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