how to do slamtaylorm/16_483f/16.483_17.pdf · 15 given: –the robot’s controls –observations...
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How to do SLAM
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How to do SLAM
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How to do SLAM
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How to do SLAM
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How to do SLAM
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How to do SLAM
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How to do SLAM
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How to do SLAM
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How to do SLAM
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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;…
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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
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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.
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Kalman Filter
Sense Move
Initial Belief
Gaussian:μ, σ2
μ’=μ+uσ2’=σ2+r2
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• Goal: Estimate state x of a system given observations z and controls u
• P(x | z,u)
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),,|(),,|(),,,|(),,|(
11
11111
nn
nnnn
zzzPzzxPzzxzPzzxP
evidenceprior likelihood
)()()|()(
yPxPxyPyxPBayes’ Rule
… with Background Knowledge
Recursive Bayesian Updating
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Recursive Bayesian Updating
),,|(),,|(),,,|(),,|(
11
11111
nn
nnnn
zzzPzzxPzzxzPzzxP
Markov assumption: zn is independent of z1,...,zn-1 if we know x.
),,|(),,|()|(),,|(
11
111
nn
nnn
zzzPzzopenPopenzPzzopenP
)()()|()|( zP
openPopenzPzopenP
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Sense Move
Initial Belief
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