This work describes the modeling, control and development of a low cost Micro Autonomous Underwater Vehicle ($\mu$-AUV), named AR2D2. The main objective of this work is to make the vehicle to detect and follow an object with defined color by means of the readings of a depth sensor and the information provided by an artificial vision system. A nonlinear PD (Proportional-Derivative) controller is implemented on the vehicle in order to stabilize the heave and surge movements. A formal stability proof of the closed-loop system using Lyapunov’s theory is given. Furthermore, the performance of the $\mu$-AUV is validated through numerical simulations in MatLab and real-time experiments.