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The principle of the method is to use online the results of a probabilistic planner to describe the free space in which the planning takes place, by computing a principal component analysis (PCA). This method identifies the locally free directions of the free space. Given that description, our algorithm accelerates the progression along these favored directions. In this way, if the free space appears as a small volume around a sub-manifold of a high-dimensional configuration space, the method overcomes the usual limitations of probabilistic motion planning algorithms and finds a solution quickly. The presented method is theoretically analyzed and experimentally compared with known motion planners.<\/jats:p>","DOI":"10.1177\/0278364911403335","type":"journal-article","created":{"date-parts":[[2011,6,3]],"date-time":"2011-06-03T20:57:18Z","timestamp":1307134638000},"page":"1461-1476","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":35,"title":["Linear dimensionality reduction in random motion planning"],"prefix":"10.1177","volume":"30","author":[{"given":"S\u00e9bastien","family":"Dalibard","sequence":"first","affiliation":[{"name":"LAAS-CNRS, University of Toulouse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Paul","family":"Laumond","sequence":"additional","affiliation":[{"name":"LAAS-CNRS, University of Toulouse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2011,6,3]]},"reference":[{"key":"bibr1-0278364911403335","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2005.I.015"},{"key":"bibr2-0278364911403335","volume-title":"Principles of Robot Motion: Theory, Algorithms, and Implementation","author":"Choset H","year":"2005"},{"key":"bibr3-0278364911403335","volume-title":"Proceedings IEEE International Conference on Robotics and Automation, 2002 (ICRA\u201902)","volume":"2","author":"Cortes J"},{"key":"bibr4-0278364911403335","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-00312-7_29"},{"key":"bibr5-0278364911403335","doi-asserted-by":"publisher","DOI":"10.1155\/S1110865704404120"},{"key":"bibr6-0278364911403335","first-page":"3149","volume-title":"2004 International Conference on Robotics and Automation (ICRA\u20192004)","author":"Ferre E"},{"key":"bibr7-0278364911403335","volume-title":"Proceedings International Conference on Intelligent Autonomous Systems","author":"Geraerts R","year":"2004"},{"key":"bibr8-0278364911403335","first-page":"233","author":"Han L","year":"2000","journal-title":"Algorithmic and Computational Robotics: New Directions. 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