This paper investigates the estimation of a straightforward mathematical model tailored for overseeing and regulating the motion of an AGV (Automated Guided Vehicle) equipped with differential drive systems. The mathematical model delineates the correlation between the input voltage signal of the DC motor and the resultant distance output, empirically tested within an open-loop system. This methodology facilitates the development of precise mathematical models aimed at mitigating errors in powertrains and mechanical motion components, including gears, chains, and ground-contacting tires, along with system friction. Moreover, a P controller system is devised to oversee the AGV motion. The stability and control efficacy are assessed through practical experimentation on the AGV’s ability to attain predefined distances. Tests were conducted under two distinct conditions: case 1) AGV operation without any payload and case 2) AGV operation while bearing a 14 kg payload. The system’s response to the input distance was meticulously observed. The average distance error is calculated at 1.74% of the designated control distance (2m, 3m, and 4m) across all cases. In the absence of a load (case 1), the average distance error remains consistent at 1.74% of the control distance, showcasing a motor speed response of 23.76 RPM (with a rise time of 2.1 s). Conversely, when subjected to a 14 kg payload (case 2), the average distance error marginally increases to 1.76% of the control distance, with a corresponding motor speed response of 23.71 RPM (and a rise time of 2.2 s). These results show the effectiveness of the control system, facilitated by the estimation of a simplistic mathematical model tailored specifically for AGV operations.