodgins, G. J. Zeglin, B. Moyer. Powered Bipeds Based on Passive Dynamic Principles. 2005 5th IEEE-RAS International Conference on Humanoid Robots, December 5, 2005 - December 7, 2005, Tsukuba, Japan, 2005:110~116
41宫明明,朱卫斌.被动动力步行机器人关键问题研究.机械工程师. 2006,(08):106~108
42王勇,杨杰.基于被动动力式的两足机器人研究现状.机械工程师. 2005,(06):31~33
43毛勇,王家廞 ,贾培发,韩灼.双足被动步行研究综述.机器人. 2007,29(3):274~280
44 Y. Mao, J. Wang, P. Jia, S. Li, Z. Qiu, L. Zhang, Z. Han. A Reinforcement Learning Based Dynamic Walking Control. 2007 IEEE International Conference on Robotics and Automation, Rome, Italy, 2007:3609~3614
45李立国,赵明国,张乃尧.平面双足机器人虚拟斜坡行走步态生成算法研究.机器人. 2009,31(1):77~81
46毛勇,王家廞,贾培发,柳宁,杨泽红,宋亦旭.半被动双足机器人的机械参数优化设计.中南大学学报(自然科学版). 2007,38(增刊1):473~477
47 Y. Huang, Q. Wang, G. Xie, L. Wang. Optimal Mass Distribution for a Passive Dynamic Biped with Upper Body Considering Speed, Efficiency and Stability. 2008 8th IEEE-RAS International Conference on Humanoid Robots, Daejeon, Korea, Republic of, 2008:515~520
48 Q. Wang, Y. Huang, L. Wang. Passive Dynamic Walking with Flat Feet and Ankle Compliance. Robotica. 2010,28:413~425
49 Q. Wang, L. Wang. Ground Contact Angle in Bipedal Locomotion Towards Passive Dynamic Walking and Running. 2007 American Control Conference, New York, NY, United states, 2007:2855~2860
50 X. Yang, Q. Wang, G. Xie, L. Wang. Fuzzy Logic Based Body State Estimation in a Bipedal Robot with Passive Dynamic Gaits. 2007 7th IEEE-RAS International Conference on Humanoid Robots, Pittsburgh, PA, United states, 2008:336~340
51黄岩,谢广明,杨晓华,王启宁,王龙.半被动双足机器人动态行走的位姿估算.北京大学学报(自然科学版). 2009,45(4):565~571
52 W. Qining, W. Long, H. Yan, Z. Jinying, C. Wei. Three-Dimensional Quasi-Passive Dynamic Bipedal Walking with Flat Feet and Compliant Ankles.
48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, 2009:8200~8205
53 N. Liu, J. F. Li, T. S. Wang. The Effects of Parameter Variation on the Basins of Attraction of Passive Walking Models. IEEE International Conference on Mechatronics and Automation, Harbin, PEOPLES R CHINA, 2007:1908~1913
54柳宁,李俊峰,王天舒.用胞胞映射计算被动行走模型不动点的吸引盆.工程力学. 2008,25(10):218~223
55柳宁,李俊峰,王天舒.简单被动行走模型仿真及不动点的吸引盆计算.力学与实践. 2008,30(1):18~22
56柳宁,李俊峰,王天舒.双足模型步行中的倍周期步态和混沌步态现象.物理学报. 2009,58(6):3772~3779
57付成龙,黄元林,王健美,陈恳.半被动双足机器人的准开环控制.机器人. 2009,31(2):110~117
58 L. Liu, Y. Tian, X. Huang. A Method to Estimate the Basin of Attraction of the System with Impulse Effects: Application to the Biped Robots. 1st International Conference on Intelligent Robotics and Applications, ICIRA 2008, Wuhan, China, 2008:953~962
59 Z. Liu, Y. Tian. Some Control Strategy on the Compass Gait Biped. IMACS Multiconference on "Computational Engineering in Systems Applications", CESA, Beijing, China, 2006:1712~1718
60 Z. Liu, Y. Tian, P. Zhang, C. Zhou. The Analysis on Bifurcation and Chaos in the Compass-Gait Biped. 2007 IEEE International Conference on Robotics and Biomimetics, ROBIO, Yalong Bay, Sanya, China, 2008:972~977
61 Z. Liu, C. Zhou, P. Zhang, Y. Tian. Anti-Phase Synchronization Control Scheme of Passive Biped Robot. Robotic Welding, Intelligence and Automation, 2007:529~539
62 P. Zhang, Y. Tian, Z. Liu. Bisection Method for Evaluation of Attraction Region of Passive Dynamic Walking. ICARA 2009 - Proceedings of the 4th International Conference on Autonomous Robots and Agents, Wellington, New zealand, 2009:692~697
63 P. Zhang, C. Zhou, L. Zhang, Y. Tian, Z. Liu. Adaptive Compliant Control of Humanoid Biped Foot with Elastic Energy Storage. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM, Singapore, Singapore, 2009:928~933
64刘振泽,田彦涛,张佩杰,周长久.无动力双足步行机器人控制策略与算法.控制理论与应用. 2009,26(2):113~121
65刘振泽,周长久,田彦涛. Compass-Like无动力双足行走机器人的运动状态.吉林大学学报(工学版). 2007,37(5):1175~1180
66张佩杰,张冬梅,田彦涛,刘振泽.欠驱动双足步行机器人动力学建模与稳定性分析.北京工业大学学报. 2009,35(2):258~263
67刘振泽.欠驱动步行机器人运动学机理与控制策略研究.吉林大学博士论文. 2007:1~142
68张冬梅.欠驱动步行机器人建模与分域控制算法的研究.吉林大学硕士论文.2008:1~56
69夏旭峰,葛文杰.仿生机器人运动稳定性的研究进展.机床与液压. 2007,35(2):229~234
