Abstract

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 [3]. However, if the exploration trajectory accumulates new information about the world slowly, then convergence of the map can be slow. By making use of the recent development of constant-time SLAM algorithms, we show how information gain for a single step can be computed in constant time. We describe the concept of an “information surface”, which represents at each point in the environment the total potential information gain that results from a complete trajectory to that point. We demonstrate an algorithm for finding this surface that leads to an efficient, global planning algorithm for exploration that is linear in the number of states to be explored in the world and the length of the trajectory. 1

Citations