#### M. L. Rodríguez-Arévalo, J. Neira and J. A. Castellanos, **On the Importance of Uncertainty Representation in Active SLAM**, IEEE Transactions on Robotics, vol. 34, no. 3, pp. 829-834 DOI: 10.1109/TRO.2018.2808902.

The purpose of this work is to highlight the paramount importance of representing and quantifying uncertainty to correctly report the associated confidence of the robot’s location estimate at each time step along its trajectory and therefore decide the correct course of action in an active SLAM mission. We analyze the monotonicity property of different decision-making criteria, both in 2-D and 3-D, with respect to the representation of uncertainty and of the orientation of the robot’s pose. Monotonicity, the property that uncertainty increases as the robot moves, is essential for adequate decision making. We analytically show that, by using differential representations to propagate spatial uncertainties, monotonicity is preserved for all optimality criteria, A-opt, D-opt, and E-opt, and for Shannon’s entropy. We also show that monotonicity does not hold for any criteria in absolute representations using Roll-Pitch-Yaw and Euler angles. Finally, using unit quaternions in absolute representations, the only criteria that preserve monotonicity are D-opt and Shannon’s entropy.