Abstract. Autonomous exploration is a frequently addressed problem in the robotics community. This paper presents an approach to mobile robot exploration that takes into account that the robot acts in the three-dimensional space. Our approach can build compact three-dimensional models autonomously and is able to deal with negative obstacles such as abysms. It applies a decision-theoretic framework which considers the uncertainty in the map to evaluate potential actions. Thereby, it trades off the cost of executing an action with the expected information gain taking into account possible sensor measurements. We present experimental results obtained with a real robot and in simulation.