Skip to main content
Engineering LibreTexts

11: Simultaneous Localization and Mapping

  1. Last updated
  2. Save as PDF
  • Page ID
    14843

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Robots are able to keep track of their position using a model of the noise arising in their drivetrain and their forward kinematics to propagate this error into a spatial probability density function (Section 8.2). The variance of this distribution can shrink as soon as the robot sees uniquely identifiable features with known locations. This can be done for discrete locations using Bayes’ rule (Section 9.2) and for continuous distributions using the Extended Kalman Filter (Section 11.3). The key insight here was that every observation will reduce the variance of the robot’s position estimate. Here, the Kalman filter performs an optimal fusion of two observations by weighting them with their variance, i.e., unreliable information counts less than reliable one. In the robot localization problem, one of the observations is typically the robot’s position estimate whereas the other observation comes from a feature with known location on a map. So far, we have assumed that these locations are known. This chapter will introduce

    • the concept of covariance (or, what all the non-diagonal elements in the covariance matrix are about),
    • how to estimate the robot’s location and that of features in the map at the same time (Simultaneous Localization and Mapping or SLAM)

    This page titled 11: Simultaneous Localization and Mapping is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Nikolaus Correll via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.