Effective path tracking control plays a pivotal role in Autonomous Ground Vehicles (AGVs). However, AGVs systems face difficulties in fast convergence and overshooting when subject to actuator communication burden and execution wear. To improve the actuator wear and achieve fast convergence, this paper proposed a fast natural logarithmic sliding mode (FLnSM) control scheme based on the dynamic event-triggered (DET) mechanism. First, a novel FLnSM is developed to enhance convergence speed and reduce chatter. By employing the fast natural logarithmic function, it is possible to achieve high gains at the equilibrium point of the AGVs system. This method exhibits enhanced tracking accuracy and higher convergence speeds compared to other SMC methods. Secondly, a DET mechanism with an adjustable threshold is introduced to mitigate the communication burden and reduce actuator execution loss. Furthermore, as the update frequency of the controller is reduced, the chatter of the sliding mode surface is effectively diminished. Compared to most existing event-triggering methods with a static threshold, the proposed DET mechanism adaptively updates the triggering threshold online to achieve enhanced resource efficiency and avoid the Zeno phenomenon. With only a few parameters requiring tuning, and given that the natural logarithm function is easy to integrate into many AGVs systems, implementing the proposed DET-FLnSM in AGVs systems becomes effortless. Finally, a composite control scheme that integrates DET with FLnSM is proposed to achieve fast convergence, suppress chattering phenomenon, and reduce communication resource consumption of the AGVs system. The excellent performance of the proposed DET-FLnSM control strategy is demonstrated through numerical simulations and experimental results.