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Reliable Range based Localization and SLAM

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Alternative methods such as range-only sensors have not received enough ... Find all pair wise intersections of a set of range measurements ... – PowerPoint PPT presentation

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Title: Reliable Range based Localization and SLAM


1
Reliable Range based Localization and SLAM
  • Joseph Djugash
  • Masters Student
  • Presenting work done by
  • Sanjiv Singh, George Kantor, Peter Corke and
    Derek Kurth

2
Motivation
3
Motivation
4
Introduction
  • Much research has been done to perform
    localization under normal/ideal conditions
  • Classical sensors fail to provide reliable
    results under non-ideal scenarios
  • Alternative methods such as range-only sensors
    have not received enough attention in the
    research field

5
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • SLAM
  • Future Work

6
Range Bearing Sensors
  • Errors in estimation of robot location and
    landmark locations are represented as ellipses.
  • Each landmark ellipse contains the error of both
    the robots current error and the error within
    the sensors.

7
Range-Only Sensors
  • We are provided with an annulus instead of an
    ellipse.
  • Extending classical approaches to localization
    requires additional considerations.

8
Range-Only Sensors
9
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • Kalman Filter
  • Particle Filter
  • Results
  • SLAM
  • Future Work

10
Predictor ? Corrector
  • Iterative Process
  • Predict the new state (and its uncertainty) based
    on current state and process model
  • Correct state estimate with new measurement

11
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • Kalman Filter
  • Particle Filter
  • Results
  • SLAM
  • Future Work

12
Kalman Filter
  • Belief Representation
  • Error Function Gaussian
  • Mean and Covariance
  • Process Model (State qk xr, yr, ?rT)
  • qk Aqk-1 Buk-1 wk-1
  • Pk APk-1AT BUk-1BT Qk-1
  • Measurement Model
  • qk qk-1 Kk(zk Hqk-1)
  • Kk PkHT(HPkHT Rk)-1
  • Pk (I KkH)Pk












13
Kalman Filter
  • Belief Representation
  • Error Function Gaussian
  • Mean and Covariance
  • Process Model (State qk xr, yr, ?rT)
  • qk Aqk-1 Buk-1 wk-1
  • Pk APk-1AT BUk-1BT Qk-1
  • Measurement Model
  • qk qk-1 Kk(zk Hqk-1)
  • Kk PkHT(HPkHT Rk)-1
  • Pk (I KkH)Pk












14
Kalman Filter
  • Belief Representation
  • Error Function Gaussian
  • Mean and Covariance
  • Process Model (State qk xr, yr, ?rT)
  • qk Aqk-1 Buk-1 wk-1
  • Pk APk-1AT BUk-1BT Qk-1
  • Measurement Model
  • qk qk-1 Kk(zk Hqk-1)
  • Kk PkHT(HPkHT Rk)-1
  • Pk (I KkH)Pk










Estimated range to beacon


15
Kalman Filter
  • Advantages
  • Computationally Efficient
  • Able to handle high dimensionality with limited
    or no extra computational cost
  • Handles short periods of sensor silence
  • Disadvantages
  • Able to represent only Gaussian distributions
  • Assumptions are too restrictive

16
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • Kalman Filter
  • Particle Filter
  • Results
  • SLAM
  • Future Work

17
Particle Filter
  • Representing belief by sets of samples or
    particles
  • Each particle is represented as (xp, yp),
    (orientation is not maintained)
  • Updating procedure is a sequential importance
    sampling approach with re-sampling
  • Sampling Standard Gaussian Formula
  • P(xrm) e( )
  • Where rm is the measured range and r is the range
    estimate from the particle to beacon


18
Particle Filter
  • Advantages
  • Able to represent arbitrary density
  • Converging to true posterior even for
    non-Gaussian and nonlinear system
  • Efficient in the sense that particles tend to
    focus on regions with high probability
  • Disadvantages
  • Worst-case complexity grows exponentially in the
    dimensions

19
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • Kalman Filter
  • Particle Filter
  • Results
  • SLAM
  • Future Work

