伸缩腿双足机器人半被动行走控制研究
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摘要
研究半被动伸缩腿双足机器人行走控制和周期解的全局稳定性问题.使用杆长可变的倒立摆机器人模型,以支撑腿的伸缩作为行走动力源,采用庞加莱映射方法分析了双足机器人行走的不动点及其稳定性.当脚与地面冲击时,假设两腿间的夹角保持为常数,设计了腿伸缩长度的支撑腿角度反馈控制率.证明了伸缩腿双足机器人行走过程不动点的全局稳定性.仿真结果表明,本文提出的腿伸缩长度反馈控制可以实现伸缩腿双足机器人在水平面上的稳定行走,并且周期步态对执行器干扰和支撑腿初始角速度干扰具有鲁棒性.
In this paper,the global stability of periodic solutions and walking control of a semi-passive biped robot with telescopic legs are studied. An inverted pendulum with variable length is used as the robot model,and the biped robot is powered by elongating and shortening the stance leg. The fixed point and its stability of the biped robot walking are discussed based on Poincaré map. With the assumption that the angle between two legs keeps constant,when the swing leg impacts with ground at heel-strike,the control law of telescopic length of the stance leg is designed by feedback of the angle between stance leg and vertical line. Then,the global stability of the fixed point is proved for the biped robot walking with telescopic legs. The simulation results show that the proposed feedback control law can make the biped robot with telescopic legs walk stably on the level ground,and the cycle gait is robust to the various disturbances of the actuator and the disturbances of the initial angular velocity of stance leg.
In this paper,the global stability of periodic solutions and walking control of a semi-passive biped robot with telescopic legs are studied. An inverted pendulum with variable length is used as the robot model,and the biped robot is powered by elongating and shortening the stance leg. The fixed point and its stability of the biped robot walking are discussed based on Poincaré map. With the assumption that the angle between two legs keeps constant,when the swing leg impacts with ground at heel-strike,the control law of telescopic length of the stance leg is designed by feedback of the angle between stance leg and vertical line. Then,the global stability of the fixed point is proved for the biped robot walking with telescopic legs. The simulation results show that the proposed feedback control law can make the biped robot with telescopic legs walk stably on the level ground,and the cycle gait is robust to the various disturbances of the actuator and the disturbances of the initial angular velocity of stance leg.
引文
1 Collins S,Ruina A,Tedrake R,et al.Efficient bipedal robots based on passive-dynamic walkers.Science,2005,307(5712):1082~1085
2 McGeer T.Passive dynamic walking.International Journal of Robotics Research,1990,9(2):62~82
3 Wisse M,Schwab A L,Linde R Q,et al.How to keep from falling forward:Elementary swing leg action for passive dynamic walkers.IEEE Transactions on Robotics,2005,21(3):393~401
4 Kuo A D.Energetics of actively powered locomotion using the simplest walking model.Journal of Biomechanical Engineering,2002,123(1):264~269
5赵明国,董浩,张乃尧.双足机器人虚拟斜坡行走的抗扰能力研究.机器人,2010,32(6):773~786(Zhao MG,Dong H,Zhang N Y.On disturbance rejection of the bipedal robots in virtual slope walking.Robot,2010,32(6):773~786(in Chinese))
6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(Liu N,Li J F,Wang T S.Study of the basin of attraction of passive models by the aid of cell-to-cell mapping method.Engineering Mechanics,2008,25(10):218~223(in Chinese))
7倪修华,陈维山,刘军考等.弹簧刚度对被动步行的稳定性影响.力学学报,2010,42(3):541~547(Ni X H,Chen W S,Liu J K,et al.The Effect of spring stiffness on the stability of passive dynamic walking.Chinese Journal of Theoretical and Applied Mechanics,2010,42(3):541~547(in Chinese))
