On mutual information-based control of range sensing robots for mapping applications

In this paper we examine the correlation between the information content and the spatial realization of range measurements taken by a mapping robot. To do so, we consider the task of constructing an occupancy grid map with a binary Bayesian filter. Using a beam-based sensor model (versus an additive white Gaussian noise model), we prove that any controller tasked to maximize a mutual information reward function is eventually attracted to unexplored space. This intuitive behavior is derived solely from the geometric dependencies of the occupancy grid mapping algorithm and the monotonic properties of mutual information. Since it is dependent on both the robot’s position and the uncertainty of the surrounding cells, mutual information encodes geometric relationships that are fundamental to robot control, thus yielding geometrically relevant reward surfaces on which the robot can navigate. We also provide an algorithmic implementation for computing mutual information and show that its worst-case time and space complexities are quadratic and linear, respectively, with respect to the map’s spatial resolution. Lastly, we present the results of experiments employing an omnidirectional ground robot equipped with a laser range finder. Our experimental results support our theoretical and computational findings.