Wireless Fidelity (Wi-Fi) based positioning has gained popularity for accurate indoor robot positioning in indoor navigation. In daily life, it is a low-cost solution because Wi-Fi infrastructure is already installed in many indoor areas. In addition, unlike the Global Navigation Satellite System (GNSS), Wi-Fi is more suitable for use indoors because signal blocking, attenuation, and reflection restrictions create a unique pattern in places with many Wi-Fi transmitters, and more precise positioning can be performed than GNSS. This paper proposes a machine learning-based method for Wi-Fi-enabled robot positioning in indoor environments. The contributions of this research include comprehensive 3D position estimation, utilization of existing Wi-Fi infrastructure, and a carefully collected dataset for evaluation. The results indicate that the AdaBoost algorithm attains a notable level of accuracy, utilizing the dBm signal strengths from Wi-Fi access points distributed throughout a four-floor building. The mean average error (MAE) values obtained in three axes with the Adaptive Boosting algorithm are 0.044 on the x-axis, 0.063 on the y-axis, and 0.003 m on the z-axis, respectively. In this study, the importance of various Wi-Fi access points was examined with explainable artificial intelligence methods, and the positioning performances obtained by using data from a smaller number of access points were examined. As a result, even when positioning was conducted with only seven selected Wi-Fi access points, the MAE value was found to be 0.811 for the x-axis, 0.492 for the y-axis, and 0.134 for the Z-axis, respectively.