1. Probabilistic Robotics
SLAM

2. The SLAM Problem A robot is exploring an unknown, static environment.
Given:
The robot’s controls (U1:t)
Observations of nearby features (Z1:t)
Estimate:
Map of features (m)
Pose / Path of the robot (xt)

3. Why is SLAM a hard problem?
Robot pose
uncertainty
In the real world, the mapping between observations and landmarks is unknown
Picking wrong data associations can have catastrophic consequences

4. Nature of the SLAM Problem
Continuous Location of objects in
component the map
Robot’s own pose
Discrete Correspondence
component
Object is the same or not

5. SLAM: Simultaneous Localization and Mapping
Full SLAM:
Estimates Entire pose (x1:t) and map (m)
Given Previous knowledge (Z1:t-1, U1:t-1) Current measurement (Zt, Ut)
Estimates entire path and map!

6. Graphical Model of Full SLAM:

7. SLAM: Simultaneous Localization and Mapping
Online SLAM:
Estimates Most recent pose (xt) and map (m)
Given Previous knowledge (Z1:t-1, U1:t-1) Current measurement (Zt, Ut)
Estimates most recent pose and map!

8. Graphical Model of Online SLAM:
Integrations typically done one at a time

9. SLAM with Extended Kalman Filter
Pre-requisites
Maps are feature-based (landmarks)
small number (< 1000)
Assumption - Gaussian Noise
Process only positive sightings
No landmark = negative
Landmark = positive

10. EKF-SLAM with known correspondences
Correspondence Data association problem
Landmarks can’t be uniquely identified
True identity of observed feature
Correspondence variable (Cit)
between feature (fit) and real landmark

11. EKF-SLAM with known correspondences
Signature Numerical value (average color)
Characterize type of landmark (integer)
Multidimensional vector
(height and color)

12. EKF-SLAM with known correspondences
Similar development to EKF localization
Diff  robot pose + coordinates of all landmarks
Combined state vector
(3N + 3)
Online posterior

13. Iteration through measurements
Mean
Motion update
Covariance
Test for new landmarks
Initialization of elements
Expected measurement
Filter is updated
Iteration through measurements

14. EKF-SLAM with known correspondences
Observing a landmark improves robot pose estimate
eliminates some uncertainty of other landmarks
Improves position estimates of the landmark + other landmarks
We don’t need to model past poses explicitly

15. EKF-SLAM with known correspondences
Example:

16. EKF-SLAM with known correspondences
Example:
Uncertainty of landmarks are mainly due to robot’s pose uncertainty (persist over time)
Estimated location of landmarks are correlated

17. EKF-SLAM with unknown correspondences
No correspondences for landmarks
Uses an incremental maximum likelihood (ML) estimator
Determines most likely value of the correspondence variable
Takes this value for granted later on

18. EKF-SLAM with unknown correspondences
Mean
Motion update
Covariance
Hypotheses of new landmark

20. General Problem Gaussian noise assumption Unrealistic
Spurious measurements Fake landmarks
Outliers
Affect robot’s localization

21. Solutions to General Problem
Provisional landmark list
New landmarks do not augment the map
Not considered to adjust robot’s pose
Consistent observation regular map

22. Solutions to General Problem
Landmark Existence Probability
Landmark is observed
Observable variable (o) increased by fixed value
Landmark is NOT observed when it should
Observable variable decreased
Removed from map when (o) drops below threshold

23. Problem with Maximum Likelihood (ML)
Once ML estimator determines likelihood of correspondence, it takes value for granted
always correct
Makes EKF susceptible to landmark confusion
Wrong results

24. Solutions to ML Problem
Spatial arrangement
Greater distance between landmarks
Less likely confusion will exist
Trade off:
few landmarks harder to localize
Little is known about optimal density of landmarks
Signatures
Give landmarks a very perceptual distinctiveness
(e,g, color, shape, …)

25. EKF-SLAM Limitations Selection of appropriate landmarks
Reduces sensor reading utilization to presence or absence of those landmarks
Lots of sensor data is discarded
Quadratic update time
Limits algorithm to scarce maps (< features)
Low dimensionality of maps harder data association problem

26. EKF-SLAM Limitations Fundamental Dilemma of EKF-SLAM
It might work well with dense maps (millions of features)
It is brittle with scarce maps
BUT
It needs scarce maps because of complexity of the algorithm (update process)

27. SLAM Techniques EKF SLAM  (chapter 10) Graph-SLAM  (chapter 11)
SEIF  (chapter 12)
Fast-SLAM  (chapter 13)

28. Graph-SLAM Solves full SLAM problem
Represents info as a graph of soft constraints
Accumulates information into its graph without resolving it (lazy SLAM)
Computationally cheap
At the other end of EKF-SLAM
Process information right away (proactive SLAM)
Computationally expensive

29. Graph-SLAM Calculates posteriors over robot path (not incremental)
Has access to the full data
Uses inference to create map using stored data
Offline algorithm

30. Sparse Extended Information Filter (SEIF)
Implements a solution to online SLAM problem
Calculates current pose and map (as EKF)
Stores information representation of all knowledge (as Graph-SLAM)
Runs Online and is computationally efficient
Applicable to multi-robot SLAM problem

31. FastSLAM Algorithm Particle filter approach to the SLAM problem
Maintain a set of particles
Particles contain a sampled robot path and a map
The features of the map are represented by own local Gaussian
Map is created as a set of separate Gaussians
Map features are conditionally independent given the path
Factoring out the path (1 per particle)
Map feature become independent
Eliminates the need to maintain correlation among them

32. FastSLAM Algorithm Updating in FastSLAM
Sample new pose update the observed features
Update can be performed online
Solves both online and offline SLAM problem
Instances Feature-based maps
Grid-based algorithm

33. Approximations for SLAM Problem
Local submaps [Leonard et al.99, Bosse et al. 02, Newman et al. 03]
Sparse links (correlations) [Lu & Milios 97, Guivant & Nebot 01]
Sparse extended information filters [Frese et al. 01, Thrun et al. 02]
Thin junction tree filters [Paskin 03]
Rao-Blackwellisation (FastSLAM) [Murphy 99, Montemerlo et al. 02, Eliazar et al. 03, Haehnel et al. 03]

34. Thanks !!