Global A-Optimal Robot Exploration in SLAM

It is well-known that the Kalman filter for simultaneous localization and mapping (SLAM) converges to a fully correlated map in the limit of infinite time and data [1]. However, the rate of convergence of the map has a strong dependence on the order of the observations. We show that conventional exploration algorithms for collecting map data are sub-optimal in both the objective function and choice of optimization procedure. We show that optimizing the a-optimal information measure results in a more accurate map than existing approaches, using a greedy, closed-loop strategy. Secondly, we demonstrate that by restricting the planning to an appropriate policy class, we can tractably find non-greedy, global planning trajectories that produce more accurate maps, explicitly planning to close loops even in open-loop scenarios.