Automation of berthing maneuvers in shipping is a pressing issue as the berthing maneuver is one of the most stressful tasks seafarers undertake. Berthing control problems are often tackled via tracking a predefined trajectory or path. Maintaining a tracking error of zero under an uncertain environment is impossible; the tracking controller is nonetheless required to bring vessels close to desired berths. The tracking controller must prioritize the avoidance of tracking errors that may cause collisions with obstacles. This paper proposes a training method based on reinforcement learning for a trajectory tracking controller that reduces the probability of collisions with static obstacles. Via numerical simulations, we show that the proposed method reduces the probability of collisions during berthing maneuvers. Furthermore, this paper shows the tracking performance in a model experiment.