RDL VL 05 Mapping

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lecture05-mapping-0.pdf

Grid Maps

Grid Maps

• Geometric model of the environment.
• The 2D world plane is divided into grid cells.
• Map cells can be free or occupied.
• The robot can only navigate in the free cells.
• It is a dense representation of the world. I Suitable for indoor environments.

Occupancy Grid Maps

Binary cells

either free or occupied

Probabilistic cells

The cell occupancy is modelled by a binary random variable.
Map occupancy probabilities:

• Free cell: $p(mi)=0$
• Occupied cell: $p(mi)=1$
• No knowledge: $p(mi)=0.5$

Assumptions:

• Cells are independent of each other.
• Range measurement $z_t$ only depends on current robot pose $x_t$ (Markov property)

Algorithm

Possible states

• p_occupied
• p_prior (unchanged)
• p_free

Inverse Sensor Model

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Scan mapping Algotithm

• Incrementally align two consecutive laser scanner measurements.
• Stitch the laser scans to create a map.
• The transformation between two measurements is used in robot Localization.

Example: Interactive closest Point

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Feature Maps

Feature Maps

• The environment is represented by a set of observed features.
• Features are obstacles in the world identified by sensor readings (e.g. laser scanner, camera).
• The robot navigates based on the distance and heading w.r.t. the features in the map.
• It is a sparse representation of the world.
• Suitable for outdoor environments.

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Loop closure

Loop closure

• Loop closing is the task of deciding whether the robot has returned to a previously visited area.
• Used in SLAM to correct the drift in mapping and localization.
• Approach: identify features that have been perceived in the past.
• When a match (i.e. loop closure) is detected, update the previous map and position estimates.

used in Grid Maps

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Bayes’ Theorem

Bayes’ Theorem

$P(A|B)=\frac{P(A|B)P(A)}{P(B)}$
$P(A|B)$ ⇒ probability of hypothesis A given data B
(posterior belief distribution)

$P(B|A)$ ⇒ likelihood of data B given hypothesis A

$P(A)$ ⇒ independent probability of hypothesis A
(prior belief distribution)

$P(B)$ ⇒ independent probability of data B

Example

Bayes Filter

Probabilistic method to estimate an unknown probability density function (PDF) recursively over time using incoming sensor measurements and a mathematical process model.

Binary Bayes Filter

Probability density function (PDF) of a binary variable.

Task

• Cleaning

• Resteraunte

• Security

• Grid based mapping

Challenges

• Fast Moving Objects

Von Sensor Daten

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ROS2 Mapping Libraries

ROS2 Mapping Libraries

• SLAM Gmapping
• Hector SLAM
  • Published by TU Darmstadt in 2011
  • It performs fast online learning of occupancy Grid Maps.
  • Low computational resources.
  • Uses Lidar and IMU data, but no odometry.
  • SLAM without Loop closure.
  • Link: http://wiki.ros.org/hector_slam
• Cartographer
  • Published by Google Research in 2016.
  • It works with a variety of sensor configurations (e.g. Lidar, IMU, cameras).
  • It implements the scan matching algorithm.
  • It performs local and global SLAM (Loop closure).
  • Link: http://wiki.ros.org/cartographer
• SLAM Toolbox
  • Published by Steve Macenski et al. in 2021 and is currently the supported ROS localization and mapping package.
  • Maps large and dynamic spaces.
  • Able to continue mapping from prior sessions.
  • Implements Loop closure.
  • Link: http://wiki.ros.org/slam_toolbox

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