复杂环境下非完整移动机器人的鲁棒镇定与约束控制研究

The presence of control constraint has not been considered in most of the existing researches of robust stabilization for uncertain nonholonomic systems. But the system with uncertain parameters or imprecise measurement is usually subject to some physical limits such as input saturation, minimum control time, minimal cost, and moving in the specified region, etc. The robust stabilization and constrained control problems will be considered in this subject research for nonholonomic wheeled mobile robots or the multi robot formation model with uncertain parameters and external disturbance. The proposal is aimed at finding a general design method for such constrained controllers. The main innovations can be summarized as: Firstly, the virtual_controller_tracked technique is proposed for the first time, based on which the saturated robust stabilization of dynamic system is addressed by using the finite time control theory and Lyapunov stability theory. Secondly, a class of switching control algorithm is given based on the original visual feedback system, which can avoid appearing the singularity due to the using of state or input transformation. Finally, the coordination control problem will be addressed for the multi robot formation system with input saturation or constrained states by applying the dynamic feedback lcal linearization method and constrained control theory of linear systems. This study will provide some new ideas and methods for the constrained control problem of nonholonomic systems.

现有不确定非完整系统的鲁棒镇定研究大多没有协同考虑控制受限的情形. 但实际在讨论参数不确定或测量不精确时, 系统还存在着诸如输入饱和、时间最短、能量最优、指定区域运动等物理的限制. 本课题拟研究具有不确定参数的非完整轮式移动机器人在外部扰动、视觉反馈或多机器人编队等复杂环境下控制受限的鲁棒镇定与协调控制问题，探讨这类约束控制器的一般设计方法. 主要研究特色与创新点是: 运用有限时间控制理论和Lyapunov稳定性定理, 提出类Backstepping的有限时间跟踪虚拟控制器技术, 实现从运动学系统到动力学系统输入饱和的鲁棒镇定；针对视觉反馈的原始模型, 给出一类切换控制设计方法, 避免通常的状态和输入变换而引起的奇异现象；采用动态反馈的局部线性化方法和线性系统的约束控制理论解决多机器人输入饱和及状态受限的协调控制问题. 课题的实施将为非完整系统约束控制的理论研究提供一个新的思路和方法.

本课题考虑了不确定非完整轮式移动机器人在受到外部扰动、 状态不可测、控制受限等复杂环境下的约束控制问题。主要研究：动态反馈的机器人系统，当模型含有不确定参数及未知的控制方向和外部扰动时， 探讨其输入饱和的鲁棒镇定；并推广到不确定动力学模型或扩展的链式系统, 将力或力矩作为新的控制输入，运用有限时间控制技术和类back-stepping技术，设计其输入饱和的鲁棒镇定控制器； 针对固定摄像机的不确定视觉反馈链式系统或扩展链式系统， 研究其输入饱和的鲁棒镇定或有限时间镇定，给出了无抖振类滑模的低通滤波控制算法；进一步探索具有记忆性的无模型分数阶跟踪问题的建模，控制器设计等。实际物理量受限下，非完整轮式移动机器人的鲁棒控制设计遇到了不少理论上的困难, 为此课题组探讨了一些创新的解决方法， 问题的解决拓宽了非完整系统控制理论的研究方法，对提高系统的控制性能产生积极的意义。