Abstract: In accordance with the point stabilization problem for an underactuated AUV in the horizontal plane, we design non-smooth controllers based on the addition of a power integrator approach. First, we avoid the limitations of Brockett's necessary conditions by using the coordinate transformation of the polar coordinate. Second, we divide the transformed system into heading subsystems and distance subsystems by using variable substitution. Thus, the high-order system is transformed into two low-order systems. Third, we design the controllers for the two subsystems by adding a power integrator. Finally, we design the controllers for the case where the starting point coincides with the target point by adding a power integrator. Through the construction of appropriate Lyapunov functions, the velocities, distances, and angles of an underactuated AUV can converge to the desired values. Simulation results demonstrate the effectiveness of the designed controllers.