Lecture 09: Localization and Mapping III

Lecture 09: Localization and Mapping III

• 1.
  Introduction to RoboticsLocalizationand Mapping IIIMarch 29, 2010
• 2.
  Before BreakBayes RuleMarkovlocalizationRobot location expressed as probability on a gridAction update: probabilities are updated using the motion modelPerception update: probabilities are updated using sensing modelParticle filterLimit number of possible robot location to a small number of particlesLast exercise
• 3.
  Kalman Filter: Intuition1.Predict2. Update
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  Basics: Fuse twoMeasurementsMultiple measurementsActual valueMean-square errorWeights 1/Optimal error
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  Kalman FilterMeasurementKalman FilterGain
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  Example: Map-based localization
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  1. PredictionError propagationlaw
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  2. Observation
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  3. Measurement PredictionObservationsin Map frameZ(k+1)=h(z,p(k+1|k))
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  4. MatchingObservations -Predicted features (based on estimated position) -> “Innovation”Measurement noisePosition error
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  5. Estimation
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  Take home messages:Kalman FilterOptimal way to fuse uncertain observationsOverall variance always decreasesRecipePredict new measurementObserve sensorsUpdate measurement weighted by validity of observation (“Innovation”)Drawback: Assumes uncertainty to be Gaussian!
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  Simultaneous Localization andMappingHen-Egg Problem:Need map to localizeNeed location to mapBrainstorming: how can we solve this problem using the tools we have just seen? Hint: map consists of distinct features.
• 14.
  Feature-based SLAM
• 15.
  Feature-based SLAM
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  Feature-based SLAM
• 17.
  Feature-based SLAM
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  Feature-based SLAM
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  Feature-based SLAM
• 20.
  From Localization toSLAM
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  FastSLAM (Montemerlo etal. 2002)Sample Gaussian distribution using particle filterUpdate particles using motion estimateEstimate sensor-input and prediction for each particleResample particles (higher weight for particles with good matching)Each particle maintains map features (Gaussian distribution)
• 22.
  Key problems inSLAMRecognize place already visitDynamic environmentsRecent directions3D pointcloudsVisual features (SIFT, SURF etc.)
• 23.
  OrganizationNext week: Planningand NavigationWeek 12 + 13: Debateshttp://courses.csail.mit.edu/6.141/spring2009/pub/debates/Debates.htmlWeek 14: Graduate student presentationsWeek 15: Final presentationsReading: Chapter 6 (pages 257-305) Final exam: Monday, May 3 7:30 p.m. - 10:00 p.m.