70 D. G. E. Hobbelen, M. Wisse. A Disturbance Rejection Measure for Limit Cycle Walkers: The Gait Sensitivity Norm. IEEE Transactions on Robotics. 2007,23(6):1213~1224
71 Y. Hurmuzlu, G. D. Moskowitz. The Role of Impact in the Stability of Bipedal Locomotion. International Journal of Dynamics and Stability of Systems. 1986,1(3):217~234
72 M. Garcia, A. Chatterjee, A. Ruina. Efficiency, Speed, and Scaling of Two-Dimensional Passive-Dynamic Walking. Dynamics and Stability of Systems. 2000,15(2):75~99
73 A. Goswami, B. Espiau, A. Keramane. Limit Cycles in a Passive Compass Gait Biped and Passivity-Mimicking Control Laws. Autonomous Robots. 1997,4(3):273~286
74 M. Garcia, A. Chatterjee, A. Ruina, M. Coleman. The Simplest Walking Model: Stability, Complexity, and Scaling. Journal of Biomechanical Engineering, Transactions of the ASME. 1998,120(2):281~288
75 A. Goswami, B. Espiau, A. Keramane. Limit Cycles and Their Stability in a Passive Bipedal Gait. IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, 1996:246~251
76 B. Thuilot, A. Goswami, B. Espiau. Bifurcation and Chaos in a Simple Passive Bipedal Gait. IEEE International Conference on Robotics and Automation, Albuquerque, NM, USA, 1997:792~798
77 A. Goswami, B. Thuilot, B. Espiau. A Study of the Passive Gait of a Compass-Like Biped Robot: Symmetry and Chaos. Int J Robot Res. 1998,17(12):1282~1301
78 K. Osuka, K. Kirihara. Motion Analysis and Experiments of Passive Walking Robot Quartet Ii. Proceedings - IEEE International Conference on Robotics and Automation, San Francisco, CA, USA, 2000:3052~3056
79 Y. Sugimoto, K. Osuka. Stability Analysis of Passive-Dynamic-Walking Focusing on the Inner Structure of Poincare Map. 2005 International Conference on Advanced Robotics, ICAR '05, Proceedings, Seattle, WA, United States, 2005:236~241
80 K. Osuka, Y. Sugimoto. Stabilization of Quasi-Passive-Dynamic-Walking Based on Delayed Feedback Control. Proceedings of the 7th International Conference on Control, Automation, Robotics and Vision, ICARCV 2002, Singapore,Singapore, 2002:803~808
81 Y. Sugimoto, K. Osuka. Walking Control of Quasi Passive Dynamic Walking Robot "Quartet Iii" Based on Continuous Delayed Feedback Control. Proceedings - 2004 IEEE International Conference on Robotics and Biomimetics, IEEE ROBIO 2004, Shenyang, China, 2004:606~611
82 M. Iribe, K. Osuka. Analysis and Stabilization of the Passive Walking Robot Via Analogy with the Phase Locked Loop Circuits. 2006 6th IEEE-RAS International Conference on Humanoid Robots, HUMANOIDS, December 4, 2006 - December 6, 2006, Genoa, Italy, 2006:548~553
83 Z. Liu, Y. Tian, C. Zhou. Controlled Anti-Phase Synchronization of Passive Gait. 2006 IEEE International Conference on Robotics and Biomimetics, ROBIO 2006, December 17, 2006 - December 20, 2006, Kunming, China, 2006:755~760
84 J. Pratt, C. M. Chew, A. Torres, P. Dilworth, G. Pratt. Virtual Model Control: An Intuitive Approach for Bipedal Locomotion. Int J Robot Res. 2001,20(2):129~143
85 Y. Ikemata, A. Sano, H. Fujimoto. A Physical Principle of Gait Generation and Its Stabilization Derived from Mechanism of Fixed Point. 2006 IEEE International Conference on Robotics and Automation, ICRA 2006, Orlando, FL, United States, 2006:836~841
86 D. G. E. Hobbelen, M. Wisse. Ankle Joints and Flat Feet in Dynamic Walking. Proceedings of the 7th International Conference CLAWAR 2004, Rome, Italy, 2004:787~800
87 M. Wisse, C. G. Atkeson, D. K. Kloimwieder. Dynamic Stability of a Simple Biped Walking System with Swing Leg Retraction. Fast Motions in Biomechanics and Robotics: Optimization and Feedback Control. 2006,340:427~443
88 C. E. Bauby, A. D. Kuo. Active Control of Lateral Balance in Human Walking. J Biomech. 2000,33(11):1433~1440
89 D. G. E. Hobbelen, M. Wisse. Active Lateral Foot Placement for 3d Stabilization of a Limit Cycle Walker Prototype. International Journal of Humanoid Robotics. 2009,6(1):93~116
