不确定非完整运动学系统鲁棒镇定
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摘要
本文探讨了非完整轮式移动机器人的不确定链式模型、鲁棒镇定和跟踪控制问题。旨在推出一系列与以往不同的新的不确定运动学系统模型，并且对不确定模型设计新的指数镇定控制器和动态反馈跟踪控制器。本文的主要结果和创新之处有如下几点：
1、基于视觉反馈信息和状态-输入变换，得到了一系列新的非完整不确定链式模型并将它们推广到更为一般的形式。创新之处是：通过固定单目摄相机的视觉反馈模型和状态-输入变换，推导出了未标定摄像机视觉参数的四种非完整机器人、带有一个拖车和多个拖车的非完整系统的不确定链式模型。与以往研究模型不同的是，这些模型的结构不满足所谓的三角条件，所以，是一系列新的不确定链式模型。
2、给出了两种不同情形下的（1,1）型机器人不确定链式模型的指数镇定控制器。创新点是，基于特殊情形下（1,1）型机器人不确定链式系统的指数镇定控制方法，提出了新的更一般情形下的（1,1）型机器人不确定链式系统的控制器设计方案，并给出了严格证明。
3、对于（1,2）型机器人的不确定链式系统，基于State-scaling、状态-输入变换和切换技术，分别提出了四种不同情形下的新的指数镇定控制器设计方案。并对每一种情形，给出了严格证明和Matlab仿真，验证了所提出的控制器的正确性。这一章内容是本文的重要创新成果之一。
4、研究了两类机器人不确定非完整系统的轨迹跟踪问题。首先介绍了基于视觉反馈的（2,0）型机器人不确定系统的动态反馈跟踪控制器设计。然后对基于视觉伺服的（1,2）型机器人的不确定链式系统，借鉴Backstepping方法，构建了两个变换和Lyapunov函数，提出了新的在特定情形下的自适应动态反馈跟踪控制器，该控制器使得跟踪误差和动态变量渐近趋于零。对控制器设计的鲁棒性给出了严格证明和仿真实验。
总之，非完整轮式移动机器人是一个复杂的非线性系统。由于未标定参数、外部扰动、测量和未建模动态等不确定性，实际中难以得到非完整系统精确的运动学模型。本文所提出的一系列非完整不确定链式模型、对两种不确定链式模型在多种情形下所设计的指数镇定控制器和自适应跟踪控制器，不仅丰富了不确定非完整系统控制理论的内容，而且对轮式机器人控制具有重要的实际意义。
For nonholonomic wheeled mobile robots with uncertainties, we discuss theexponential stabilization problems and the adaptive dynamic feedback trackingproblems in this thesis. Our objective is to propose a few new exciting uncertainchained form models, then design new robust controllers of exponential stabilizationand propose the new tacking controllers for the uncertain systems. The main results andthe innovations for this thesis are shown as follows:
1. A few new uncertain chained models are obtained based on visual feedback andstate-input transformations for nonholonomic wheeled mobile robots. The innovationsare that a few new uncertain chained models of four types of nonholonomic wheeledmobile robots and a car with one or n trailers are obtained by using state-inputtransformations and visual feedback of fixed camera with unknown parameters. Then,we derived the more general uncertain chained models from the deduced uncertainmodels. The deduced uncertain chained models are different from those discussed bycontrol experts before. The structures of our new uncertain models do not satisfy theso-called triangularity condition. So the deduced models are a series of novel uncertainchained models.
2. For the uncertain chained systems of type (1,1) robots, the exponentialstabilization controllers are addressed in two particular cases. The innovation is that anew exponential stabilization controller in more general case for the uncertain chainedsystem of type (1,1) robot is proposed based on the exponential regulation algorithm inthe particular case. The strict proof is given and the simulation results are shown.
3. For the uncertain chained system of type (1,2) robot, four kinds of new controlschemes are presented in four different cases based on the state-scaling, state-inputtransformations and switching strategies. The strict proof is given and the simulationresults are shown for every case which means that the new controllers are effective.
4. For the uncertain nonholonomic system of type (2,0) mobile robot, a newdynamic feedback tracking controller is introduced. Then, the new adaptive dynamictracking controller is obtained for type (1,2) robot in particular case. The innovation isthat a new adaptive and dynamic feedback tracking controller is obtained based on thebackstepping method, two transformations and Lyapunov function for the uncertain chained system of type (1,2) nonholonomic wheeled mobile robot. The controller canmake the tracking errors converge to zero asymptotically.
To sum up, nonholonomic wheeled mobile robots are kinds of quite complexnonlinear control systems. In practice, precise kinematic models of robots are difficultto obtained due to imprecise measurements, unmodeling and disturbance etc.. Theproposed new uncertain chained models, the new exponential stabilization controllersand the tracking controller for the uncertain chained systems in this thesis not onlyenrich the contents of nonholonomic control theories of uncertain systems but also haveimportant practical significance for the control of wheeled mobile robots.
