The autonomy of mobile robots has been greatly improved in recent decades. For these robots, the field of search and rescue is of particular interest. This thesis introduces a new method to let a mobile robot (Spot by Boston Dynamics) explore and search for victims in unknown environments. Existing methods include coverage, which aims to fully cover the environment as efficiently as possible. Exploration methods place more emphasis on gaining knowledge of the environment quickly, but do not actively search for victims. A new method based on active inference is introduced with the aim of combining exploration and exploitation behaviour within one framework. The active inference model is based on a graph representation of the environment, formulated as a POMDP. The framework is built up by incrementally more difficult cases. The first case allows a mobile robot to navigate a known graph to search for victims. The second case assumes a partially unknown graph. Uncertainty about the existence of unvisited nodes is included in the predictions. The final case adjusts the model to the agent's point-cloud- and camera sensors. The framework is then used in a simulation environment, showing how it can be implemented in real-world scenarios. To do so, the active inference framework is combined with techniques from information gain exploration. This thesis shows that active inference can be used in large unknown environments to carry out search and exploration.