This paper introduces a proposed control method for autonomous personal mobility vehicles, specifically the Single-passenger Electric Autonomous Transporter (SEATER), using Nonlinear Model Predictive Control (NMPC). The proposed method leverages a single-shooting approach to solve the optimal control problem (OCP) via non-linear programming (NLP). The proposed NMPC is implemented to a non-holonomic vehicle with a differential drive system, using odometry data as localization feedback to guide the vehicle towards its target pose while achieving objectives and adhering to constraints, such as obstacle avoidance. To evaluate the performance of the proposed method, a number of simulations have been conducted in both obstacle-free and static obstacle environments. The SEATER model and testing environment have been developed in the Gazebo Simulation and the NMPC are implemented within the Robot Operating System (ROS) framework. The simulation results demonstrate that the NMPC-based approach successfully controls the vehicle to reach the desired target location while satisfying the imposed constraints. Furthermore, this study highlights the robustness and real-time effectiveness of NMPC with a single-shooting approach for autonomous vehicle control in the evaluated scenarios.