1、基于视觉反馈信息和状态-输入变换，得到了一系列新的非完整不确定链式模型并将它们推广到更为一般的形式。创新之处是：通过固定单目摄相机的视觉反馈模型和状态-输入变换，推导出了未标定摄像机视觉参数的四种非完整机器人、带有一个拖车和多个拖车的非完整系统的不确定链式模型。与以往研究模型不同的是，这些模型的结构不满足所谓的三角条件，所以，是一系列新的不确定链式模型。
2、给出了两种不同情形下的（1,1）型机器人不确定链式模型的指数镇定控制器。创新点是，基于特殊情形下（1,1）型机器人不确定链式系统的指数镇定控制方法，提出了新的更一般情形下的（1,1）型机器人不确定链式系统的控制器设计方案，并给出了严格证明。
3、对于（1,2）型机器人的不确定链式系统，基于State-scaling、状态-输入变换和切换技术，分别提出了四种不同情形下的新的指数镇定控制器设计方案。并对每一种情形，给出了严格证明和Matlab仿真，验证了所提出的控制器的正确性。这一章内容是本文的重要创新成果之一。
4、研究了两类机器人不确定非完整系统的轨迹跟踪问题。首先介绍了基于视觉反馈的（2,0）型机器人不确定系统的动态反馈跟踪控制器设计。然后对基于视觉伺服的（1,2）型机器人的不确定链式系统，借鉴Backstepping方法，构建了两个变换和Lyapunov函数，提出了新的在特定情形下的自适应动态反馈跟踪控制器，该控制器使得跟踪误差和动态变量渐近趋于零。对控制器设计的鲁棒性给出了严格证明和仿真实验。
总之，非完整轮式移动机器人是一个复杂的非线性系统。由于未标定参数、外部扰动、测量和未建模动态等不确定性，实际中难以得到非完整系统精确的运动学模型。本文所提出的一系列非完整不确定链式模型、对两种不确定链式模型在多种情形下所设计的指数镇定控制器和自适应跟踪控制器，不仅丰富了不确定非完整系统控制理论的内容，而且对轮式机器人控制具有重要的实际意义。
For nonholonomic wheeled mobile robots with uncertainties, we discuss theexponential stabilization problems and the adaptive dynamic feedback trackingproblems in this thesis. Our objective is to propose a few new exciting uncertainchained form models, then design new robust controllers of exponential stabilizationand propose the new tacking controllers for the uncertain systems. The main results andthe innovations for this thesis are shown as follows:
1. A few new uncertain chained models are obtained based on visual feedback andstate-input transformations for nonholonomic wheeled mobile robots. The innovationsare that a few new uncertain chained models of four types of nonholonomic wheeledmobile robots and a car with one or n trailers are obtained by using state-inputtransformations and visual feedback of fixed camera with unknown parameters. Then,we derived the more general uncertain chained models from the deduced uncertainmodels. The deduced uncertain chained models are different from those discussed bycontrol experts before. The structures of our new uncertain models do not satisfy theso-called triangularity condition. So the deduced models are a series of novel uncertainchained models.
2. For the uncertain chained systems of type (1,1) robots, the exponentialstabilization controllers are addressed in two particular cases. The innovation is that anew exponential stabilization controller in more general case for the uncertain chainedsystem of type (1,1) robot is proposed based on the exponential regulation algorithm inthe particular case. The strict proof is given and the simulation results are shown.
3. For the uncertain chained system of type (1,2) robot, four kinds of new controlschemes are presented in four different cases based on the state-scaling, state-inputtransformations and switching strategies. The strict proof is given and the simulationresults are shown for every case which means that the new controllers are effective.
4. For the uncertain nonholonomic system of type (2,0) mobile robot, a newdynamic feedback tracking controller is introduced. Then, the new adaptive dynamictracking controller is obtained for type (1,2) robot in particular case. The innovation isthat a new adaptive and dynamic feedback tracking controller is obtained based on thebackstepping method, two transformations and Lyapunov function for the uncertain chained system of type (1,2) nonholonomic wheeled mobile robot. The controller canmake the tracking errors converge to zero asymptotically.
To sum up, nonholonomic wheeled mobile robots are kinds of quite complexnonlinear control systems. In practice, precise kinematic models of robots are difficultto obtained due to imprecise measurements, unmodeling and disturbance etc.. Theproposed new uncertain chained models, the new exponential stabilization controllersand the tracking controller for the uncertain chained systems in this thesis not onlyenrich the contents of nonholonomic control theories of uncertain systems but also haveimportant practical significance for the control of wheeled mobile robots.
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