90 A. Silder, B. Whittington, B. Heiderscheit, D. G. Thelen. Identification of Passive Elastic Joint Moment-Angle Relationships in the Lower Extremity. J Biomech. 2007,40(12):2628~2635
91 J. Morimoto, J. Nakanishi, G. Endo, G. Cheng, C. G. Atkeson, G. Zeglin. Poincare-Map-Based Reinforcement Learning for Biped Walking. 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain,2005:2381~2386
92 E. Schuitema, D. G. E. Hobbelen, P. P. Jonker, M. Wisse, J. G. D. Karssen. Using a Controller Based on Reinforcement Learning for a Passive Dynamic Walking Robot. Proceedings of 2005 5th IEEE-RAS International Conference on Humanoid Robots, Tsukuba, Japan, 2005:232~237
93毛勇,李实,贾培发,杨泽红,丘振.基于再励学习的被动动态步行机器人.清华大学学报(自然科学版). 2008,48(1):92~96
94 B. Whittington, A. Silder, B. Heiderscheit, D. G. Thelen. The Contribution of Passive-Elastic Mechanisms to Lower Extremity Joint Kinetics During Human Walking. Gait & Posture. 2008,27(4):628~634
95李宏凯,孙久荣,戴振东.动物运动指令的中枢模式发生器对机器人运动控制的启示.机器人. 2008,30(3):279~288
96张龙,刘颖,孟惚之,王田苗.基于labview的舵机驱动爬壁机器人cpg神经网络运动控制的实现研究.机器人. 2009,31(3):254~261
97郑浩峻,张秀丽,李铁民,段广洪.基于cpg原理的机器人运动控制方法基于cpg原理的机器人运动控制方法.高技术通讯. 2003,(7):64~68
98 G. Endo, J. Morimoto, J. Nakanishi, G. Cheng. An Empirical Exploration of a Neural Oscillator for Biped Locomotion Control. Proceedings- 2004 IEEE International Conference on Robotics and Automation, New Orleans, LA, United states, 2004:3036~3042
99 M. W. Spong, G. Bhatia. Further Results on Control of the Compass Gait Biped. 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, NV, United states, 2003:1933~1938
100 M. W. Spong, F. Bullo. Controlled Symmetries and Passive Walking. IEEE Transactions on Automatic Control. 2005,50(7):1025~1031
101 M. W. Spong, J. K. Holm, D. Lee. Passivity - Based Control of Bipedal Locomotion. IEEE Robotics and Automation Magazine. 2007,14(2):30~40
102 M. Yamakita, F. Asano. Extended Passive Velocity Field Control with Variable Velocity Fields for a Kneed Biped. Advanced Robotics. 2001,15(2):139~168
103 F. Asano, M. Hashimoto, N. Kamamichi, M. Yamakita. Extended Virtual Passive Dynamic Walking and Virtual Passivity-Mimicking Control Laws. 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea, Republic of, 2001:3139~3144
104 F. Asano, M. Yamakita, K. Furuta. Virtual Passive Dynamic Walking and Energy-Based Control Laws. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems, Takamatsu, Japan, 2000:1149~1154
105 F. Asano, M. Yamakita, N. Kamamichi, Z. W. Luo. A Novel Gait Generation for Biped Walking Robots Based on Mechanical Energy Constraint. IEEE Transactions on Robotics and Automation. 2004,20(3):565~573
106 J. Hass, J. M. Herrmann, T. Geisel. Optimal Mass Distribution for Passivity-Based Bipedal Robots. International Journal of Robotics Research. 2006,25(11):1087~1098
107刘恒,陈绍汀.非线性系统全局动态特性分析的pcm法及其在转子轴承系统中的应用.应用力学学报. 1995,12(3):7~16
108熊光楞,李伯虎,柴旭东.虚拟样机技术.系统仿真学报. 2001,13(1):114~117
109 J.-H. Yoo, M. S. Nixon, C. J. Harris. Model-Driven Statistical Analysis of Human Gait Motion. International Conference on Image Processing Rochester, NY, United states, 2002:I/285~I/288
110 C. A. Oatis. The Use of a Mechanical Model to Describe the Stiffness and Damping Characteristics of the Knee Joint in Healthy Adults. Physical Therapy. 1993,73(11):740~749
111刘信安,王宗笠,蒋启华,肖维平,张环.胞映射基本理论与算法实现.计算机与应用化学. 2000,17(5):427~435
112 D. A. Winter. The Biomechanics and Motor Control of Human Movement. 2nd ed. John Wiley & Sons, 1990
113苏学敏,赵明国,张楫,董浩.被动行走周期性步态不动点搜索的新算法.清华大学学报(自然科学版). 2009,49(8):1109~1112
114李洁. Bp网络的算法及在matlab上的程序仿真.西安航空技术高等专科学校学报. 2009,27(1):41~43
115 R. Hecht-Nielsen. Theory of the Backpropagation Neural Network. IJCNN International Joint Conference on Neural Networks, Washington, DC, USA, 1989:593~605
116陈锦言,姚芳莲,孙经武,许涌深,邓联东,周志莲.人工神经网络及其在化学领域中的应用.高技术通讯. 1999,16(2):111~115
117郭亮,王鹏,赵英.基于bp神经网络的松花江四方台水质预测.哈尔滨工业大学学报. 2009,41(6):62~66
118王小平,曹立明.遗传算法——理论、应用与软件实现.西安交通大学出版社, 2002:4~13
119柳贺,黄猛,柳桂国,黄道.基于混沌搜索和模式搜索的混合优化方法.华东理工大学学报(自然科学版). 2008,34(1):126~130
