SummaryIn 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.