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Autonomous wheeled mobile robots (WMRs) are widely used in safety-critical systems, such as robotic visual infrastructure inspection, warehouse automation, delivery robots, and autonomous vehicles, where it is essential for WMRs to reliably follow predetermined paths while effectively maintaining lane position and avoiding collisions. However, frequent observations required for control execution to account for environmental uncertainty result in increased sensing, computation, and energy costs. This research addresses the problem of optimal, safe trajectory tracking control for WMRs by developing a safe reinforcement learning (RL)-based trajectory tracking control framework integrated with event-based sensing and computation. The first part of the research reviews the state-of-the-art approaches for safe, resource-aware, and optimal control frameworks for WMRs in uncertain environments. It primarily focuses on defining the rationale for selecting the control barrier function (CBF) as the safety certificate in the trajectory tracking control algorithm, and the event-triggered control (ETC) that can reduce sensing and computation costs. Subsequently, a near-optimal event-based sampling and optimal tracking control scheme under input constraints for WMRs is developed by extending an existing event-based RL-based control. Numerical simulation results indicate a 61.2% reduction in computation and sensing. Finally, the event-based optimal trajectory tracking control is extended to incorporate safety by reformulating the cost function using CBF and validated through MATLAB-based numerical simulations in a lane-keeping scenario with safety constraints.