120陈炳瑞,冯夏庭,丁秀丽,徐平.基于模式–遗传–神经网络的流变参数反演.岩石力学与工程学报. 2005,24(4):554~556
121王健美,付成龙,陈恳,黄元林.正弦驱动与传感反馈结合的双足机器人仿生行走控制.机器人. 2009,31(6):599~604
2 Y. Sakagami, R. Watanabe, C. Aoyama, S. Matsunaga, N. Higaki, K. Fujimura. The Intelligent Asimo: System Overview and Integration. 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, 2002:2478~2483
3 M. Vukobratovic, B. Borovac. Zero-Moment Point-Thirty Five Years of Its Life. Int J Hum Robot. 2004,1(1):157~173
4毛勇.半被动双足机器人的设计与再励学习控制.清华大学博士论文. 2007:2
5 S. Collins, A. Ruina, R. Tedrake, M. Wisse. Efficient Bipedal Robots Based on Passive-Dynamic Walkers. Science. 2005,307(5712):1082~1085
6张秀丽,郑浩峻.机器人仿生学研究综述.机器人. 2002,24(2):188~192
7柳宁.双足被动行走器动力学仿真与实验研究.清华大学博士论文. 2009:3,82,67~68
8 R. M. Alexander. Walking Made Simple. Science. 2005,308(5718):58~59
9 R. Pfeifer, M. Lungarella, F. Iida. Self-Organization, Embodiment, and Biologically Inspired Robotics. Science. 2007,318(5853):1088~1093
10 M. Srinivasan, A. Ruina. Computer Optimization of a Minimal Biped Model Discovers Walking and Running. Nature. 2006,439(7072):72~75
11张更林,金宝士,张宇光.人体下肢假肢发展概况.佳木斯大学学报(自然科学版). 2002,20(03):336~342
12 T. McGeer. Passive Walking with Knees. Proceedings of the 1990 IEEE International Conference on Robotics and Automation, Cincinnati, OH, USA, 1990:1640~1645
13 T. McGeer. Passive Dynamic Walking. International Journal of Robotics Research. 1990,9(2):62~82
14 T. McGeer. Passive Dynamic Biped Catalogue. The 2nd International Symposium on Experimental Robotics II, Springer-Verlag, 1991:465~490
15 S. Mochon, T. A. McMahon. Ballistic Walking: An Improved Model. Mathematical Biosciences. 1980,52(3-4):241~260
16 J. V. Basmajian, Tuttle. Emg of Locomotion in Gorilla and Man. Plenum Press, 1973
17 M. Wisse, J. van Frankenhuyzen. Design and Construction of Mike; a 2-DAutonomous Biped Based on Passive Dynamic Walking. International Symposium on Adaptive Motion of Animals and Machines (AMAM), Kyoto, JAPAN, 2003:143~154
18 N. Liu, J. F. Li, T. S. Wang. Passive Walker That Can Walk Down Steps: Simulations and Experiments. Acta Mechanica Sinica. 2008,24(5):569~573
19 A. L. Schwab, M. Wisse. Basin of Attraction of the Simplest Walking Model. Proceedings of the ASME Design Engineering Technical Conference, Pittsburgh, PA, United States, 2001:531~539
20 R. Tedrake, T. W. Zhang, M.-F. Fong, H. S. Seung. Actuating a Simple 3d Passive Dynamic Walker. 2004 IEEE International Conference on Robotics and Automation New Orleans, LA, United States, 2004:4656~4661
21 R. Tedrake, T. W. Zhang, H. S. Seung. Stochastic Policy Gradient Reinforcement Learning on a Simple 3d Biped. 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Sendai, Japan, 2004:2849~2854
22 N. Liu, J. F. Li, T. S. Wang. The Effects of Parameter Variation on the Gaits of Passive Walking Models: Simulations and Experiments. Robotica. 2009,27:511~528
23 S. H. Collins, M. Wisse, A. Ruina. A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees. International Journal of Robotics Research. 2001,20(7):607~615
24 S. H. Collins, A. Ruina. A Bipedal Walking Robot with Efficient and Human-Like Gait. 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, 2005:1983~1988
25 M. Wisse, A. L. Schwab, R. Q. van der Linde, F. C. T. van der Helm. How to Keep from Falling Forward: Elementary Swing Leg Action for Passive Dynamic Walkers. Ieee Transactions on Robotics. 2005,21(3):393~401
26 M. Wisse, D. G. E. Hobbelen, A. L. Schwab. Adding an Upper Body to Passive Dynamic Walking Robots by Means of a Bisecting Hip Mechanism. Ieee Transactions on Robotics. 2007,23(1):112~123
27 M. Wisse, G. Feliksdal, J. van Frankenhuyzen, B. Moyer. Passive-Based Walking Robot - Denise, a Simple, Efficient, and Lightweight Biped. Ieee Robot Autom Mag. 2007,14(2):52~62
28 M. Wisse, A. L. Schwab. Skateboards, Bicycles, and Three-Dimensional Biped Walking Machines: Velocity-Dependent Stability by Means of Lean-to-Yaw Coupling. International Journal of Robotics Research. 2005,24(6):417~429
