带扰动补偿的移动机器人轨迹跟踪反演控制
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摘要
为解决在外部扰动下轮式移动机器人轨迹跟踪易出现速度跳变的问题,提出一种基于扰动补偿的模糊自适应反演控制方法。该方法采用模糊系统对系统模型不确定性和外部干扰组成的复合扰动进行估计,同时引入滑模鲁棒控制项来抑制扰动估计误差对系统控制性能的影响,并应用反演设计法推导出相应的控制律和模糊系统参数自适应律,稳定性分析证明了所得闭环系统是全局一致渐近稳定的。仿真结果表明在较大外部扰动下该控制器能够使系统保持快速瞬态响应,且能够有效克服滑模抖动,并消除速度跳变问题。
In order to eliminate the velocity jump in the wheeled mobile robot trajectory tracking under external disturbances, a fuzzy adaptive backstepping control method with disturbance compensation is proposed. The disturbances caused by the system model uncertainty and external disturbances are estimated by a fuzzy system and the effect of disturbance estimation error on the controlled system is restrained by introducing the sliding-mode control. The corresponding control law and parameter adaptive law for the fuzzy system are given through the backstepping method. The stability analysis has proved that the closed-loop system is globally uniformly asymptotically stable. The simulation results show that the controlled system under external disturbances can achieve a fast transient response, overcome the sliding mode chattering and eliminate the velocity jump.
In order to eliminate the velocity jump in the wheeled mobile robot trajectory tracking under external disturbances, a fuzzy adaptive backstepping control method with disturbance compensation is proposed. The disturbances caused by the system model uncertainty and external disturbances are estimated by a fuzzy system and the effect of disturbance estimation error on the controlled system is restrained by introducing the sliding-mode control. The corresponding control law and parameter adaptive law for the fuzzy system are given through the backstepping method. The stability analysis has proved that the closed-loop system is globally uniformly asymptotically stable. The simulation results show that the controlled system under external disturbances can achieve a fast transient response, overcome the sliding mode chattering and eliminate the velocity jump.
引文
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[9]Das T,Kar I N.Design and Implementation of an Adaptive Fuzzy Logic-Based Controller for Wheeled Mobile Robots[J].IEEETransactions on Control Systems Technology,2006,14(3):501-510.
[10]王宗义,李艳东,刘涛,等.移动机器人的自适应模糊滑模动力学控制[J].哈尔滨工程大学学报,2011,32(6):792-799.Wang Z Y,Li Y D,Liu T,et al.Dynamic Control of Mobile Robots Based on Adaptive Fuzzy Sliding Mode[J].Journal of Harbin Engineering University,2011,32(6):792-799.
[11]邹细勇,徐德,李子印.非完整移动机器人路径跟踪的模糊控制[J].控制与决策,2008,23(6):655-659.Zou X Y,Xu D,Li Z Y.Piecewise Fuzzy Control for Path Tracking of Nonholonomic Mobile Robots[J].Control and Decision,2008,23(6):655-659.
[12]孙棣华,崔明月,李永福.具有参数不确定性的轮式移动机器人自适Backstepping控制[J].控制理论与应用,2012,29(9):1198-1204.Sun D H,Cui M Y,Li Y F.Adaptive Backstepping Control of Wheeled Mobile Robots with Parameter Uncertainties[J].Control Theory&Applications,2012,29(9):1198-1204.
[13]闫茂德,吴青云,贺昱曜.非完整移动机器人的自适应滑模轨迹跟踪控制[J].系统仿真学报,2007,19(3):579-584.Yan M D,Wu Q Y,He Y Y.Adaptive Sliding Mode Control for the Global Trajectory Tracking of Mobile Robots[J].Journal of System Simulation,2007,19(3):579-584.
[14]李世华,田玉平.非完整移动机器人的轨迹跟踪控制[J].控制与决策,2002,17(3):301-305.Li S H,Tian Y P.Trajectory Tracking Control of Nonholonomic Mobile Robots[J].Control and Decision,2002,17(3):301-305.
