一种球形移动机器人爬坡运动的自适应滑模控制
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摘要
针对一种球形机器人爬坡运动的位置控制问题,提出了一种自适应滑模控制方法。基于对实际系统的合理简化,利用拉格朗日方法建立了球形机器人爬坡运动的动力学模型,并将动力学模型表示为状态空间形式。基于系统的状态空间模型,将整个系统划分为两个子系统,并分别定义各子系统的滑动面。将其中一个子系统的滑动面引入到另一个子系统的控制设计中,采用李亚普诺夫稳定性理论设计了滑模控制律,并通过自适应律在线调节其切换增益。从理论上分析了闭环控制系统的稳定性,并通过数值仿真和样机实验验证了所提控制方法的有效性。
An adaptive sliding mode control method is proposed for position control of a spherical mobile robot in climbing state.Based on the reasonable simplifications of the actual robotic system,the dynamic model of the climbing motion is established by using the Lagrangian method,and the dynamic model is transformed into state space form.Based on the state space model,the whole system is divided into two subsystems,and the sliding surfaces of the subsystems are defined respectively.The sliding surface of one subsystem is incorporated into the control design of another subsystem,and the sliding mode control law is derived by using Lyapunov stability theory.The time-varying switching gain is included in the proposed control law,which is adjusted online by an adaptation law.The stability of the closed-loop control system is analyzed,and the effectiveness of the proposed control method is verified through numerical simulation and prototype experiment.
An adaptive sliding mode control method is proposed for position control of a spherical mobile robot in climbing state.Based on the reasonable simplifications of the actual robotic system,the dynamic model of the climbing motion is established by using the Lagrangian method,and the dynamic model is transformed into state space form.Based on the state space model,the whole system is divided into two subsystems,and the sliding surfaces of the subsystems are defined respectively.The sliding surface of one subsystem is incorporated into the control design of another subsystem,and the sliding mode control law is derived by using Lyapunov stability theory.The time-varying switching gain is included in the proposed control law,which is adjusted online by an adaptation law.The stability of the closed-loop control system is analyzed,and the effectiveness of the proposed control method is verified through numerical simulation and prototype experiment.
引文
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[15]郑一力,孙汉旭,刘晋浩.球形移动机器人基于神经网络的反馈线性化运动控制研究与实验[J].机器人,2012,34(4):455-459.
[2]Roozegar M,Mahjoob M J,Jahromi M.DP-based path planning of a spherical mobile robot in an environment with obstacles[J].Journal of the Franklin Institute,2014,351(10):4923-4938.
[3]Li M X,Cuo S X,Hirata H,et al.Design and performance evaluation of an amphibious spherical robot[J].Robotics and Autonomous Systems,2015,64:21-34.
[4]孙汉旭,于涛.全方位陆地作业球形机器人[M].北京:北京邮电大学出版社,2015.
[5]岳明,邓宗全.球形机器人爬坡状态下动力学建模及最优控制器设计[J].机械工程学报,2009,45(11):46-51.
[6]Abbott M S.Kinematics,dynamics and control of single-axle,two-wheel vehicles(biplanar bicycles)[D].Blacksburg:Virginia Polytechnic Institute and State University,2000.
[7]Lewis J.Reference frame regulation for a biplanar bicycle[D].Blacksburg:Virginia Polytechnic Institute and State University,2000.
[8]Yu T,Sun H X,Jia Q X,et al.Decoupled sliding mode control for the climbing motion of spherical mobile robots[J].Advances in Intelligent and Soft Computing,2012,160:671-677.
[9]孙汉旭,张延恒,贾庆轩,等.一种基于模糊滑模控制器的球形机器人坡面运动控制方法:中国,201310322138.9[P].2013-07-29.
[10]Mahmoodabadi M J,Momennejad S,Bagheri A.Online optimal decoupled sliding mode control based on moving least squares and particle swarm optimization[J].Information Sciences,2014,268(6):342-356.
[11]Hwang C L,Chiang C C,Yeh Y W.Adaptive fuzzy hierarchical sliding-mode control for the trajectory tracking of uncertain underactuated nonlinear dynamic systems[J].IEEE Transactions on Fuzzy Systems,2014,22(2);286-299.
[12]蔡自兴,谢斌.机器人学[M].3版.北京:清华大学出版社,2015.
[13]Utkin V,Guldner J,Shi J M.Sliding Mode Control in Electro-Mechanical Systems[M].Second Edition.Boca Raton CRC Press,2009.
[14]闵颖颖,刘允刚.Barbalat引理及其在系统稳定性分析中的应用[J].山东大学学报(工学版),2007,37(1):51-55.
[15]郑一力,孙汉旭,刘晋浩.球形移动机器人基于神经网络的反馈线性化运动控制研究与实验[J].机器人,2012,34(4):455-459.