29 J. E. Pratt, B. T. Krupp. Series Elastic Actuators for Legged Robots. Proceedings of SPIE - The International Society for Optical Engineering, Orlando, FL, Unitedstates, 2004:135~144
30 G. A. Pratt, M. M. Williamson. Series Elastic Actuators. IEEE International Conference on Intelligent Robots and Systems, Pittsburgh, PA, USA, 1995:399~406
31 D. G. E. Hobbelen, M. Wisse. Swing-Leg Retraction for Limit Cycle Walkers Improves Disturbance Rejection. IEEE Transactions on Robotics. 2008,24(2):377~389
32 D. W. Robinson, J. E. Pratt, D. J. Paluska, G. A. Pratt. Series Elastic Actuator Development for a Biomimetic Walking Robot. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM. 1999:561~568
33 J. E. Pratt, G. A. Pratt. Exploiting Natural Dynamics in the Control of a Three-Dimensional Bipedal Walking Simulation. Proceedings of the 2nd International Conference on Climbing and Walking Robots, Clawar 99, 1999:797~807
34 D. Hobbelen, T. De Boer, M. Wisse. System Overview of Bipedal Robots Flame and Tulip: Tailor-Made for Limit Cycle Walking. 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, Nice, France, 2008:2486~2491
35 D. G. E. Hobbelen, M. Wisse. Ankle Actuation for Limit Cycle Walkers. International Journal of Robotics Research. 2008,27(6):709~735
36 M. Wisse, D. G. E. Hobbelen, R. J. J. Rotteveel, S. O. Anderson, G. J. Zeglin. Ankle Springs Instead of Arc-Shaped Feet for Passive Dynamic Walkers. Proceedings of the 2006 6th IEEE-RAS International Conference on Humanoid Robots, HUMANOIDS, Genoa, Italy, 2006:110~116
37 D. G. E. Hobbelen, M. Wisse. Controlling the Walking Speed in Limit Cycle Walking. International Journal of Robotics Research. 2008,27(9):989~1005
38 T. Geng, B. Porr, F. Worgotter. Fast Biped Walking with a Sensor-Driven Neuronal Controller and Real-Time Online Learning. International Journal of Robotics Research. 2006,25(3):243~259
39 J. Morimoto, G. Zeglin, C. G. Atkeson. Minimax Differential Dynamic Programming: Application to a Biped Walking Robot. 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, October 27, 2003 - October 31, 2003, Las Vegas, NV, United states, 2003:1927~1932
40 S. O. Anderson, M. Wisse, C. G. Atkeson, J. K. Hodgins, G. J. Zeglin, B. Moyer. Powered Bipeds Based on Passive Dynamic Principles. 2005 5th IEEE-RAS International Conference on Humanoid Robots, December 5, 2005 - December 7, 2005, Tsukuba, Japan, 2005:110~116
41宫明明,朱卫斌.被动动力步行机器人关键问题研究.机械工程师. 2006,(08):106~108
42王勇,杨杰.基于被动动力式的两足机器人研究现状.机械工程师. 2005,(06):31~33
43毛勇,王家廞 ,贾培发,韩灼.双足被动步行研究综述.机器人. 2007,29(3):274~280
44 Y. Mao, J. Wang, P. Jia, S. Li, Z. Qiu, L. Zhang, Z. Han. A Reinforcement Learning Based Dynamic Walking Control. 2007 IEEE International Conference on Robotics and Automation, Rome, Italy, 2007:3609~3614
45李立国,赵明国,张乃尧.平面双足机器人虚拟斜坡行走步态生成算法研究.机器人. 2009,31(1):77~81
46毛勇,王家廞,贾培发,柳宁,杨泽红,宋亦旭.半被动双足机器人的机械参数优化设计.中南大学学报(自然科学版). 2007,38(增刊1):473~477
47 Y. Huang, Q. Wang, G. Xie, L. Wang. Optimal Mass Distribution for a Passive Dynamic Biped with Upper Body Considering Speed, Efficiency and Stability. 2008 8th IEEE-RAS International Conference on Humanoid Robots, Daejeon, Korea, Republic of, 2008:515~520
48 Q. Wang, Y. Huang, L. Wang. Passive Dynamic Walking with Flat Feet and Ankle Compliance. Robotica. 2010,28:413~425
49 Q. Wang, L. Wang. Ground Contact Angle in Bipedal Locomotion Towards Passive Dynamic Walking and Running. 2007 American Control Conference, New York, NY, United states, 2007:2855~2860
50 X. Yang, Q. Wang, G. Xie, L. Wang. Fuzzy Logic Based Body State Estimation in a Bipedal Robot with Passive Dynamic Gaits. 2007 7th IEEE-RAS International Conference on Humanoid Robots, Pittsburgh, PA, United states, 2008:336~340
51黄岩,谢广明,杨晓华,王启宁,王龙.半被动双足机器人动态行走的位姿估算.北京大学学报(自然科学版). 2009,45(4):565~571
52 W. Qining, W. Long, H. Yan, Z. Jinying, C. Wei. Three-Dimensional Quasi-Passive Dynamic Bipedal Walking with Flat Feet and Compliant Ankles.
