1
$\begingroup$

I was reading about the SLAM problem in a research paper, Multi-robot Simultaneous Localization and Mapping using Particle Filters by Andrew Howard.

What does '$m$' mean here?

The SLAM problem for a single robot is treated as follows.

Let $x_{1:t}$ denote a sequence of robot poses at times 1, 2, ...t, let $z_{1:t}$ denote a corresponding sequence of observations, and let $u_{0:t−1}$ denote the sequence of actions executed by the robot.

Our (intermediate) aim is to compute the posterior probability $p(x_{1:t}, m | z_{1:t}, u_{0:t−1}, x_0)$ over the robot trajectory $x_{1:t}$ and map $m$, given some initial pose $x_0$. We write this as the product of two factors:

$p(x_{1:t}, m | z_{1:t}, u_{0:t−1}, x_0) = p(m | x_{1:t}, z_{1:t}, > u_{0:t−1}, x_0)p(x_{1:t} | z_{1:t}, u_{0:t−1}, x_0)$.

$\endgroup$
2
  • 1
    $\begingroup$ Please format using MathJax in future, to make the question more legible. Now it should be obvious what m represents, as it is clearly stated in the definition. $\endgroup$ – Greenonline Feb 27 at 9:33
  • 1
    $\begingroup$ If you use a quote, or an excerpt, from a research paper, you should include a title, author and a link to the source. $\endgroup$ – Greenonline Feb 27 at 13:48
3
$\begingroup$

m is an abstract representation of the map. In practice, m typically is some form of parametric model, whose parameters need to be estimated. Some very typical models:

  • A set of point locations of objects in space. m becomes a vector of (x,y,[z]) coordinates (each for one object).

  • A grid of cells which can have distinct states, in the simplest form just free/occupied. m becomes a vector of cell states (which each refer to a certain part of 2d/3d space).

The formula given above is a very abstract problem formulation. For actual solutions allowing calculation, it is required to choose a concrete state representation (where SLAM state = combination of environment state + robot location), as well as certain models describing the robot's(/environment's) behavior and the sensor used to observe.

$\endgroup$
0
$\begingroup$

It represents the map. It is mentioned above the product.

$\endgroup$
1
  • $\begingroup$ Welcome to Robotics skpro19. Thanks for your answer but we are looking for comprehensive answers that provide some explanation and context. Very short answers cannot do this, so please edit your answer to explain why it is right, ideally with citations. Answers that don't include explanations may be removed. See How to Answer for more info. $\endgroup$ – Ben Feb 28 at 0:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.