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SLAM: Simultaneous Localization and Mapping: Part II BY TIM BAILEY AND HUGH DURRANT-WHYTE. Presented by Chang Young Kim. These slides are based on: Probabilistic Robotics , S. Thrun, W. Burgard, D. Fox, MIT Press, 2005. Many images are also taken from Probabilistic Robotics .

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slam simultaneous localization and mapping part ii by tim bailey and hugh durrant whyte

SLAM: Simultaneous Localization and Mapping: Part IIBY TIM BAILEY AND HUGH DURRANT-WHYTE

Presented by Chang Young Kim

These slides are based on:

Probabilistic Robotics,

S. Thrun, W. Burgard,

D. Fox, MIT Press, 2005

Many images are also taken from

Probabilistic Robotics.

http://www.probabilistic-robotics.com

overview
Overview
  • Review
  • SLAM
    • Reducing complexity
      • State Augmentation
      • Partitioned Updates
      • Sparsification
    • Data association
      • Batch Gating
      • SIFT
      • Multi-Hypothesis
  • Future works
what is slam
What is SLAM?

A robot is exploring an unknown, static environment.

Given:

  • The robot’s controls
  • Observations of nearby features

Estimate:

  • Map of features
  • Path of the robot
terminology

f

g

f

f

g

u

u

u

u

z

z

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=

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2

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:

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)

µ

z

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x

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Terminology
  • Robot State (or pose):
    • Position and heading
  • Robot Controls:
    • Robot motion and manipulation
  • Sensor Measurements:
    • Range scans, images, etc.
  • Landmark or Map:
    • Landmarks or Map

}

terminology1
Terminology
  • Observation model: or
    • The probability of a measurement zt given that the robot is at position xt and map m.
  • Motion Model:
    • The posterior probability that action ut carries the robot from xt-1 to xt.
slam algorithm
SLAM algorithm
  • Prediction
  • Update
ekf state space model
EKF State Space Model
  • Prediction
  • Update

where

7

ekf slam
Maintaining values: Bel(xt,m) and its covariance matrix Pt.

Map with N landmarks:(3+2N)-dimensional Gaussian.

EKF-SLAM

8

overview1
Overview
  • Review
  • SLAM
    • Reducing complexity
      • State Augmentation
      • Partitioned Updates
      • Sparsification
    • Data association
      • Batch Gating
      • SIFT
      • Multi-Hypothesis
  • Future works
ekf slam complexity
Complexity O(N3) with N landmarks due to the covariance matrix and matrix multiplication of Jacobian.

Can handle hundreds of dimensions?

It can be reduced by approximation methods:

State Augmentation for the prediction stage

Partitioned Updates for the update stage

Sparsification using an information form

EKF-SLAM : Complexity

10

state augmentation
State Augmentation

Prediction :

  • Solution : State Augmentation
  • Separating the state into an augmented states
  • Update only affected matrixes

Static

11

state augmentation1
State Augmentation

O(N3)

Covariance prediction

State Augmentation

O(N)

Covariance prediction

Static

partitioned updates
Partitioned Updates

Update :

  • Solution : Partitioned Update with local submap.
  • Confines the map to a small local region.
  • Only Updates the small local region.
  • Updates the whole map only at a much lower frequency

13

partitioned updates1
Partitioned Updates

Updated by Local SLAM

Local State :

Global State:

Periodically registers

sparsification
Sparsification
  • State Bel(xt ,m) and covariance matrix Ptare Gaussian probability density which,
    • implicitly describes the two central moments of Gaussian
  • Using Moment or Information Form
  • Sparsification Pt Yt
    • Many of none diagonal components are very close to 0
    •  they can be set to zero.
sparsification1
Sparsification

O(N3)

Covariance prediction

Sparsification using the information form

O(N)

Covariance prediction

overview2
Overview
  • Review
  • SLAM
    • Computational complexity
      • State Augmentation
      • Partitioned Updates
      • Sparsification
    • Data association
      • Batch Gating
      • SIFT
      • Multi-Hypothesis
  • Future works
data association problem
Data Association Problem
  • Which observation belongs to which landmark?
  • A robust SLAM must consider possible data associations
  • Solutions: three key methods :
    • Batch Gating
    • SIFT
    • Multi-Hypothesis
batch gating
Batch Gating
  • Basic Principle of Batch: RANSAC
  • Gating : constrained by robot position estimation

< taken from T. Bailey, “Mobile robot localization and mapping in extensive outdoor environments,” Ph.D. dissertation>

    • If true robot movement is

==> the left case is chosen by using the gating

slide20
SIFT
  • Batch Gating is not enough for reliable data association
  • SIFT features have “landmark-quality” for SLAM
    • SIFT correspondences tend to be reliable and recognizable under variable conditions

< taken from “Distinctive Image Featuresfrom Scale-Invariant Keypoints”, David G. Lowe – IJCV 2004 >

  • Gating
    • If true robot movement is

==> the left case is chosen by using the gating

multi hypothesis data association

x, y, 

Landmark 1

Landmark 2

Landmark M

Particle

#1

x, y, 

Landmark 1

Landmark 2

Landmark M

Particle

#2

x, y, 

Landmark 1

Landmark 2

Landmark M

Particle

N

Multi-Hypothesis Data Association
  • Multi-hypothesis data association
    • Generate a separate track estimate for each association hypothesis.
    • Low-likelihood tracks are pruned
  • FastSLAM is inherently a Multi-hypothesis solution because its data association is done on a per-particle basis.
per particle data association
Per-Particle Data Association

Was the observation

generated by the red

or the blue landmark?

P(observation|red) = 0.3

P(observation|blue) = 0.7

  • Per-particle data association
    • Pick the most probable match
  • If the probability is too low, generate a new landmark
future woks
Future Woks
  • Large scale mapping
    • including many vehicles
    • in mixed environments
    • with sensor networks and dynamic landmark.
  • The delayed data-fusion concept instead of batch association and iterative smoothing to improve estimation quality and robustness