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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. <\/jats:p>","DOI":"10.1177\/0278364912467485","type":"journal-article","created":{"date-parts":[[2012,12,1]],"date-time":"2012-12-01T04:52:30Z","timestamp":1354337550000},"page":"3-18","update-policy":"http:\/\/dx.doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":109,"title":["Active planning for underwater inspection and the benefit of adaptivity"],"prefix":"10.1177","volume":"32","author":[{"given":"Geoffrey A","family":"Hollinger","sequence":"first","affiliation":[{"name":"Department of Computer Science, Viterbi School of Engineering, University of Southern California, USA"}]},{"given":"Brendan","family":"Englot","sequence":"additional","affiliation":[{"name":"Center for Ocean Engineering, Department of Mechanical Engineering, Massachusetts Institute of Technology, USA"}]},{"given":"Franz S","family":"Hover","sequence":"additional","affiliation":[{"name":"Center for Ocean Engineering, Department of Mechanical Engineering, Massachusetts Institute of Technology, USA"}]},{"given":"Urbashi","family":"Mitra","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Viterbi School of Engineering, University of Southern California, USA"}]},{"given":"Gaurav S","family":"Sukhatme","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Viterbi School of Engineering, University of Southern California, USA"}]}],"member":"179","published-online":{"date-parts":[[2012,11,30]]},"reference":[{"key":"bibr1-0278364912467485","doi-asserted-by":"publisher","DOI":"10.1007\/BF00133571"},{"key":"bibr2-0278364912467485","doi-asserted-by":"publisher","DOI":"10.1109\/38.909011"},{"volume-title":"The Traveling Salesman Problem: A Computational Study","year":"2006","author":"Applegate DL","key":"bibr3-0278364912467485"},{"key":"bibr4-0278364912467485","doi-asserted-by":"publisher","DOI":"10.1016\/S0262-8856(00)00103-7"},{"key":"bibr5-0278364912467485","unstructured":"Asadpour A, Nazerzadeh H, Saberi A (2009) Maximizing stochastic monotone submodular functions. 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