  Modern robotic systems sense the environment geometrically, through sensors
like cameras, lidar, and sonar, as well as semantically, often through visual
models learned from data, such as object detectors. We aim to develop robots
that can use all of these sources of information for reliable navigation, but
each is corrupted by noise. Rather than assume that object detection will
eventually achieve near perfect performance across the lifetime of a robot, in
this work we represent and cope with the semantic and geometric uncertainty
inherent in methods like object detection. Specifically, we model data
association ambiguity, which is typically non-Gaussian, in a way that is
amenable to solution within the common nonlinear Gaussian formulation of
simultaneous localization and mapping (SLAM). We do so by eliminating data
association variables from the inference process through max-marginalization,
preserving standard Gaussian posterior assumptions. The result is a
max-mixture-type model that accounts for multiple data association hypotheses
as well as incorrect loop closures. We provide experimental results on indoor
and outdoor semantic navigation tasks with noisy odometry and object detection
and find that the ability of the proposed approach to represent multiple
hypotheses, including the "null" hypothesis, gives substantial robustness
advantages in comparison to alternative semantic SLAM approaches.
