Mobile robot navigation has been studied for a long time, and it is nowadays widely used in multiple applications. However, it is traditionally focused on two-dimensional geometric characteristics of the environments. There are situations in which robots need to share space with people, so additional aspects, such as social distancing, need to be considered. In this work, an approach for social navigation is presented. A multi-layer model of the environment containing geometric and topological characteristics is built based on the fusion of multiple sensor information. This is later used for navigating the environment considering social distancing from individuals and groups of people. The main novelty is combining fast marching square for path planning and navigation with Gaussian models to represent people. This combination allows to create a continuous representation of the environment from which smooth paths can be extracted and modified according to dynamically captured data. Results prove the practical application of the method on an assistive robot for navigating indoor scenarios, including a behavior for crossing narrow passages. People are efficiently detected and modeled to assure their comfort when robots are around.