[2]Walsh G,Tilbury D,Sastry S,et al.Stabilization of trajectories for systems with nonholonomic constraints[J].IEEE Transactions on Automatic Control,1994,39(1):216-222.
[3]吴卫国,陈辉堂,王月娟.移动机器人的全局轨迹跟踪控制[J].自动化学报,2001,27(3):326-331.Wu W G,Chen H T,Wang Y J.Global Trajectory Tracking Control of Mobile Robots[J].Acta Automatica Sinica,2001,27(3):326-331.
[4]陈罡,高婷婷,贾庆伟,等.带有未知参数和有界干扰的移动机器人轨迹跟踪控制[J].控制理论与应用,2015,23(4):491-496.Chen G,Gao T T,Jia Q W,et al.Trajectory Tracking Control for Nonholonomic Mobile Robots with Unknown Parameters and Bounded Disturbance[J].Control Theory&Applications,2015,23(4):491-496.
[5]于浩,宿浩,杨雪,等.基于引导角的轮式移动机器人轨迹跟踪控制[J].控制与决策,2015,30(4):635-639.Yu H,Xu H,Yang X,et al.Guidance Angle Based Trajectory Tracking for Wheeled Mobile Robots[J].Control and Decision,2015,30(4):635-639.
[6]Park B S,Yoo S J,Park J B.Adaptive Neural Sliding Mode Control of Nonholonomic Wheeled Mobile Robots with Model Uncertainty[J].IEEE Transactions on Control Systems Techonology,2009,17(1):207-214.
[7]庞海龙,马保离.不确定轮式移动机器人的任意轨迹跟踪[J].控制理论与应用,2014,31(3):285-292.Pang H L,Ma B L.Adaptive Unified Controller of Arbitrary Trajectory Tracking for Wheeled Mobile Robots with Unknown Parameters[J].Control Theory&Applications,2014,31(3):285-292.
[8]朱玲,李艳东,孙明,等.移动机器人编队的神经网络滑模控制[J].电机与控制学报,2014,18(3):113-118.Zhu L,Li Y D,Sun M,et al.Sliding Mode Control of Mobile Robot Formation Based on Neural Networks[J].Electric Machines and Control,2014,18(3):113-118.
[9]Das T,Kar I N.Design and Implementation of an Adaptive Fuzzy Logic-Based Controller for Wheeled Mobile Robots[J].IEEETransactions on Control Systems Technology,2006,14(3):501-510.
[10]王宗义,李艳东,刘涛,等.移动机器人的自适应模糊滑模动力学控制[J].哈尔滨工程大学学报,2011,32(6):792-799.Wang Z Y,Li Y D,Liu T,et al.Dynamic Control of Mobile Robots Based on Adaptive Fuzzy Sliding Mode[J].Journal of Harbin Engineering University,2011,32(6):792-799.
[11]邹细勇,徐德,李子印.非完整移动机器人路径跟踪的模糊控制[J].控制与决策,2008,23(6):655-659.Zou X Y,Xu D,Li Z Y.Piecewise Fuzzy Control for Path Tracking of Nonholonomic Mobile Robots[J].Control and Decision,2008,23(6):655-659.
[12]孙棣华,崔明月,李永福.具有参数不确定性的轮式移动机器人自适Backstepping控制[J].控制理论与应用,2012,29(9):1198-1204.Sun D H,Cui M Y,Li Y F.Adaptive Backstepping Control of Wheeled Mobile Robots with Parameter Uncertainties[J].Control Theory&Applications,2012,29(9):1198-1204.
[13]闫茂德,吴青云,贺昱曜.非完整移动机器人的自适应滑模轨迹跟踪控制[J].系统仿真学报,2007,19(3):579-584.Yan M D,Wu Q Y,He Y Y.Adaptive Sliding Mode Control for the Global Trajectory Tracking of Mobile Robots[J].Journal of System Simulation,2007,19(3):579-584.
[14]李世华,田玉平.非完整移动机器人的轨迹跟踪控制[J].控制与决策,2002,17(3):301-305.Li S H,Tian Y P.Trajectory Tracking Control of Nonholonomic Mobile Robots[J].Control and Decision,2002,17(3):301-305.