how to do slamtaylorm/16_483f/16.483_17.pdf · 15 given: –the robot’s controls –observations...

How to do SLAM

How to do SLAM

How to do SLAM

How to do SLAM

How to do SLAM

How to do SLAM

How to do SLAM

How to do SLAM

How to do SLAM

Slides based on:Probabilistic Robotics

http://www.probabilistic‐robotics.org/

&

Cyrill Stachniss http://ais.informatik.uni‐freiburg.de/teaching/ws13/mapping/index_en.php

(Sensors on wheels)

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Given:– The robot’s controls

– Observations of nearby features

Estimate:– Map of features

– Path of the robot

The SLAM ProblemA robot is exploring an unknown, static environment.

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Structure of the Landmark‐based SLAM‐Problem 

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SLAM Applications

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Representations

• Grid maps or scans

[Lu & Milios, 97; Gutmann, 98: Thrun 98; Burgard, 99; Konolige & Gutmann, 00; Thrun, 00; Arras, 99; Haehnel, 01;…]

• Landmark‐based

[Leonard et al., 98; Castelanos et al., 99: Dissanayake et al., 2001; Montemerlo et al., 2002;…

iRobot Roomba 980Visual SLAM• http://spectrum.ieee.org/automaton/robotics/home‐robots/irobot‐brings‐visual‐

mapping‐and‐navigation‐to‐the‐roomba‐980• https://www.youtube.com/watch?v=oj3Vawn‐kRE

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Why is SLAM a hard problem?SLAM: robot path and map are both unknown

Robot path error correlates errors in the map

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Why is SLAM a hard problem?

• In the real world, the mapping between observations and landmarks is unknown

• Picking wrong data associations can have catastrophic consequences

• Pose error correlates data associations

Robot poseuncertainty

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Graphical Model of Full SLAM: 

),|,( :1:1:1 ttt uzmxp Arrows = influences

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Graphical Model of Online SLAM: 

121:1:1:1:1:1 ...),|,(),|,( ttttttt dxdxdxuzmxpuzmxp

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SLAM: Simultaneous Localization and Mapping

• Full SLAM:

• Online SLAM:

Integrations typically done one at a time 

),|,( :1:1:1 ttt uzmxp

121:1:1:1:1:1 ...),|,(),|,( ttttttt dxdxdxuzmxpuzmxp

Estimates most recent pose and map!

Estimates entire path and map!

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• Kalman filter• Graph‐based• Particle‐based

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P(xt | xt‐1, ut)  

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P(zt | xt)38

http://ais.informatik.uni‐freiburg.de/teaching/ws13/mapping/

index_en.php

For Thursday:

Watch (Extended) Kalman Filter (~45 min) and EKF SLAM (~80 min)on Piazza write 1) A paragraph on each describing what the lectures are about and 2) Questions you had during the lecture. Please this info by 11:59pm, Tuesday the 15th.

Kalman Filter

Sense Move

Initial Belief

Gaussian:μ, σ2

μ’=μ+uσ2’=σ2+r2

• Goal: Estimate state x of a system given observations z and controls u

• P(x | z,u)

),,|(),,|(),,,|(),,|(

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11111

nn

nnnn

zzzPzzxPzzxzPzzxP

evidenceprior likelihood

)()()|()(

yPxPxyPyxPBayes’ Rule

… with Background Knowledge

Recursive Bayesian Updating

Recursive Bayesian Updating

),,|(),,|(),,,|(),,|(

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11111

nn

nnnn

zzzPzzxPzzxzPzzxP

Markov assumption: zn is independent of z1,...,zn-1 if we know x.

),,|(),,|()|(),,|(

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111

nn

nnn

zzzPzzopenPopenzPzzopenP

)()()|()|( zP

openPopenzPzopenP

Sense Move

Initial Belief