In addition to its crucial impact on customer satisfaction, last-mile delivery (LMD) is notorious for being the most time-consuming and costly stage of the shipping process. Pressing environmental concerns combined with the recent surge of e-commerce sales have sparked renewed interest in automation and electrification of last-mile logistics. To address the hurdles faced by existing robotic couriers, this paper introduces a customer-centric and safety-conscious LMD system for small urban communities based on AI-assisted autonomous delivery robots. The presented framework enables end-to-end automation and optimization of the logistic process while catering for real-world imposed operational uncertainties, clients' preferred time schedules, and safety of pedestrians. To this end, the integrated optimization component is modeled as a robust variant of the Cumulative Capacitated Vehicle Routing Problem with Time Windows, where routes are constructed under uncertain travel times with an objective to minimize the total latency of deliveries (i.e., the overall waiting time of customers, which can negatively affect their satisfaction). We demonstrate the proposed LMD system's utility through real-world trials in a university campus with a single robotic courier. Implementation aspects as well as the findings and practical insights gained from the deployment are discussed in detail. Lastly, we round up the contributions with numerical simulations to investigate the scalability of the developed mathematical formulation with respect to the number of robotic vehicles and customers.