This study addresses the problem of high-precision visual target tracking for an integrated mobile robot system equipped with a pan/tilt stereo camera. The research presents a unified dynamic model that fully couples the differential-drive robot and the two-degree-of-freedom camera orientation mechanism, incorporating both nonholonomic motion constraints and stereo vision-based feedback. An optimal nonlinear control law is designed, combining position, velocity, and integral actions for both platform and camera dynamics, with smooth actuator saturation and anti-windup protection. The control framework is validated through advanced MATLAB-based numerical simulations under a time-varying circular reference trajectory. Simulation results demonstrate that the proposed approach achieves a mean position tracking error of 0.0232 m, a maximum position error of 0.0713 m, and a mean pan error of 0.0114 radians, while maintaining total energy consumption at 0.34 Joules, all well within specified performance thresholds. The tilt actuation remains negligible, confirming the system’s ability to avoid unnecessary movements. These results confirm that the control strategy delivers good, accurate, and energy-efficient performance in challenging dynamic tracking scenarios. The methodology provides a rigorous foundation for future real-world deployment and further extension to more complex multi-target environments.