Introduction to SLAM

In this lesson we give a short overview of Simultaneous Localization and Mapping (SLAM) — what it is, why we need it, and how it works at a high level. We will also outline the main components, the approaches we'll study, some helpful prerequisites, and provide suggested readings.

What is SLAM?

SLAM is the problem of estimating a robot's pose and a map of the environment at the same time. Formally, given controls $u_{1:T}$ and observations $z_{1:T}$, SLAM estimates the joint posterior:

where $x_{1:T}$ are the robot poses and $m$ is the map.

It is often described as a chicken-and-egg problem:

• Localization: estimating the robot's position and orientation (pose).
• Mapping: building a consistent representation of the world.
• SLAM: solving both simultaneously, where each depends on the other.

This coupling makes SLAM challenging:

• A map helps localization, but
• good localization is required to build a good map.

Typical assumptions:

• Static world during mapping.
• Markovian process/measurement models.
• Conditional independence structure.

Why SLAM?

SLAM is a fundamental capability for autonomous robotics:

• Enables operation in unknown and infrastructure-free environments.
• Underpins most navigation and exploration systems.
• Critical for autonomous driving, search and rescue, inspection, warehouses, planetary exploration, and more.

How does SLAM work?

SLAM combines sensor data with probabilistic estimation to track both the robot's poses and the state of the map.

Common sensors:

• Visual SLAM (vSLAM): monocular, stereo or RGB-D cameras that extract and track image features (lines, edges, etc.) or directly align intensity/depth; great when there are distinct visual cues.
• Range-based SLAM: 2D/3D LiDAR, radar, sonar producing sparse or dense point clouds; robust to lighting and often more geometrically accurate; primarily scan matching.
• Multi-modal fusion: fuses IMU, wheel odometry, GPS (if available), LiDAR or vision to increase robustness and reduce drift (e.g., LiDAR-Visual–Inertial odometry).

Two main components:

• Front-end: acquires raw sensor data, extracts key features, and performs data association. It converts measurements into an intermediate representation — landmark observations or relative-pose constraints — that can be fed to the estimator.
• Back-end: performs estimation and optimization over those inputs to produce a consistent robot trajectory and map. It solves the underlying state-estimation / optimization problem to refine poses and landmarks.

Both front-end and back-end operate in a loop, continuously updating the map and robot pose in real time.

Main SLAM approaches

• Kalman Filter family (EKF / UKF): recursive prediction + correction using Gaussian models. EKF-SLAM was the first practical SLAM algorithm.
• Particle filters (FastSLAM): represent uncertainty with samples (particles). Particle filtering uses a set of particles to represent the posterior distribution of a stochastic process given the noisy and/or partial observations.
• Least squares (graph-based): model SLAM as a graph optimization problem — nodes are robot poses and landmarks, edges are constraints (odometry, observations) — and optimize to find the most consistent solution that minimizes an objective function.

SLAM timeline

A condensed history of the field. Click any era to expand its references.

Prerequisites (nice to have)

Knowledge of the following will help you understand and derive the main SLAM concepts — you don't need to be an expert.

• Probability / statistics: Bayes rule, Gaussians, MAP / MLE, etc.
• Linear algebra: vectors, matrix multiplication, eigen decomposition, etc.
• Calculus and analysis: Taylor expansion, derivatives, etc.
• Optimization: Gauss–Newton, Levenberg–Marquardt, etc.
• Programming: Python (for the code notebooks).

Reading material

Videos

• If you are serious about SLAM and want an in-depth study, this series is a must:
  • Full SLAM Course on YouTube — Prof. Cyrill Stachniss
• A nice tutorial on running SLAM in ROS 2:
  • Easy SLAM with ROS using slam_toolbox

Books

• An excellent book on probabilistic robotics with in-depth treatment:
  • Sebastian Thrun, Wolfram Burgard, and Dieter Fox. Probabilistic Robotics. MIT Press, 2005.
• An introduction to robotics in general that includes localization:
  • Peter Corke. Robotics, Vision and Control: Fundamental Algorithms in MATLAB (2nd ed.). Springer, 2017.
• Pure state estimation for robotics:
  • Timothy D. Barfoot. State Estimation for Robotics (2nd ed.). Cambridge University Press, 2024.
• The most recent and complete handbook on SLAM:
  • From Localization and Mapping to Spatial Intelligence — SLAM Handbook
• A tutorial approach to SLAM:
  • SLAM for Dummies

Papers

• A brief overview on the history of SLAM and its solutions:
  • Simultaneous Localization and Mapping — Part I & Part II
• A tutorial specifically for Graph-based SLAM:
  • A Tutorial on Graph-Based SLAM
• A tutorial specifically for particle-filter localization:
  • A Particle Filter Tutorial for Mobile Robot Localization

Other

• A book on Bayesian and Kalman filters with Python implementations — by Roger Labbe:
  • Kalman-and-Bayesian-Filters-in-Python
• Slides giving an overview of SLAM methods — by Marios Xanthidis et al.:
  • SLAM Tutorial Slides
• A GitHub with Python functions for SLAM — by Daniels Kraus:
  • SLAM-python
• A nice blog post on Graph SLAM — by Federico Sarrocco:
  • Graph SLAM: From Theory to Implementation
• Pose Graph SLAM 2D/3D implementations using GTSAM — by Dhyey Manish Rajani:
  • Pose-Graph-SLAM
• More on Recursive Bayesian Filtering — by Michael Rubinstein:
  • Introduction to Recursive Bayesian Filtering
• Last but not least, the SLAM toolbox for ROS 2 — by Steve Macenski:
  • slam_toolbox