考虑参数不确定性的移动机器人轨迹跟踪控制
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摘要
针对移动机器人系统中轮胎半径和轮胎间距存在的参数不确定性问题,提出自适应轨迹跟踪控制方法.首先,推导适合进行自适应控制器设计的系统误差模型,将原有控制问题转化为不确定参数的自适应更新率和虚拟控制输入的设计问题;然后,针对系统中的不确定性参数,设计自适应更新率对其进行在线估计,并设计虚拟的控制输入,得到移动机器人驱动电机的左右轮转速;其次在Lyapunov稳定性框架下证明闭环跟踪误差系统的渐近稳定性和估计误差系统的稳定性;最后通过仿真和实验表明,所提出方法能够通过在线学习估计出参数真实值,使得实际运行轨迹收敛到参考轨迹,同时表明所提出方法能够抑制系统参数不确定性对控制系统的影响.
In order to improve the motion control accuracy of mobile robots, this paper proposes an adaptive tracking control method for mobile robots, considering the uncertainty of tire radius and tire pitch. Firstly, a kinematic based system error model for adaptive controller design is derived, and the original control problem is transformed into the design of adaptive updating rate and virtual control input. Then, in order to do with the uncertainty of tire radius and tire pitch in the system, an adaptive method is used to estimate it online, and a virtual control input is designed. By combining the virtual control input with the adaptive estimation algorithm, the left and right wheel speed of the driving motor is obtained. At the same time, it is proved that the closed-loop system is asymptotic stable and the estimation error is bounded in the Lyapunov framework. Finally, the simulation and experimental results show that, the proposed method can estimate the true values of these parameters by online learning, which makes the actual trajectory converge to the reference trajectory, and shows that the proposed method can suppress the influence of the system parameters variation on the control performance.
In order to improve the motion control accuracy of mobile robots, this paper proposes an adaptive tracking control method for mobile robots, considering the uncertainty of tire radius and tire pitch. Firstly, a kinematic based system error model for adaptive controller design is derived, and the original control problem is transformed into the design of adaptive updating rate and virtual control input. Then, in order to do with the uncertainty of tire radius and tire pitch in the system, an adaptive method is used to estimate it online, and a virtual control input is designed. By combining the virtual control input with the adaptive estimation algorithm, the left and right wheel speed of the driving motor is obtained. At the same time, it is proved that the closed-loop system is asymptotic stable and the estimation error is bounded in the Lyapunov framework. Finally, the simulation and experimental results show that, the proposed method can estimate the true values of these parameters by online learning, which makes the actual trajectory converge to the reference trajectory, and shows that the proposed method can suppress the influence of the system parameters variation on the control performance.
引文
[1] Sutoh M, Otsuki M, Wakabayashi S, et al. The right path:Comprehensive path planning for lunar exploration rovers[J]. IEEE Robotics and Automation Magazine,2015, 22(1):22-33.
[2] Cen Y, Song C, Xie N, et al. Path planning method for mobile robot based on ant colony optimization algorithm[C]. The 3rd IEEE Conf on Industrial Electronics and Applications. Singapore:IEEE, 2008:298-301.
[3]鄢立夏,马保离.轮式移动机器人的位置量测输出反馈轨迹跟踪控制[J].控制理论与应用, 2016, 33(6):763-771.(Yan L X, Ma B L. Output feedback trajectory tracking control of wheeled mobile robots with position measurements[J]. Control Theory&Applications, 2016,33(6):763-771.)
[4]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.)
[5]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, 32(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, 32(4):491-496.)
[6] Jiang Z P, Nijmeijer H. Tracking control of mobile robots:A case study in backstepping[J]. Automatica, 1997, 33(7):1393-1399.
[7] Zhang Q, Shippen J, Jones B. Robust backstepping and neural network control of a low-quality nonholonomic mobile robot[J]. Int J of Machine Tools and Manufacture,1999, 39(7):1117-1134.
[8] d’Andréa-Novel B, Campion G, Bastion G. Control of nonholonomic wheeled mobile robots by state feedback linearization[J]. Int J of Robotics Research, 1995, 14(6):543-559.
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[10]陈浩.基于自适应模糊滑模控制器的非完整轮式移动机器人轨迹跟踪控制[D].西安:长安大学信息工程学院, 2013.(Chen H. Adaptive fuzzy sliding mode controller for trajectory tracking control of a nonholonomic mobile robot[D]. Xi’an:School of Information Engineering,Chang’an University, 2013.)
[11]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应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.)
[12] Das T, Kar I N. Design and implementation of an adaptive fuzzy logic-based controller for wheeled mobile robots[J]. IEEE Trans on Control Systems Technology,2006, 14(3):501-510.
[13] Mohareri O, Dhaouad R, Rad A B. Indirect adaptive tracking control of a nonholonomic mobile robot via neural networks[J]. Neurocomputing, 2012, 88:54-66.