48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, 2009:8200~8205
53 N. Liu, J. F. Li, T. S. Wang. The Effects of Parameter Variation on the Basins of Attraction of Passive Walking Models. IEEE International Conference on Mechatronics and Automation, Harbin, PEOPLES R CHINA, 2007:1908~1913
54柳宁,李俊峰,王天舒.用胞胞映射计算被动行走模型不动点的吸引盆.工程力学. 2008,25(10):218~223
55柳宁,李俊峰,王天舒.简单被动行走模型仿真及不动点的吸引盆计算.力学与实践. 2008,30(1):18~22
56柳宁,李俊峰,王天舒.双足模型步行中的倍周期步态和混沌步态现象.物理学报. 2009,58(6):3772~3779
57付成龙,黄元林,王健美,陈恳.半被动双足机器人的准开环控制.机器人. 2009,31(2):110~117
58 L. Liu, Y. Tian, X. Huang. A Method to Estimate the Basin of Attraction of the System with Impulse Effects: Application to the Biped Robots. 1st International Conference on Intelligent Robotics and Applications, ICIRA 2008, Wuhan, China, 2008:953~962
59 Z. Liu, Y. Tian. Some Control Strategy on the Compass Gait Biped. IMACS Multiconference on "Computational Engineering in Systems Applications", CESA, Beijing, China, 2006:1712~1718
60 Z. Liu, Y. Tian, P. Zhang, C. Zhou. The Analysis on Bifurcation and Chaos in the Compass-Gait Biped. 2007 IEEE International Conference on Robotics and Biomimetics, ROBIO, Yalong Bay, Sanya, China, 2008:972~977
61 Z. Liu, C. Zhou, P. Zhang, Y. Tian. Anti-Phase Synchronization Control Scheme of Passive Biped Robot. Robotic Welding, Intelligence and Automation, 2007:529~539
62 P. Zhang, Y. Tian, Z. Liu. Bisection Method for Evaluation of Attraction Region of Passive Dynamic Walking. ICARA 2009 - Proceedings of the 4th International Conference on Autonomous Robots and Agents, Wellington, New zealand, 2009:692~697
63 P. Zhang, C. Zhou, L. Zhang, Y. Tian, Z. Liu. Adaptive Compliant Control of Humanoid Biped Foot with Elastic Energy Storage. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM, Singapore, Singapore, 2009:928~933
64刘振泽,田彦涛,张佩杰,周长久.无动力双足步行机器人控制策略与算法.控制理论与应用. 2009,26(2):113~121
65刘振泽,周长久,田彦涛. Compass-Like无动力双足行走机器人的运动状态.吉林大学学报(工学版). 2007,37(5):1175~1180
66张佩杰,张冬梅,田彦涛,刘振泽.欠驱动双足步行机器人动力学建模与稳定性分析.北京工业大学学报. 2009,35(2):258~263
67刘振泽.欠驱动步行机器人运动学机理与控制策略研究.吉林大学博士论文. 2007:1~142
68张冬梅.欠驱动步行机器人建模与分域控制算法的研究.吉林大学硕士论文.2008:1~56
69夏旭峰,葛文杰.仿生机器人运动稳定性的研究进展.机床与液压. 2007,35(2):229~234
70 D. G. E. Hobbelen, M. Wisse. A Disturbance Rejection Measure for Limit Cycle Walkers: The Gait Sensitivity Norm. IEEE Transactions on Robotics. 2007,23(6):1213~1224
71 Y. Hurmuzlu, G. D. Moskowitz. The Role of Impact in the Stability of Bipedal Locomotion. International Journal of Dynamics and Stability of Systems. 1986,1(3):217~234
72 M. Garcia, A. Chatterjee, A. Ruina. Efficiency, Speed, and Scaling of Two-Dimensional Passive-Dynamic Walking. Dynamics and Stability of Systems. 2000,15(2):75~99
73 A. Goswami, B. Espiau, A. Keramane. Limit Cycles in a Passive Compass Gait Biped and Passivity-Mimicking Control Laws. Autonomous Robots. 1997,4(3):273~286
74 M. Garcia, A. Chatterjee, A. Ruina, M. Coleman. The Simplest Walking Model: Stability, Complexity, and Scaling. Journal of Biomechanical Engineering, Transactions of the ASME. 1998,120(2):281~288
75 A. Goswami, B. Espiau, A. Keramane. Limit Cycles and Their Stability in a Passive Bipedal Gait. IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, 1996:246~251
76 B. Thuilot, A. Goswami, B. Espiau. Bifurcation and Chaos in a Simple Passive Bipedal Gait. IEEE International Conference on Robotics and Automation, Albuquerque, NM, USA, 1997:792~798
