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A Discussion of Simultaneous Localization and Mapping

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Abstract

This paper aims at a discussion of the structure of the SLAM problem. The analysis is not strictly formal but based both on informal studies and mathematical derivation. The first part highlights the structure of uncertainty of an estimated map with the key result being “Certainty of Relations despite Uncertainty of Positions”. A formal proof for approximate sparsity of so-called information matrices occurring in SLAM is sketched. It supports the above mentioned characterization and provides a foundation for algorithms based on sparse information matrices.

Further, issues of nonlinearity and the duality between information and covariance matrices are discussed and related to common methods for solving SLAM.

Finally, three requirements concerning map quality, storage space and computation time an ideal SLAM solution should have are proposed. The current state of the art is discussed with respect to these requirements including a formal specification of the term “map quality”.

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  1. Department of Computer Science, Universität Bremen, Germany

    Udo Frese

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  1. Udo Frese
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Correspondence to Udo Frese.

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This article is based on research conducted during the author's Ph.D. studies at the German Aerospace Center (DLR) in Oberpfaffenhofen.

Udo Frese was born in Minden, Germany in 1972. He received the Diploma degree in computer science from the University of Paderborn in 1997. From 1998 to 2003 he was a Ph.D. student at the German Aerospace Center in Oberpfaffenhofen. In 2004 he joined University of Bremen. His research interests are mobile robotic, simultaneous localization and mapping and computer vision.

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Frese, U. A Discussion of Simultaneous Localization and Mapping. Auton Robot 20, 25–42 (2006). https://doi.org/10.1007/s10514-006-5735-x

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