8 Wang Q N,Huang Y,Wang L.Passive dynamic walking with flat feet and ankle compliance.Robotica,2010,28(3):413~425
9付成龙,黄元林,王健美等.半被动双足机器人的准开环控制.机器人,2009,31(2):110~117(Fu C L,Huang Y L,Wang J M,et al.Quasi open-loop control for semi-passive biped robots.Robot,2009,31(2):110~117(in Chinese))
10张奇志,周亚丽.双足机器人半被动行走固定点全局稳定性分析.工程力学,2013,30(3):431~436(Zhang QZ,Zhou Y L.Global stability analysis for the fixed point of semi-passive biped robot walking.Engineering Mechanics,2013,30(3):431~436(in Chinese))
11张奇志,周亚丽,徐鑫鑫等.单电动机驱动的半被动双足机器人设计与实现.北京信息科技大学学报,2016,36(2):1~6(Zhang Q Z,Zhou Y L,Xu X X,et al.Design and realization of semi-passive biped robot driven by single motor.Journal of Beijing Information Science&Technology University,2016,36(2):1~6(in Chinese))
12田强,刘铖,李培等.多柔体系统动力学研究进展与挑战.动力学与控制学报,2017,15(5):385~405(Tian Q,Liu C,Li P,et al.Advances and challenges in dynamics of flexible multibody systems.Journal of Dynamics and Control,2017,15(5):385~405(in Chinese))
13田富洋,曹东,董小宁等.主被动关节柔性树形机器人系统动力学建模与仿真.动力学与控制学报,2017,15(1):59~67(Tian F Y,Cao D,Dong X N,et al.The dynamic modeling and simulation of flexible tree robots system with active-passive joint.Journal of Dynamics and Control,2017,15(1):59~67(in Chinese))
2 McGeer T.Passive dynamic walking.International Journal of Robotics Research,1990,9(2):62~82
3 Wisse M,Schwab A L,Linde R Q,et al.How to keep from falling forward:Elementary swing leg action for passive dynamic walkers.IEEE Transactions on Robotics,2005,21(3):393~401
4 Kuo A D.Energetics of actively powered locomotion using the simplest walking model.Journal of Biomechanical Engineering,2002,123(1):264~269
5赵明国,董浩,张乃尧.双足机器人虚拟斜坡行走的抗扰能力研究.机器人,2010,32(6):773~786(Zhao MG,Dong H,Zhang N Y.On disturbance rejection of the bipedal robots in virtual slope walking.Robot,2010,32(6):773~786(in Chinese))
6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(Liu N,Li J F,Wang T S.Study of the basin of attraction of passive models by the aid of cell-to-cell mapping method.Engineering Mechanics,2008,25(10):218~223(in Chinese))
7倪修华,陈维山,刘军考等.弹簧刚度对被动步行的稳定性影响.力学学报,2010,42(3):541~547(Ni X H,Chen W S,Liu J K,et al.The Effect of spring stiffness on the stability of passive dynamic walking.Chinese Journal of Theoretical and Applied Mechanics,2010,42(3):541~547(in Chinese))
8 Wang Q N,Huang Y,Wang L.Passive dynamic walking with flat feet and ankle compliance.Robotica,2010,28(3):413~425
9付成龙,黄元林,王健美等.半被动双足机器人的准开环控制.机器人,2009,31(2):110~117(Fu C L,Huang Y L,Wang J M,et al.Quasi open-loop control for semi-passive biped robots.Robot,2009,31(2):110~117(in Chinese))
10张奇志,周亚丽.双足机器人半被动行走固定点全局稳定性分析.工程力学,2013,30(3):431~436(Zhang QZ,Zhou Y L.Global stability analysis for the fixed point of semi-passive biped robot walking.Engineering Mechanics,2013,30(3):431~436(in Chinese))
11张奇志,周亚丽,徐鑫鑫等.单电动机驱动的半被动双足机器人设计与实现.北京信息科技大学学报,2016,36(2):1~6(Zhang Q Z,Zhou Y L,Xu X X,et al.Design and realization of semi-passive biped robot driven by single motor.Journal of Beijing Information Science&Technology University,2016,36(2):1~6(in Chinese))
12田强,刘铖,李培等.多柔体系统动力学研究进展与挑战.动力学与控制学报,2017,15(5):385~405(Tian Q,Liu C,Li P,et al.Advances and challenges in dynamics of flexible multibody systems.Journal of Dynamics and Control,2017,15(5):385~405(in Chinese))
13田富洋,曹东,董小宁等.主被动关节柔性树形机器人系统动力学建模与仿真.动力学与控制学报,2017,15(1):59~67(Tian F Y,Cao D,Dong X N,et al.The dynamic modeling and simulation of flexible tree robots system with active-passive joint.Journal of Dynamics and Control,2017,15(1):59~67(in Chinese))