FSMI: Fast computation of Shannon Mutual Information for information-theoretic mapping

Information-based mapping algorithms are critical to robot exploration tasks in several applications ranging from disaster response to space exploration. Unfortunately, most existing information-based mapping algorithms are plagued by the computational difficulty of evaluating the Shannon mutual information between potential future sensor measurements and the map. This has lead researchers to develop approximate methods, such as Cauchy-Schwarz Quadratic Mutual Information (CSQMI). In this paper, we propose a new algorithm, called Fast Shannon Mutual Information (FSMI), which is significantly faster than existing methods at computing the exact Shannon mutual information. The key insight behind FSMI is recognizing that the integral over the sensor beam can be evaluated analytically, removing an expensive numerical integration. In addition, we provide a number of approximation techniques for FSMI, which significantly improve computation time. Equipped with these approximation techniques, the FSMI algorithm is more than three orders of magnitude faster than the existing computation for Shannon mutual information; it also outperforms the CSQMI algorithm significantly, being roughly twice as fast, in our experiments.