In the present work, a novel method is devised for controlling an uncertain wheeled mobile robot (WMR) in a desired path. To achieve this objective, an optimal and robust control system with adaptive gains is combined to benefit from the advantages of both methods. In fact, applying this controller not only controls a nonlinear system robustly against uncertainties and external disturbances, but also optimizes a quadratic cost function. Also, since the upper bound of uncertainty is determined by an adaptive law, it does not need to be adjusted manually. To ensure the designed controller's finite time stability, Lyapunov theory is used. Finally, to illustrate the effectiveness of the proposed control method, a case study involving a WMR is presented. By comparing the results of this approach with those of an adaptive sliding mode control (ASMC), it is shown that the proposed controller uses less control effort, relative to the ASMC controller, to stabilize the uncertain WMR in the presence of external disturbances.

中文翻译：

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存在匹配不确定性的轮式移动机器人轨迹跟踪控制的复合控制方法

在目前的工作中，设计了一种新方法来控制不确定的轮式移动机器人（WMR）在所需的路径上。为了实现这一目标，将具有自适应增益的最优且稳健的控制系统结合起来，以从这两种方法的优点中受益。实际上，应用该控制器不仅可以针对不确定性和外部干扰鲁棒地控制非线性系统，还可以优化二次成本函数。此外，由于不确定性的上限是由自适应律决定的，因此不需要手动调整。为了确保设计控制器的有限时间稳定性，使用了李雅普诺夫理论。最后，为了说明所提出的控制方法的有效性，介绍了一个涉及 WMR 的案例研究。通过将这种方法的结果与自适应滑模控制 (ASMC) 的结果进行比较，