工程科学学报，第41卷，第9期：1176-1186,2019年9月 Chinese Journal of Engineering,Vol.41,No.9:1176-1186,September 2019 DOI:10.13374/j.issn2095-9389.2019.09.009;http://journals.ustb.edu.cn 具有状态约束与输入饱和的全向移动机器人自适应跟 踪控制 郑文昊，贾英民四 北京航空航天大学自动化科学与电气工程学院，北京100191 区通信作者，E-mail:ymjiat@buaa.cdu.cm 摘要研究了全状态约束与输入饱和情况下的全向移动机器人轨迹跟踪控制问题.首先，针对一类三轮驱动的全向移动机 器人，考虑系统存在模型参数不确定与外部扰动，建立了运动学与动力学模型：其次，利用障碍Lyapunov函数，结合反步设计 方法，有效处理全向移动机器人跟踪过程中存在的状态约束，保证所有状态变量不会超出状态约束的限制区域：然后，针对系 统参数不确定和未知有界扰动，设计相应的自适应律进行处理：同时，提出一种抗饱和补偿器保证机器人输入力矩满足饱和 约束；并且利用Lyapunov理论分析证明了当选取合适的控制参数时闭环系统中的所有信号均能保证一致有界：最后，通过与 未考虑状态约束和输入饱和的控制器以及经典比例-微分控制器进行仿真对比，验证了该方法的有效性和鲁棒性 关键词全向移动机器人；跟踪控制；自适应控制：状态约束；输入饱和 分类号TP242.6 Adaptive tracking control for omnidirectional mobile robots with full-state constraints and input saturation ZHENG Wen-hao,JIA Ying-min School of Automation Science and Electrical Engineering,Beihang University,Beijing 100191,China Corresponding author,E-mail:ymjia@buaa.edu.cn ABSTRACT The omnidirectional mobile robot (OMR),which is different from the two-wheeled differential drive mobile robots,can achieve three-degree-of-freedom motion in a plane with no non-holonomic constraint.Therefore,this type of robot has been widely used in many fields owing to its superior maneuverability and controllability.In practical applications,the trajectory tracking problem of the OMRs is a key issue that requires an urgent solution.The challenges with respect to the tracking performance can be categorized into the following:first,the parameter uncertainty of the OMR model and external disturbances affect the accuracy of the control.Second, on account of the limited workspace and the security requirements,the positions,attitudes,and speeds of the OMRs are subject to state constraints during the tracking process.Finally,the limited capability of the actuators can lead to input saturation,which will further degrade the tracking performance or even result in failure to track the desired trajectory.Thus,this study investigates the trajectory- tracking control problem of the OMRs with full-state constraints and input saturation.The kinematics and dynamics for a class of three- wheeled omnidirectional mobile robots were presented with the model uncertainties and external disturbance.Moreover,the barrier Lya- punov method was applied to handle the state constraints using the backstepping technique so that none of the state variables violated the restrictions.Meanwhile,adaptive control laws were designed to deal with the parameter uncertainties and unknown bounded dis- turbance.Moreover,an anti-windup compensator was adopted to ensure the input torque of the robot met the input constraints.The 收稿日期：2019-01-11 基金项目：国家自然科学基金资助项目(61327807,61521091,61520106010,61134005)：国家重点基础研究发展规划资助项目 (2012CB821200,2012CB821201)工程科学学报,第 41 卷,第 9 期:1176鄄鄄1186,2019 年 9 月 Chinese Journal of Engineering, Vol. 41, No. 9: 1176鄄鄄1186, September 2019 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2019. 09. 009; http: / / journals. ustb. edu. cn 具有状态约束与输入饱和的全向移动机器人自适应跟 踪控制 郑文昊, 贾英民苣 北京航空航天大学自动化科学与电气工程学院, 北京 100191 苣通信作者, E鄄mail: ymjia@ buaa. edu. cn 摘 要 研究了全状态约束与输入饱和情况下的全向移动机器人轨迹跟踪控制问题. 首先,针对一类三轮驱动的全向移动机 器人,考虑系统存在模型参数不确定与外部扰动,建立了运动学与动力学模型;其次,利用障碍 Lyapunov 函数,结合反步设计 方法,有效处理全向移动机器人跟踪过程中存在的状态约束,保证所有状态变量不会超出状态约束的限制区域;然后,针对系 统参数不确定和未知有界扰动,设计相应的自适应律进行处理;同时,提出一种抗饱和补偿器保证机器人输入力矩满足饱和 约束;并且利用 Lyapunov 理论分析证明了当选取合适的控制参数时闭环系统中的所有信号均能保证一致有界;最后,通过与 未考虑状态约束和输入饱和的控制器以及经典比例鄄鄄微分控制器进行仿真对比,验证了该方法的有效性和鲁棒性. 关键词 全向移动机器人; 跟踪控制; 自适应控制; 状态约束; 输入饱和 分类号 TP242郾 6 收稿日期: 2019鄄鄄01鄄鄄11 基金项目: 国 家 自 然 科 学 基 金 资 助 项 目 ( 61327807, 61521091, 61520106010, 61134005 ); 国 家 重 点 基 础 研 究 发 展 规 划 资 助 项 目 (2012CB821200, 2012CB821201) Adaptive tracking control for omnidirectional mobile robots with full鄄state constraints and input saturation ZHENG Wen鄄hao, JIA Ying鄄min 苣 School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China 苣Corresponding author, E鄄mail: ymjia@ buaa. edu. cn ABSTRACT The omnidirectional mobile robot (OMR), which is different from the two鄄wheeled differential drive mobile robots, can achieve three鄄degree鄄of鄄freedom motion in a plane with no non鄄holonomic constraint. Therefore, this type of robot has been widely used in many fields owing to its superior maneuverability and controllability. In practical applications, the trajectory tracking problem of the OMRs is a key issue that requires an urgent solution. The challenges with respect to the tracking performance can be categorized into the following: first, the parameter uncertainty of the OMR model and external disturbances affect the accuracy of the control. Second, on account of the limited workspace and the security requirements, the positions, attitudes, and speeds of the OMRs are subject to state constraints during the tracking process. Finally, the limited capability of the actuators can lead to input saturation, which will further degrade the tracking performance or even result in failure to track the desired trajectory. Thus, this study investigates the trajectory鄄 tracking control problem of the OMRs with full鄄state constraints and input saturation. The kinematics and dynamics for a class of three鄄 wheeled omnidirectional mobile robots were presented with the model uncertainties and external disturbance. Moreover, the barrier Lya鄄 punov method was applied to handle the state constraints using the backstepping technique so that none of the state variables violated the restrictions. Meanwhile, adaptive control laws were designed to deal with the parameter uncertainties and unknown bounded dis鄄 turbance. Moreover, an anti鄄windup compensator was adopted to ensure the input torque of the robot met the input constraints. The