In this article, we introduce a novel family of Lyapunov-based adaptive kinematic control laws developed to solve the trajectory tracking problem for a differential-drive mobile robot under the influence of both longitudinal and lateral wheel slip. Each adaptive controller in this family is constructed by augmenting a nonadaptive nominal controller, originally designed for the slip-free case, with an update rule capable of estimating the longitudinal slip. In the absence of lateral slip and under constant longitudinal slip, we establish the convergence of the trajectory tracking error to zero and, assuming a persistent excitation condition, we also demonstrate the convergence of the slip estimate error to zero. When lateral slip is present, we analyse a particular control law from our family of adaptive controllers. This law ensures the trajectory tracking error is uniformly ultimately bounded around the origin, demonstrating the robustness of our adaptive control scheme in dealing with time-varying longitudinal and lateral slip. The validity of our approach is assessed through comprehensive numerical simulations.

中文翻译：

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基于Lyapunov的轮滑移动机器人自适应控制通用更新规则

在本文中，我们介绍了一系列基于李亚普诺夫的新型自适应运动控制律，旨在解决差动驱动移动机器人在纵向和横向车轮滑移影响下的轨迹跟踪问题。该系列中的每个自适应控制器都是通过增强非自适应标称控制器来构建的，该标称控制器最初是为无滑移情况设计的，具有能够估计纵向滑移的更新规则。在没有横向滑移且纵向滑移恒定的情况下，我们建立了轨迹跟踪误差收敛到零的模型，并且假设持续激励条件，我们还证明了滑移估计误差收敛到零。当存在横向滑移时，我们分析自适应控制器系列中的特定控制律。该定律确保轨迹跟踪误差最终均匀地限制在原点周围，证明了我们的自适应控制方案在处理时变纵向和横向滑移方面的鲁棒性。我们的方法的有效性是通过全面的数值模拟来评估的。