[14] Fukao T, Nakagawa H, Adachi N. Adaptive tracking control of a nonholonomic mobile robot[J]. IEEE Trans on Robotics and Automation, 2000, 16(5):609-615.
[15]马海涛,王永.输入饱和约束下的非完整移动机器人轨迹跟踪控制[J].中国科学技术大学学报, 2009,39(5):499-503.(Ma H T, Wang Y. Trajectory tracking control of nonholonomic mobile robot with input saturation constraints[J]. J of University of Science and Technology of China, 2009, 39(5):499-503.)
[16] Huang J, Wen C, Wang W, et al. Adaptive stabilization and tracking control of a nonholonomic mobile robot with input saturation and disturbance[J]. Systems and Control Letters, 2013, 62(3):234-241.
[17] Huang J, Wen C, Wang W, et al. Adaptive output feedback tracking control of a nonholonomic mobile robot[J].Automatica, 2014, 50(3):821-831.
[18]姚钟尧,丁剑平,林惠音.轮胎气压-负荷-下沉量之间的关系[J].特种橡胶制品, 1999, 20(5):52-55.(Yao Z Y, Ding J P, Lin H Y. Relationship of tire pressure-load-sinkage[J]. Special Purpose Rubber Products, 1999, 20(5):52-55.)
[2] Cen Y, Song C, Xie N, et al. Path planning method for mobile robot based on ant colony optimization algorithm[C]. The 3rd IEEE Conf on Industrial Electronics and Applications. Singapore:IEEE, 2008:298-301.
[3]鄢立夏,马保离.轮式移动机器人的位置量测输出反馈轨迹跟踪控制[J].控制理论与应用, 2016, 33(6):763-771.(Yan L X, Ma B L. Output feedback trajectory tracking control of wheeled mobile robots with position measurements[J]. Control Theory&Applications, 2016,33(6):763-771.)
[4]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.)
[5]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, 32(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, 32(4):491-496.)
[6] Jiang Z P, Nijmeijer H. Tracking control of mobile robots:A case study in backstepping[J]. Automatica, 1997, 33(7):1393-1399.
[7] Zhang Q, Shippen J, Jones B. Robust backstepping and neural network control of a low-quality nonholonomic mobile robot[J]. Int J of Machine Tools and Manufacture,1999, 39(7):1117-1134.
[8] d’Andréa-Novel B, Campion G, Bastion G. Control of nonholonomic wheeled mobile robots by state feedback linearization[J]. Int J of Robotics Research, 1995, 14(6):543-559.
[9] Yang J M, Kim J H. Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots[J].IEEE Trans on Robotics and Automation, 1999, 15(3):578-587.
[10]陈浩.基于自适应模糊滑模控制器的非完整轮式移动机器人轨迹跟踪控制[D].西安:长安大学信息工程学院, 2013.(Chen H. Adaptive fuzzy sliding mode controller for trajectory tracking control of a nonholonomic mobile robot[D]. Xi’an:School of Information Engineering,Chang’an University, 2013.)
[11]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应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.)
[12] Das T, Kar I N. Design and implementation of an adaptive fuzzy logic-based controller for wheeled mobile robots[J]. IEEE Trans on Control Systems Technology,2006, 14(3):501-510.
[13] Mohareri O, Dhaouad R, Rad A B. Indirect adaptive tracking control of a nonholonomic mobile robot via neural networks[J]. Neurocomputing, 2012, 88:54-66.
[14] Fukao T, Nakagawa H, Adachi N. Adaptive tracking control of a nonholonomic mobile robot[J]. IEEE Trans on Robotics and Automation, 2000, 16(5):609-615.
[15]马海涛,王永.输入饱和约束下的非完整移动机器人轨迹跟踪控制[J].中国科学技术大学学报, 2009,39(5):499-503.(Ma H T, Wang Y. Trajectory tracking control of nonholonomic mobile robot with input saturation constraints[J]. J of University of Science and Technology of China, 2009, 39(5):499-503.)
[16] Huang J, Wen C, Wang W, et al. Adaptive stabilization and tracking control of a nonholonomic mobile robot with input saturation and disturbance[J]. Systems and Control Letters, 2013, 62(3):234-241.
[17] Huang J, Wen C, Wang W, et al. Adaptive output feedback tracking control of a nonholonomic mobile robot[J].Automatica, 2014, 50(3):821-831.
[18]姚钟尧,丁剑平,林惠音.轮胎气压-负荷-下沉量之间的关系[J].特种橡胶制品, 1999, 20(5):52-55.(Yao Z Y, Ding J P, Lin H Y. Relationship of tire pressure-load-sinkage[J]. Special Purpose Rubber Products, 1999, 20(5):52-55.)