20
The Experiments
21
Dead Reckoning Results
22
Kalman Filter Results
XTE ATE
Mean Abs. Error 0.5539 m 0.3976 m
Max. Error 1.9033 m 2.0447 m
Std (s) 0.4173 m 0.3558 m
23
Particle Filter Results
XTE ATE
Mean Abs. Error 2.8200 m 2.0898 m
Max. Error 8.6526 m 7.7012 m
Std (s) 1.0345 m 1.1943 m
24
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • SLAM
  • Batch Slam
  • Kalman Filter
  • Results
  • Future Work

25
SLAM
  • Beacon Locations are unknown
  • Measurements are used to predict beacon locations
  • Due to errors in measurements, not all
    measurements can be weighed equally
  • Consistency between inliers help provide a
    reliable estimates

26
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • SLAM
  • Batch Slam
  • Kalman Filter
  • Results
  • Future Work

27
Batch Slam
  • Approaches the SLAM problem by solving two
    non-linear optimization problems
  • One to generate the initial estimate of the
    beacon locations
  • One to simultaneously refine the vehicle and
    beacon estimates
  • Estimated Beacon locations are feed to the Kalman
    filter localization algorithm

28
Batch Slam
  • Initializing the Beacons
  • Assumes robots odometry is perfect
  • Using the range measurements predicts the most
    likely beacon estimates
  • Estimates are acquired by minimizing the cost
    function
  • and,
  • Refining estimates
  • Assumes error distributions of each measurement
    is independent
  • Most likely beacon positions and vehicle relative
    motion can be found by minimizing the cost
    function

29
Batch Slam
  • Advantages
  • Produces accurate estimates of beacon locations
  • Requires very little data to acquire good results
  • Disadvantages
  • Computationally Expensive
  • Requires fairly accurate dead reckoning data to
    acquire its initial beacon estimate

30
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • SLAM
  • Batch Slam
  • Kalman Filter
  • Results
  • Future Work

31
Beacon Initialization
  • Find all pair wise intersections of a set of
    range measurements
  • Create a histogram grid with the circle
    intersections
  • Find the first two peaks on the grid
  • When the ratio between the peaks reaches a
    threshold (set to 2), declare the higher of the
    peaks as the beacon location

32
Beacon Initialization
33
Kalman Filter SLAM
  • Kalman filter localization algorithm can be
    easily extended for SLAM
  • The state vector becomes
  • qk xr, yr, ?k, xb1, yb1, , xbn, ybnT
  • As new beacons are initialized, expand the state
    vector and covariance matrix to the correct
    dimension
  • q 2n3
  • P 2n3 square
  • where n is the number of initialized beacons

34
Kalman Filter SLAM
  • Advantages
  • Similar to Kalman Filter Localization
  • Settles to locally accurate solution
  • Disadvantages
  • Wrong Beacon Initialization could lead to
    diverged solution

35
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • SLAM
  • Batch Slam
  • Kalman Filter
  • Results
  • Future Work

36
Kalman Filter SLAM Results
Raw XTE ATE
Mean Abs. Error 8.5544 m 5.1776 m
Max. Error 18.0817 m 19.2575 m
Std (s) 4.8216 m 4.5486 m
Aff. Trans. XTE ATE
Mean Abs. Error 0.7297 m 0.6872 m
Max. Error 2.6787 m 2.7621 m
Std (s) 0.6004 m 0.5745 m
37
Kalman Filter Batch Slam Results (Another
Example)
Batch Slam using only 5 of data set
Batch Slam XTE ATE
Mean Abs. Error 1.5038 m 2.0871 m
Max. Error 4.9149 m 5.8212 m
Std (s) 1.0527 m 1.4968 m
38
Outline
  • Introduction
  • Range-Only Sensor
  • Localization
  • SLAM
  • Future Work

39
Future Work
  • Develop robust algorithms that produce reliable
    results with poor sensor data
  • Develop an approach that relies on multiple
    algorithms at various points during the data set
    to produce better results

40
Questions
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