77 A. Goswami, B. Thuilot, B. Espiau. A Study of the Passive Gait of a Compass-Like Biped Robot: Symmetry and Chaos. Int J Robot Res. 1998,17(12):1282~1301
78 K. Osuka, K. Kirihara. Motion Analysis and Experiments of Passive Walking Robot Quartet Ii. Proceedings - IEEE International Conference on Robotics and Automation, San Francisco, CA, USA, 2000:3052~3056
79 Y. Sugimoto, K. Osuka. Stability Analysis of Passive-Dynamic-Walking Focusing on the Inner Structure of Poincare Map. 2005 International Conference on Advanced Robotics, ICAR '05, Proceedings, Seattle, WA, United States, 2005:236~241
80 K. Osuka, Y. Sugimoto. Stabilization of Quasi-Passive-Dynamic-Walking Based on Delayed Feedback Control. Proceedings of the 7th International Conference on Control, Automation, Robotics and Vision, ICARCV 2002, Singapore,Singapore, 2002:803~808
81 Y. Sugimoto, K. Osuka. Walking Control of Quasi Passive Dynamic Walking Robot "Quartet Iii" Based on Continuous Delayed Feedback Control. Proceedings - 2004 IEEE International Conference on Robotics and Biomimetics, IEEE ROBIO 2004, Shenyang, China, 2004:606~611
82 M. Iribe, K. Osuka. Analysis and Stabilization of the Passive Walking Robot Via Analogy with the Phase Locked Loop Circuits. 2006 6th IEEE-RAS International Conference on Humanoid Robots, HUMANOIDS, December 4, 2006 - December 6, 2006, Genoa, Italy, 2006:548~553
83 Z. Liu, Y. Tian, C. Zhou. Controlled Anti-Phase Synchronization of Passive Gait. 2006 IEEE International Conference on Robotics and Biomimetics, ROBIO 2006, December 17, 2006 - December 20, 2006, Kunming, China, 2006:755~760
84 J. Pratt, C. M. Chew, A. Torres, P. Dilworth, G. Pratt. Virtual Model Control: An Intuitive Approach for Bipedal Locomotion. Int J Robot Res. 2001,20(2):129~143
85 Y. Ikemata, A. Sano, H. Fujimoto. A Physical Principle of Gait Generation and Its Stabilization Derived from Mechanism of Fixed Point. 2006 IEEE International Conference on Robotics and Automation, ICRA 2006, Orlando, FL, United States, 2006:836~841
86 D. G. E. Hobbelen, M. Wisse. Ankle Joints and Flat Feet in Dynamic Walking. Proceedings of the 7th International Conference CLAWAR 2004, Rome, Italy, 2004:787~800
87 M. Wisse, C. G. Atkeson, D. K. Kloimwieder. Dynamic Stability of a Simple Biped Walking System with Swing Leg Retraction. Fast Motions in Biomechanics and Robotics: Optimization and Feedback Control. 2006,340:427~443
88 C. E. Bauby, A. D. Kuo. Active Control of Lateral Balance in Human Walking. J Biomech. 2000,33(11):1433~1440
89 D. G. E. Hobbelen, M. Wisse. Active Lateral Foot Placement for 3d Stabilization of a Limit Cycle Walker Prototype. International Journal of Humanoid Robotics. 2009,6(1):93~116
90 A. Silder, B. Whittington, B. Heiderscheit, D. G. Thelen. Identification of Passive Elastic Joint Moment-Angle Relationships in the Lower Extremity. J Biomech. 2007,40(12):2628~2635
91 J. Morimoto, J. Nakanishi, G. Endo, G. Cheng, C. G. Atkeson, G. Zeglin. Poincare-Map-Based Reinforcement Learning for Biped Walking. 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain,2005:2381~2386
92 E. Schuitema, D. G. E. Hobbelen, P. P. Jonker, M. Wisse, J. G. D. Karssen. Using a Controller Based on Reinforcement Learning for a Passive Dynamic Walking Robot. Proceedings of 2005 5th IEEE-RAS International Conference on Humanoid Robots, Tsukuba, Japan, 2005:232~237
93毛勇,李实,贾培发,杨泽红,丘振.基于再励学习的被动动态步行机器人.清华大学学报(自然科学版). 2008,48(1):92~96
