User:Bazuz/sandbox/Simultaneous localization and mapping

2005 DARPA Grand Challenge winner STANLEY performed SLAM as part of its autonomous driving system

A map generated by a SLAM Robot.

In navigation, robotic mapping and odometry for virtual reality or augmented reality, simultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it. While this initially appears to be a chicken-and-egg problem there are several algorithms known for solving it, at least approximately, in tractable time for certain environments. Popular approximate solution methods include the particle filter, extended Kalman filter, Covariance intersection, and GraphSLAM.

SLAM algorithms are tailored to the available resources, hence not aimed at perfection, but at operational compliance. Published approaches are employed in self-driving cars, unmanned aerial vehicles, autonomous underwater vehicles, planetary rovers, newer domestic robots and even inside the human body.

See also

• Computational photography
• Visual odometry
• Kalman filter
• Inverse depth parametrization
• List of SLAM Methods
• The Mobile Robot Programming Toolkit (MRPT) project: A set of open-source, cross-platform libraries covering SLAM through particle filtering and Kalman Filtering.
• Monte Carlo localization
• Multi Autonomous Ground-robotic International Challenge: A $1.6 million international challenge requiring multiple vehicles to collaboratively map a large area
• Neato Robotics
• Particle filter
• Project Tango
• Robotic mapping
• Stanley, a DARPA Grand Challenge vehicle winner using SLAM techniques
• Stereophotogrammetry
• Structure from motion.

History

A seminal work in SLAM is the research of R.C. Smith and P. Cheeseman on the representation and estimation of spatial uncertainty in 1986. Other pioneering work in this field was conducted by the research group of Hugh F. Durrant-Whyte in the early 1990s. which showed that solutions to SLAM exist in the infinite data limit. This finding motivates the search for algorithms which are computationally tractable and approximate the solution.

The self-driving STANLEY and JUNIOR cars, led by Sebastian Thrun, won the DARPA Grand Challenge and came second in the DARPA Urban Challenge in the 2000s, and included SLAM systems, bringing SLAM to worldwide attention. Mass-market SLAM implementations can now be found in consumer robot vacuum cleaners.

Optional: mathematical formulation

Given a series of controls $u_{t}$ and sensor observations $o_{t}$ over discrete time steps $t$, the SLAM problem is to compute an estimate of the agent's location $x_{t}$ and a map of the environment $m_{t}$. All quantities are usually probabilistic, so the objective is to compute:

$P(m_{t+1},x_{t+1}|o_{1:t+1},u_{1:t})$

Applying Bayes' rule gives a framework for sequentially updating the location posteriors, given a map and a transition function $P(x_{t}|x_{t-1})$,

$P(x_{t}|o_{1:t},u_{1:t},m_{t})=\sum _{m_{t-1}}P(o_{t}|x_{t},m_{t},u_{1:t})\sum _{x_{t-1}}P(x_{t}|x_{t-1})P(x_{t-1}|m_{t},o_{1:t-1},u_{1:t})/Z$

Similarly the map can be updated sequentially by

$P(m_{t}|x_{t},o_{1:t},u_{1:t})=\sum _{x_{t}}\sum _{m_{t}}P(m_{t}|x_{t},m_{t-1},o_{t},u_{1:t})P(m_{t-1},x_{t}|o_{1:t-1},m_{t-1},u_{1:t})$

Like many inference problems, the solutions to inferring the two variables together can be found, to a local optimum solution, by alternating updates of the two beliefs in a form of EM algorithm.

External links

• Probabilistic Robotics by Sebastian Thrun, Wolfram Burgard and Dieter Fox with a clear overview of SLAM.
• SLAM For Dummies (A Tutorial Approach to Simultaneous Localization and Mapping).
• Andrew Davison research page at the Department of Computing, Imperial College London about SLAM using vision.
• openslam.org A good collection of open source code and explanations of SLAM.
• Matlab Toolbox of Kalman Filtering applied to Simultaneous Localization and Mapping Vehicle moving in 1D, 2D and 3D.
• FootSLAM research page at DLR including the related Wifi SLAM and PlaceSLAM approaches.
• SLAM lecture Online SLAM lecture based on Python.