In Japan, where the birthrates are declining and the population is aging rapidly, there is a critical shortage of medical and nursing personnel to support the elderly. Under these circumstances, various monitoring systems using robots have been proposed.In this study, we focused on the path planning method for robots and applied Deep Reinforcement Learning, which has been shown to be capable of creating a path that takes various environmental information into account, to a monitoring robot. In this paper, in order to recognize a map as an image in an environment where the destination is moving, we perform path finding using a Convolutional Neural Network (CNN) and three types of deep reinforcement learning algorithms, which are effective for image recognition, and evaluate each path finding method by simulation.