欠驱动双足机器人的指数稳定周期行走
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摘要
步行机器人环境适应性强、结构复杂、运动控制难.本文研究了基于控制Lyapunov函数和混杂零动态控制的五关节欠驱动双足机器人RABBIT的指数稳定周期步态的行走方法.根据拉格朗日原理建立了机器人腿的混杂动力学模型,并对系统进行了输入/输出线性化处理.结合零动态的思想,构造了控制Lyapunov函数,设计了使混杂模型实现指数稳定的状态反馈控制器,利用限制Poincare的原理,证明了其周期轨道的指数稳定性.仿真结果验证该方法的有效性.
The biped robots have characteristics of strong environmental adaptability,complex structure and difficult motion control.This paper addresses the problem of exponential stable walking of a five-link under-actuated biped robot(RABBIT) through control Lyapunov function and hybrid zero dynamics.The walking system is input-output linearized after the full-order dynamic model is described with Lagrange dynamic equations.Based on hybrid zero dynamics,a state feedback controller is then utilized to realize exponential stability of periodic orbit by designing control Lyapunov function,which is proved to be exponentially stable by restricted Poincare Return Map.The effectiveness of the mentioned method is illustrated by simulations.
The biped robots have characteristics of strong environmental adaptability,complex structure and difficult motion control.This paper addresses the problem of exponential stable walking of a five-link under-actuated biped robot(RABBIT) through control Lyapunov function and hybrid zero dynamics.The walking system is input-output linearized after the full-order dynamic model is described with Lagrange dynamic equations.Based on hybrid zero dynamics,a state feedback controller is then utilized to realize exponential stability of periodic orbit by designing control Lyapunov function,which is proved to be exponentially stable by restricted Poincare Return Map.The effectiveness of the mentioned method is illustrated by simulations.
引文
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16 Chevallereau C,Grizzle J W,Ching-Long Shih J W.Asymptotically stable walking of a five-link underactuated 3-D bipedal robot.IEEE Trans Robot,2009,25:37-50
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22 Xing D P,Su J B.Arm/trunk motion generation for humanoid robot.Sci China Inf Sci,2010,53:1603-1612
23 Ames A D,Galloway K,Sreenath K,et al.Rapidly exponentially stabilizing control lyapunov functions and hybrid zero dynamics.IEEE Trans Automat Contr,2014,59:876-891
24 Jiang Z P,Wang Y.A converse Lyapunov theorem for discrete-time systems with disturbances.Syst Control Lett,2002,45:49-58
25 Zhang W,Abate A,Hu J,et al.Exponential stabilization of discrete-time switched linear systems.Automatica,2009,45:2526-2536
2 Xu T,Chen Q.Learning gait of quadruped robot without prior knowledge of the environment.Chin J Mech Eng,2012,25:1068-1074
3安康,陈启军.具有屈膝行为的双足被动行走模型.控制理论与应用,2013,30:346-354
4 Huang Q,Yokoi K,Kajita S,et al.Planning walking patterns for a biped robot.IEEE Trans Robot Automat,2001,17:280-289
5杜明晓,陈启军.基于场地模型的多机器人动态协作技术.华中科技大学学报(自然科学版),2015,1:84-87
6 Wang H,Zhang H,Chen Q.Gait generation and control of biped robot with moving torso based on virtual constraint.In:Proceedings of the IEEEInternational Conference on Systems,Man and Cybernetics.IEEE,2017.1435-1440
7 Gouaillier D,Hugel V,Blazevic P,et al.Mechatronic design of NAO humanoid.In:Proceedings of the IEEE International Conference on Robotics and Automation.IEEE,2009.769-774
8 Ding L.Key technology analysis of bigdog quadruped robot.JME,2015,51:1
9 Kuindersma S,Deits R,Fallon M,et al.Optimization-based locomotion planning,estimation,and control design for the atlas humanoid robot.Auton Robot,2016,40:429-455
10 Feng S,Xinjilefu X,Atkeson C G,et al.Optimization based controller design and implementation for the Atlas robot in the DARPA robotics challenge finals.In:Proceedings of the IEEE International Conference on Humanoid Robots.IEEE,2015.1028-1035
11刘莉,汪劲松,陈恳,等.THBIP-I拟人机器人研究进展.机器人,2002,24:262-267
12 Zhao M,Liu L,Wang J,et al.Control system design of THBIP-I humanoid robot.In:Proceedings of the IEEE International Conference on Robotics and Automation.IEEE,2002.2253-2258
13 Grizzle J W,Abba G,Plestan F.Asymptotically stable walking for biped robots:Analysis via systems with impulse effects.IEEE Trans Automat Contr,2001,46:51-64
14 Hodgins J K,Raibert M N.Adjusting step length for rough terrain locomotion.IEEE Trans Robot Automat,1991,7:289-298
15 Spong M,Holm J,Lee D.Passivity-based control of bipedal locomotion.IEEE Robot Automat Mag,2007,14:30-40
16 Chevallereau C,Grizzle J W,Ching-Long Shih J W.Asymptotically stable walking of a five-link underactuated 3-D bipedal robot.IEEE Trans Robot,2009,25:37-50
17 Westervelt E,Grizzle J,Chevallereau C,et al.Feedback control of dynamic bipedal robot locomotion.British J Philosophy Sci,2007,4:302
18 Grizzle J W,Chevallereau C,Sinnet R W,et al.Models,feedback control,and open problems of 3D bipedal robotic walking.Automatica,2014,50:1955-1988
19 Montano O,Orlov Y,Aoustin Y,et al.H∞-stabilization of a 3D bipedal locomotion under a unilateral constraint.New Perspect Appl Modern Control Theory,2018,15:371-396
20祁峰,毕来业,王天舒.被动行走测试系统的建立与实验研究.中国科学:物理学力学天文学,2013,43:557-563
21 Morris B,Grizzle J W.Hybrid invariant manifolds in systems with impulse effects with application to periodic locomotion in bipedal robots.IEEE Trans Automat Contr,2009,54:1751-1764
22 Xing D P,Su J B.Arm/trunk motion generation for humanoid robot.Sci China Inf Sci,2010,53:1603-1612
23 Ames A D,Galloway K,Sreenath K,et al.Rapidly exponentially stabilizing control lyapunov functions and hybrid zero dynamics.IEEE Trans Automat Contr,2014,59:876-891
24 Jiang Z P,Wang Y.A converse Lyapunov theorem for discrete-time systems with disturbances.Syst Control Lett,2002,45:49-58
25 Zhang W,Abate A,Hu J,et al.Exponential stabilization of discrete-time switched linear systems.Automatica,2009,45:2526-2536