This paper presents the development of simple but powerful path-following and obstacle-avoidance control laws for an underactuated autonomous underwater vehicle (AUV). Potential function-based proportional derivative (PFPD) as well as a potential function-based augmented proportional derivative (PFAPD) control laws are developed to govern the motion of the AUV in an obstacle-rich environment. For obstacle avoidance, a mathematical potential function is used, which formulates the repulsive force between the AUV and the solid obstacles intersecting the desired path. Numerical simulations are carried out to study the efficacy of the proposed controllers and the results are observed. To reduce the values of the overshoots and steady-state errors identified due to the application of PFPD controller a PFAPD controller is designed that drives the AUV along the desired trajectory. From the simulation results, it is observed that the proposed controllers are able to drive the AUV to track the desired path, avoiding the obstacles in an obstacle-rich environment. The results are compared and it is observed that the PFAPD outperforms the PFPD to drive the AUV along the desired trajectory. It is also proved that it is not necessary to employ highly complicated controllers for solving obstacle-avoidance and path-following problems of underactuated AUVs. These problems can be solved with the application of PFAPD controllers.