无膝双足被动机器人的运动特性和稳定性研究
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摘要
双足被动机器人具有简单的结构、少量的控制、自然的步态和类似于人类步行的能量效率等优点,是机器人研究领域的一个崭新而重要的分支,近年来已成为研究的热点。当前被动机器人研究存在基础理论尚不完善、运动机理尚不明朗和行走稳定性差等问题。为了更准确地理解双足被动机器人运动的本质特征,加强模型研究对实际样机研制的指导作用,本文采用了Matlab数值仿真和Adams仿真验证的方法深入分析和研究了无边轮辐和无膝双足被动模型的运动特性及稳定性问题,并通过样机实验验证了仿真分析的结论。
首先,给出无边轮辐和无膝双足被动机器人的物理模型,分析了模型结构特征和运动特点。将其每步运动过程分为摆动和碰撞两个阶段,根据拉格朗日方程和角动量守恒方程准确建立这两个模型的动力学方程。
其次,利用Adams对被动无边轮辐进行动力学仿真,分析各参数,包括轮辐质心初速度、轮辐质量、辐条的足半径、辐条数、辐条长度、转动惯量和斜面坡度对无边轮辐稳定运动的影响;利用Matlab数值仿真和Adams仿真验证的方法,详细深入分析无膝双足被动机器人运动特性;根据庞加莱映射的原理,利用局部线性化的理论和Newton-Raphson迭代方程求解了双足被动机器人的稳定不动点,并描述了机器人运动过程中可能出现的周期分岔现象;同时结合无边轮辐和无膝双足模型的特点,在Adams中构建了带躯体无膝被动模型并分析了其运动特点。
然后,根据庞加莱映射原理,利用局部线性化方法,通过求出模型雅克比矩阵特征值的模对无膝双足被动模型局部稳定性进行了详细分析;根据胞映射的理论通过求解模型稳定吸引域的方法对双足被动模型全局稳定性进行分析,详细分析了各参数(腿质量、腿的质心位置、足半径、腿相对质心的转动惯量、腿长、斜面坡度和髋关节质量)对机器人行走稳定性的影响;同时分析各参数对被动机器人稳定运动形态(步长、步速和步态周期)的影响;并用Adams验证了通过提高髋关节质量和增加足半径能提高双足被动模型的稳定行走的鲁棒性。
最后,根据双足被动模型稳定性分析的结论,获得了被动模型一个优化后的参数组合,并以此研制了双足被动机器人样机;构建样机实验环境,根据数学中的概率理论,采用统计被动机器人样机成功行走路面次数的方法,验证了各参数(腿的质心位置、足半径和斜面坡度)对双足被动机器人运动稳定性的影响。
Passive biped robot has some advantages such as a simple structure, a small amount of control, natural gait and high energy efficiency similar to human walking, etc. It has become a new and important branch in the field of robot research and has become a hot spot in recent years. Currently, the research of passive robot has some problems such as the not perfect basic theory, unclear mechanism of movement and the poor stability of walking. In this paper, A depth-analysis has been performed by the means of Matlab numerical simulation and Adams simulation-verification in order to catch on the essential characteristics of passive biped robot more accurately and to enhance the conherence between the model and the actual prototype better, where the essential characteristics of passive biped robot are classified as: the motion characteristics and the walking stability of Ramless-wheel and the passive biped robot without knees. The conclusions of simulation analysis above were verified through the domenstration of actual prototype.
Firstly, two important physical models were put forward: Ramless-wheel and passive biped robot without knees. The structure characteristics and motion characteristics of models were analysed. The each step of the walking models was divided into two stages: swing movement process and collision process. According to Lagrange's equation and the equation of conservation of angular momentum, the dynamic equations of the two models were accurately established.
Secondly, The influences on ramless-wheel’s stable walking which closely related to the parameters such as initial velocity of ramless-wheel’s centroid, ramless-wheel’s quality, ramless-wheel’s foot radius, the number of spoke, spoke length, moment of inertia and slope gradient were analyzed by performing the Adams simulation. The fundamental property of the robot motion was analyzed through the method of Matlab simulation and Adams verification. According to the theories including the Poincare mapping, the local linear theory, and the Newton-Raphson iteration equation, the stable fixed point was calculated to describe the robot’s stable walking. The phenomenon of periodic bifurcations which would be possible arised during the stable walking was described. After that, according to the characteristics of ramless-wheel and biped model without knees, a passive model with upper body was constructed and analysed based on Adams.
