  Autonomous robot operation in unstructured and unknown environments requires
efficient techniques for mapping and exploration using streaming range and
visual observations. Information-based exploration techniques, such as
Cauchy-Schwarz quadratic mutual information (CSQMI) and fast Shannon mutual
information (FSMI), have successfully achieved active binary occupancy mapping
with range measurements. However, as we envision robots performing complex
tasks specified with semantically meaningful concepts, it is necessary to
capture semantics in the measurements, map representation, and exploration
objective. This work presents Semantic octree mapping and Shannon Mutual
Information (SSMI) computation for robot exploration. We develop a Bayesian
multi-class mapping algorithm based on an octree data structure, where each
voxel maintains a categorical distribution over semantic classes. We derive a
closed-form efficiently-computable lower bound of the Shannon mutual
information between a multi-class octomap and a set of range-category
measurements using semantic run-length encoding of the sensor rays. The bound
allows rapid evaluation of many potential robot trajectories for autonomous
exploration and mapping. We compare our method against state-of-the-art
exploration techniques and apply it in a variety of simulated and real-world
experiments.
