We discuss the problem of inspecting an underwater structure, such as a submerged ship hull, with an autonomous underwater vehicle (AUV). Unlike a large body of prior work, we focus on planning the views of the AUV to improve the quality of the inspection, rather than maximizing the accuracy of a given data stream. We formulate the inspection planning problem as an extension to Bayesian active learning, and we show connections to recent theoretical guarantees in this area. We rigorously analyze the benefit of adaptive re-planning for such problems, and we prove that the potential benefit of adaptivity can be reduced from an exponential to a constant factor by changing the problem from cost minimization with a constraint on information gain to variance reduction with a constraint on cost. Such analysis allows the use of robust, non-adaptive planning algorithms that perform competitively with adaptive algorithms. Based on our analysis, we propose a method for constructing 3D meshes from sonar-derived point clouds, and we introduce uncertainty modeling through non-parametric Bayesian regression. Finally, we demonstrate the benefit of active inspection planning using sonar data from ship hull inspections with the Bluefin-MIT Hovering AUV.United States. Office of Naval Research (ONR Grant N00014-09-1-0700)United States. Office of Naval Research (ONR Grant N00014-07-1-00738)National Science Foundation (U.S.) (NSF grant 0831728)National Science Foundation (U.S.) (NSF grant CCR-0120778)National Science Foundation (U.S.) (NSF grant CNS-1035866
