Introduction to Mobile Robotics EKF Localization Wolfram Burgard, - - PowerPoint PPT Presentation

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Introduction to Mobile Robotics EKF Localization Wolfram Burgard, - - PowerPoint PPT Presentation

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Introduction to Mobile Robotics EKF Localization Wolfram Burgard, Cyrill Stachniss, Maren Bennewitz, Kai Arras Slides by Kai Arras and Wolfram Burgard Last update: June 2010 Localization Using sensory information to locate the robot in

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SLIDE 1

Wolfram Burgard, Cyrill Stachniss, Maren Bennewitz, Kai Arras

EKF Localization Introduction to Mobile Robotics

Slides by Kai Arras and Wolfram Burgard Last update: June 2010

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Localization

  • Given
  • Map of the environment.
  • Sequence of sensor measurements.
  • Wanted
  • Estimate of the robot’s position.
  • Problem classes
  • Position tracking
  • Global localization
  • Kidnapped robot problem (recovery)

“Using sensory information to locate the robot in its environment is the most fundamental problem to providing a mobile robot with autonomous capabilities.” [Cox ’91]

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Landmark-based Localization

EKF Localization: Basic Cycle

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Landmark-based Localization

EKF Localization: Basic Cycle

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Landmark-based Localization

EKF Localization: Basic Cycle

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raw sensory data landmarks innovation from matched landmarks predicted measurements in sensor coordinates landmarks in global coordinates encoder measurements predicted state posterior state

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State Prediction (Odometry)

Landmark-based Localization

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Control uk: wheel displacements sl , sr Error model: linear growth Nonlinear process model f :

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State Prediction (Odometry)

Landmark-based Localization

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Control uk: wheel displacements sl , sr Error model: linear growth Nonlinear process model f :

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SLIDE 8

Landmark-based Localization

Landmark Extraction (Observation)

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Extracted lines Hessian line model Extracted lines in model space Raw laser range data

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Landmark-based Localization

Measurement Prediction

  • ...is a coordinate frame transform world-to-sensor
  • Given the predicted state (robot pose),

predicts the location and location uncertainty of expected

  • bservations in sensor coordinates

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model space

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Data Association (Matching)

  • Associates predicted measurements

with observations

  • Innovation

and innovation covariance

  • Matching on

significance level alpha

Landmark-based Localization

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model space

Green: observation Magenta: measurement prediction

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SLIDE 11

Landmark-based Localization

Update

  • Kalman gain
  • State update (robot pose)
  • State covariance update

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Red: posterior estimate

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SLIDE 12
  • EKF Localization with Point Features

Landmark-based Localization

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  • 1. EKF_localization ( µt-1, Σt-1, ut, zt, m):

Prediction: 2. 3. 4. 5. 6.

Σt = GtΣt−1Gt

T + BtQtBt T

Bt = ∂g(ut,µt−1) ∂ut = ∂x' ∂vt ∂x' ∂ωt ∂y' ∂vt ∂y' ∂ωt ∂θ' ∂vt ∂θ' ∂ωt                

Qt = α1 |vt |+α2 |ωt |

( )

2

α3 |vt |+α4 |ωt |

( )

2

       

Motion noise Jacobian of g w.r.t location Predicted mean Predicted covariance Jacobian of g w.r.t control

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SLIDE 14
  • 1. EKF_localization ( µt-1, Σt-1, ut, zt, m):

Correction:

2. 3. 4. 5. 6. 7. 8.

St = HtΣ

tHt T + Rt

Rt = σ r

2

σ r

2

     

Predicted measurement mean Innovation covariance Kalman gain Updated mean Updated covariance Jacobian of h w.r.t location

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EKF Prediction Step

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EKF Observation Prediction Step

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EKF Correction Step

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Estimation Sequence (1)

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Estimation Sequence (2)

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Comparison to GroundTruth

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  • [Arras et al. 98]:
  • Laser range-finder and vision
  • High precision (<1cm accuracy)

Courtesy of K. Arras

EKF Localization Example

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EKF Localization Example

  • Line and point landmarks
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EKF Localization Example

  • Line and point landmarks
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EKF Localization Example

  • Expo.02: Swiss National Exhibition 2002
  • Pavilion "Robotics"
  • 11 fully autonomous robots
  • tour guides, entertainer, photographer
  • 12 hours per day
  • 7 days per week
  • 5 months
  • 3,316 km travel distance
  • almost 700,000 visitors
  • 400 visitors per hour
  • Localization method: Line-Based EKF
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EKF Localization Example

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Global EKF Localization

Interpretation tree

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Global EKF Localization

  • Env. Dynamics
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Global EKF Localization

Geometric constraints we can exploit Location independent constraints Unary constraint: intrinsic property of feature e.g. type, color, size Binary constraint: relative measure between features e.g. relative position, angle

All decisions on a significance level α

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SLIDE 29

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Global EKF Localization

Interpretation Tree

[Grimson 1987], [Drumheller 1987], [Castellanos 1996], [Lim 2000]

Algorithm

  • backtracking
  • depth-first
  • recursive
  • uses geometric constraints
  • worst-case exponential

complexity

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Global EKF Localization

Pygmalion

α = 0.95 , p = 2

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Global EKF Localization

α = 0.95 , p = 3

Pygmalion

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Global EKF Localization

α = 0.95 , p = 4 texe: 633 ms

PowerPC at 300 MHz

Pygmalion

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Global EKF Localization

α = 0.95 , p = 5 texe: 633 ms (PowerPC at 300 MHz)

Pygmalion

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05.07.02, 17.23 h

Global EKF Localization

α = 0.999 At Expo.02

[Arras et al. 03]

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texe = 105 ms

05.07.02, 17.23 h

Global EKF Localization

α = 0.999 At Expo.02

[Arras et al. 03]

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05.07.02, 17.32 h

Global EKF Localization

α = 0.999 At Expo.02

[Arras et al. 03]

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SLIDE 37

05.07.02, 17.32 h

Global EKF Localization

α = 0.999 texe = 446 ms At Expo.02

[Arras et al. 03]

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EKF Localization Summary

  • EKF localization implements pose tracking
  • Very efficient and accurate

(positioning error down to subcentimeter)

  • Filter divergence can cause lost situations from

which the EKF cannot recover

  • Industrial applications
  • Global EKF localization can be achieved using

interpretation tree-based data association

  • Worst-case complexity is exponential
  • Fast in practice for small maps