Then, according to the principle of Poincare mapping, the local linear method was used to obtain eigenvalues of Jacobian matrix of the passive biped model. A detailed analysis of local stability of the passive biped model was done. Based on the cell mapping theory, a detailed analysis of global stability of the passive model was done by the means of calculating the model’s stable basin of attraction. A detailed analysis of impact of the various parameters (legs’quality, the mass center position of legs, foot radius, moment of inertia, leg’s length , slope gradient and hip quality) on the walking stability of the robot was given. At the same time, the impact of the parameters on the stable walking state (step length, walking speed and gait cycle) of the passive biped robot was analysed. Furthermore, based on the simulation of Adams, conclution was drawn as follow: the larger of hip quality and foot radius, the higher robustness of the passive robot.
Finally, the optimized group of parameters which contributes the passive robot to be more stable and much better walking gait in walking was established, according to the results of the sability analysis of the robot’s walking. Based on the the optimized group of parameters, an actual prototype was developed. In the experimentation, the stable motion of robot which influenced by the parameters (center position of leg’s mass, foot radius and slope gradient) was verified based on statistical method, that is, the memorization of the times for the successful walking.
首先,给出无边轮辐和无膝双足被动机器人的物理模型,分析了模型结构特征和运动特点。将其每步运动过程分为摆动和碰撞两个阶段,根据拉格朗日方程和角动量守恒方程准确建立这两个模型的动力学方程。
其次,利用Adams对被动无边轮辐进行动力学仿真,分析各参数,包括轮辐质心初速度、轮辐质量、辐条的足半径、辐条数、辐条长度、转动惯量和斜面坡度对无边轮辐稳定运动的影响;利用Matlab数值仿真和Adams仿真验证的方法,详细深入分析无膝双足被动机器人运动特性;根据庞加莱映射的原理,利用局部线性化的理论和Newton-Raphson迭代方程求解了双足被动机器人的稳定不动点,并描述了机器人运动过程中可能出现的周期分岔现象;同时结合无边轮辐和无膝双足模型的特点,在Adams中构建了带躯体无膝被动模型并分析了其运动特点。
然后,根据庞加莱映射原理,利用局部线性化方法,通过求出模型雅克比矩阵特征值的模对无膝双足被动模型局部稳定性进行了详细分析;根据胞映射的理论通过求解模型稳定吸引域的方法对双足被动模型全局稳定性进行分析,详细分析了各参数(腿质量、腿的质心位置、足半径、腿相对质心的转动惯量、腿长、斜面坡度和髋关节质量)对机器人行走稳定性的影响;同时分析各参数对被动机器人稳定运动形态(步长、步速和步态周期)的影响;并用Adams验证了通过提高髋关节质量和增加足半径能提高双足被动模型的稳定行走的鲁棒性。
最后,根据双足被动模型稳定性分析的结论,获得了被动模型一个优化后的参数组合,并以此研制了双足被动机器人样机;构建样机实验环境,根据数学中的概率理论,采用统计被动机器人样机成功行走路面次数的方法,验证了各参数(腿的质心位置、足半径和斜面坡度)对双足被动机器人运动稳定性的影响。
Passive biped robot has some advantages such as a simple structure, a small amount of control, natural gait and high energy efficiency similar to human walking, etc. It has become a new and important branch in the field of robot research and has become a hot spot in recent years. Currently, the research of passive robot has some problems such as the not perfect basic theory, unclear mechanism of movement and the poor stability of walking. In this paper, A depth-analysis has been performed by the means of Matlab numerical simulation and Adams simulation-verification in order to catch on the essential characteristics of passive biped robot more accurately and to enhance the conherence between the model and the actual prototype better, where the essential characteristics of passive biped robot are classified as: the motion characteristics and the walking stability of Ramless-wheel and the passive biped robot without knees. The conclusions of simulation analysis above were verified through the domenstration of actual prototype.
