Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions

dc.contributor.author Carlone, Luca
dc.contributor.author Rosen, David W.
dc.contributor.author Calafiore, Giuseppe
dc.contributor.author Leonard, John J.
dc.contributor.author Dellaert, Frank
dc.contributor.corporatename Georgia Institute of Technology. Institute for Robotics and Intelligent Machines en_US
dc.contributor.corporatename Georgia Institute of Technology. College of Computing en_US
dc.contributor.corporatename Georgia Institute of Technology. School of Interactive Computing en_US
dc.contributor.corporatename Massachusetts Institute of Technology en_US
dc.contributor.corporatename Politecnico di Torino en_US
dc.date.accessioned 2016-07-27T19:18:24Z
dc.date.available 2016-07-27T19:18:24Z
dc.date.issued 2015
dc.description © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. en_US
dc.description DOI: 10.1109/IROS.2015.7353364
dc.description.abstract State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide guarantees on the quality of the estimate. This paper shows that Lagrangian duality is a powerful tool to assess the quality of a given candidate solution. Our contribution is threefold. First, we discuss a revised formulation of the SLAM inference problem. We show that this formulation is probabilistically grounded and has the advantage of leading to an optimization problem with quadratic objective. The second contribution is the derivation of the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex) semidefinite program, which can be solved reliably and globally by off-the-shelf solvers. The third contribution is to discuss the relation between the original SLAM problem and its dual. We show that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality. Moreover, when the duality gap is zero, one can compute a guaranteed optimal SLAM solution from the dual problem, circumventing non-convex optimization. We present extensive (real and simulated) experiments supporting our claims and discuss practical relevance and open problems. en_US
dc.embargo.terms null en_US
dc.identifier.citation Carlone, L., Rosen, D. M., Calafiore, G., Leonard, J. J., & Dellaert, F. (2015). Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2015), September 28-October 2, 2015, pp. 125-132. en_US
dc.identifier.doi 10.1109/IROS.2015.7353364
dc.identifier.uri http://hdl.handle.net/1853/55415
dc.language.iso en_US en_US
dc.publisher Georgia Institute of Technology en_US
dc.publisher.original Institute of Electrical and Electronics Engineers
dc.subject Lagrangian duality en_US
dc.subject Semidefinite program en_US
dc.subject Simultaneous localization and mapping en_US
dc.subject SLAM
dc.title Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions en_US
dc.type Text
dc.type.genre Proceedings
dspace.entity.type Publication
local.contributor.author Rosen, David W.
local.contributor.author Dellaert, Frank
local.contributor.corporatename Institute for Robotics and Intelligent Machines (IRIM)
relation.isAuthorOfPublication 8670f309-1b84-4a52-9641-bbb31a1d8af6
relation.isAuthorOfPublication dac80074-d9d8-4358-b6eb-397d95bdc868
relation.isOrgUnitOfPublication 66259949-abfd-45c2-9dcc-5a6f2c013bcf
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