94 B. Whittington, A. Silder, B. Heiderscheit, D. G. Thelen. The Contribution of Passive-Elastic Mechanisms to Lower Extremity Joint Kinetics During Human Walking. Gait & Posture. 2008,27(4):628~634
95李宏凯,孙久荣,戴振东.动物运动指令的中枢模式发生器对机器人运动控制的启示.机器人. 2008,30(3):279~288
96张龙,刘颖,孟惚之,王田苗.基于labview的舵机驱动爬壁机器人cpg神经网络运动控制的实现研究.机器人. 2009,31(3):254~261
97郑浩峻,张秀丽,李铁民,段广洪.基于cpg原理的机器人运动控制方法基于cpg原理的机器人运动控制方法.高技术通讯. 2003,(7):64~68
98 G. Endo, J. Morimoto, J. Nakanishi, G. Cheng. An Empirical Exploration of a Neural Oscillator for Biped Locomotion Control. Proceedings- 2004 IEEE International Conference on Robotics and Automation, New Orleans, LA, United states, 2004:3036~3042
99 M. W. Spong, G. Bhatia. Further Results on Control of the Compass Gait Biped. 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, NV, United states, 2003:1933~1938
100 M. W. Spong, F. Bullo. Controlled Symmetries and Passive Walking. IEEE Transactions on Automatic Control. 2005,50(7):1025~1031
101 M. W. Spong, J. K. Holm, D. Lee. Passivity - Based Control of Bipedal Locomotion. IEEE Robotics and Automation Magazine. 2007,14(2):30~40
102 M. Yamakita, F. Asano. Extended Passive Velocity Field Control with Variable Velocity Fields for a Kneed Biped. Advanced Robotics. 2001,15(2):139~168
103 F. Asano, M. Hashimoto, N. Kamamichi, M. Yamakita. Extended Virtual Passive Dynamic Walking and Virtual Passivity-Mimicking Control Laws. 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea, Republic of, 2001:3139~3144
104 F. Asano, M. Yamakita, K. Furuta. Virtual Passive Dynamic Walking and Energy-Based Control Laws. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems, Takamatsu, Japan, 2000:1149~1154
105 F. Asano, M. Yamakita, N. Kamamichi, Z. W. Luo. A Novel Gait Generation for Biped Walking Robots Based on Mechanical Energy Constraint. IEEE Transactions on Robotics and Automation. 2004,20(3):565~573
106 J. Hass, J. M. Herrmann, T. Geisel. Optimal Mass Distribution for Passivity-Based Bipedal Robots. International Journal of Robotics Research. 2006,25(11):1087~1098
107刘恒,陈绍汀.非线性系统全局动态特性分析的pcm法及其在转子轴承系统中的应用.应用力学学报. 1995,12(3):7~16
108熊光楞,李伯虎,柴旭东.虚拟样机技术.系统仿真学报. 2001,13(1):114~117
109 J.-H. Yoo, M. S. Nixon, C. J. Harris. Model-Driven Statistical Analysis of Human Gait Motion. International Conference on Image Processing Rochester, NY, United states, 2002:I/285~I/288
110 C. A. Oatis. The Use of a Mechanical Model to Describe the Stiffness and Damping Characteristics of the Knee Joint in Healthy Adults. Physical Therapy. 1993,73(11):740~749
111刘信安,王宗笠,蒋启华,肖维平,张环.胞映射基本理论与算法实现.计算机与应用化学. 2000,17(5):427~435
112 D. A. Winter. The Biomechanics and Motor Control of Human Movement. 2nd ed. John Wiley & Sons, 1990
113苏学敏,赵明国,张楫,董浩.被动行走周期性步态不动点搜索的新算法.清华大学学报(自然科学版). 2009,49(8):1109~1112
114李洁. Bp网络的算法及在matlab上的程序仿真.西安航空技术高等专科学校学报. 2009,27(1):41~43
115 R. Hecht-Nielsen. Theory of the Backpropagation Neural Network. IJCNN International Joint Conference on Neural Networks, Washington, DC, USA, 1989:593~605
116陈锦言,姚芳莲,孙经武,许涌深,邓联东,周志莲.人工神经网络及其在化学领域中的应用.高技术通讯. 1999,16(2):111~115
117郭亮,王鹏,赵英.基于bp神经网络的松花江四方台水质预测.哈尔滨工业大学学报. 2009,41(6):62~66
118王小平,曹立明.遗传算法——理论、应用与软件实现.西安交通大学出版社, 2002:4~13
119柳贺,黄猛,柳桂国,黄道.基于混沌搜索和模式搜索的混合优化方法.华东理工大学学报(自然科学版). 2008,34(1):126~130
120陈炳瑞,冯夏庭,丁秀丽,徐平.基于模式–遗传–神经网络的流变参数反演.岩石力学与工程学报. 2005,24(4):554~556
121王健美,付成龙,陈恳,黄元林.正弦驱动与传感反馈结合的双足机器人仿生行走控制.机器人. 2009,31(6):599~604