{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T02:05:54Z","timestamp":1778292354390,"version":"3.51.4"},"reference-count":25,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[1996,2,1]],"date-time":"1996-02-01T00:00:00Z","timestamp":823132800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[1996,2]]},"abstract":"<jats:p>This article addresses the problem of manipulation planning in the presence of uncertainty. We begin by reviewing the worst-case planning techniques introduced by Lozano-P\u00e9rez et al. (1984) and show that these methods are limited by an information gap inherent to worst-case analysis techniques. As the task uncertainty increases, these methods fail to produce useful information, even though a high-quality plan may exist. To fill this gap, we present the notion of a probabilistic back projection, which describes the likelihood that a given action will achieve the task goal from a given initial state. We provide a constructive definition of the probabilistic backprojection and related probabilistic models of manipulation task mechanics and show how these models unify and enhance several past results in manipulation planning. These models capture the fundamental nature of the task behavior but appear to be very complex. We present the results of laboratory experiments, comprising over 100,000 grasping trials, that measured the probabilistic backprojection of a grasping task under varying conditions. The resulting data support the probabilistic back projection model and illustrate a task in which probabilistic analysis is required. We sketch methods for computing these models and using them to construct multiple-step plans.<\/jats:p>","DOI":"10.1177\/027836499601500101","type":"journal-article","created":{"date-parts":[[2007,3,4]],"date-time":"2007-03-04T20:24:06Z","timestamp":1173039846000},"page":"1-23","source":"Crossref","is-referenced-by-count":11,"title":["Probabilistic Analysis of Manipulation Tasks: A Conceptual Framework"],"prefix":"10.1177","volume":"15","author":[{"given":"Randy C.","family":"Brost","sequence":"first","affiliation":[{"name":"Intelligent Systems and Robotics Center Sandia National Laboratories Albuquerque, New Mexico 87185"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alan D.","family":"Christiansen","sequence":"additional","affiliation":[{"name":"Department of Computer Science Tulane University New Orleans, Louisiana 70118"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1996,2,1]]},"reference":[{"key":"atypb1","volume-title":"Stochastic Differential Equations: Theory and Applications","author":"Arnold, L.","year":"1992"},{"key":"atypb2","volume-title":"VCP: un module interactif de verification et correction de programme en robotique d'assemblage. 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PhD thesis","author":"Christiansen, A.D.","year":"1992"},{"key":"atypb6","volume-title":"DARPA Workshop on Innovative Approaches to Planning, Scheduling and Control","author":"Christiansen, A.D."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(88)90056-2"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900101"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1177\/027836498700600301"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1109\/JRA.1987.1087096"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1177\/027836498600500102"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1177\/027836499201100501"},{"key":"atypb13","volume-title":"Introduction to Stochastic Differential Equations","author":"Gard, T.C.","year":"1988"},{"key":"atypb14","volume-title":"(June). Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies. 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