Firstly, two important physical models were put forward: Ramless-wheel and passive biped robot without knees. The structure characteristics and motion characteristics of models were analysed. The each step of the walking models was divided into two stages: swing movement process and collision process. According to Lagrange's equation and the equation of conservation of angular momentum, the dynamic equations of the two models were accurately established.
Secondly, The influences on ramless-wheel’s stable walking which closely related to the parameters such as initial velocity of ramless-wheel’s centroid, ramless-wheel’s quality, ramless-wheel’s foot radius, the number of spoke, spoke length, moment of inertia and slope gradient were analyzed by performing the Adams simulation. The fundamental property of the robot motion was analyzed through the method of Matlab simulation and Adams verification. According to the theories including the Poincare mapping, the local linear theory, and the Newton-Raphson iteration equation, the stable fixed point was calculated to describe the robot’s stable walking. The phenomenon of periodic bifurcations which would be possible arised during the stable walking was described. After that, according to the characteristics of ramless-wheel and biped model without knees, a passive model with upper body was constructed and analysed based on Adams.
Then, according to the principle of Poincare mapping, the local linear method was used to obtain eigenvalues of Jacobian matrix of the passive biped model. A detailed analysis of local stability of the passive biped model was done. Based on the cell mapping theory, a detailed analysis of global stability of the passive model was done by the means of calculating the model’s stable basin of attraction. A detailed analysis of impact of the various parameters (legs’quality, the mass center position of legs, foot radius, moment of inertia, leg’s length , slope gradient and hip quality) on the walking stability of the robot was given. At the same time, the impact of the parameters on the stable walking state (step length, walking speed and gait cycle) of the passive biped robot was analysed. Furthermore, based on the simulation of Adams, conclution was drawn as follow: the larger of hip quality and foot radius, the higher robustness of the passive robot.
Finally, the optimized group of parameters which contributes the passive robot to be more stable and much better walking gait in walking was established, according to the results of the sability analysis of the robot’s walking. Based on the the optimized group of parameters, an actual prototype was developed. In the experimentation, the stable motion of robot which influenced by the parameters (center position of leg’s mass, foot radius and slope gradient) was verified based on statistical method, that is, the memorization of the times for the successful walking.
引文
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2刘静,赵晓光,谭明.腿式机器人的研究综述.机器人.2006,(01):81~88
3 M.Wisse, A.L.Schwab, R.Q.VD.Linde. A 3D passive dynamic biped with yaw and roll compensation [J].Robotica, 2001, 19(3): 275~284.
4 T.Ishida. Development of a Small Biped Entertainment Robot QRID. Proceedings of the 2004 International Symposium on Micro-Nanomechatronics and Human Science [C]. New York, NY, USA :IEEE, 2004:23~28.
5 Sakagami Y, Watanabe R, Aoyama C, etal. The intelligent ASIMO: system overview and integration. Proceedings of the IEEE International Conference on Intelligent Robots and Systems. Piscataway, NJ, USA, 2002:2478~2483.
6 Hirai K, HiroseM, Haikawa Y, et al. Development of Honda humanoid robot. Proceedings of the IEEE International Conference on Robotics and Automation. Piscataway, NJ, USA, 1998:1321~1326.
7 Espian B, Sardain P. The anthropomorphic biped robot BIP2000[C]. Proceedings of the 2000 IEEE Conference on Robotics and Automation, San Francisco, CA:2000:3997~4002.
8 Huang Q, Yokoi K, Kajita S, et al. Planning walking pattems for a biped robot[J]. IEEE Transactions on Robotics and Automation.2001,17(3):280~289.
9 S. H. Collins, M. Wisse and A. Ruina. A two legged kneedpassive dynamic walking robot [J]. Int. J. Robotics Research 20 (2001), PP: 607~615.
10 R.H.Maskrey, W.J.Thayer. A brief history of electrobohydraulic servomechanisms[J]. in: ASME Journal of Dynamic Systems Measurement and Control, June 1978.
11 D.G.E. Hobbelen and M. Wisse, A disturbance rejection measure for limit cycle walkers: The gait sensitivity norm, IEEE Trans. Robot. 23 (2007), pp. 1213~1224.
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