作者：于涛¹, 孙汉旭², 赵伟³, 杨昆¹

作者单位：1. 辽宁工业大学机械工程与自动化学院, 辽宁 锦州 121001;
2. 北京邮电大学自动化学院, 北京 100876;
3. 北京印刷学院信息工程学院, 北京 102600

关键词：三驱动;球形机器人;定位控制;自适应分级滑模控制

摘要：

探讨一种三驱动球形机器人的定位控制问题，提出基于控制增益自适应调节的分级滑模控制方法。相比于现有定位控制方法，所提出的控制方法对于系统不确定性具有很强的鲁棒性。将球形机器人系统分解为球体子系统和偏心质块子系统，并在此基础上分别设计系统的各级滑动面。基于Lyapunov函数法选取分级滑模控制律和控制增益自适应律，并采用边界层法削弱分级滑模控制器的抖振。应用Barbalat引理证明闭环系统的稳定性，并利用数值仿真实验验证所提控制方法的可行性和有效性。数值仿真结果表明，该控制方法能够实现带有不确定性的球形机器人系统的定位控制。

Positioning control of a spherical robot based on adaptive hierarchical sliding mode control

YU Tao¹, SUN Hanxu², ZHAO Wei³, YANG Kun¹

1. College of Mechanical Engineering and Automation, Liaoning University of Technology, Jinzhou 121001, China;
2. School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China;
3. School of Information Engineering, Beijing Institute of Graphic Communication, Beijing 102600, China

Abstract: The positioning control problem of a triple-drive spherical robot is discussed, and a hierarchical sliding mode control method based on adaptive control gain regulation is proposed. Compared with the existing positioning control methods, the proposed control method has strong robustness against system uncertainties. The spherical robot system is decomposed into sphere subsystem and eccentric mass subsystem, based on which the sliding surfaces of both levels are designed respectively. The hierarchical sliding mode control law and control gain adaption law are selected based on Lyapunov function approach, and the chattering of the hierarchical sliding mode controller is reduced by adopting boundary layer method. The stability of the closed-loop system is proved by applying Barbalat's lemma, and numerical simulation tests are utilized to verify the feasibility and effectiveness of the proposed control method. Numerical simulation results show that positioning control of the spherical robot system with uncertainties can be achieved by the proposed control method.

Keywords: triple-drive;spherical robot;positioning control;adaptive hierarchical sliding mode control

2018, 44(5): 97-102  收稿日期: 2017-10-09;收到修改稿日期: 2017-11-28

基金项目: 国家自然科学基金面上项目（51175048）；辽宁省自然科学基金指导计划项目（201602379）；辽宁省教育厅科学技术研究一般项目（L2015241）

作者简介: 于涛(1980-),男,天津市人,讲师,博士,研究方向为机器人运动分析与控制、滑模控制理论与应用。

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