2009. 10. 22. 16:53
Computer Vision
Probabilistic Robotics
Sebastian Thrun, Wolfram Burgard and Dieter Fox
MIT Press, September 2005
Introduction
probabilistic robotics
: explicit representation of uncertainty using the calculus of probability theory
perception
action
Bayes filters are a probabilistic tool for estimating the state of dynamic systems.
Bayes Filters are Familiar!
• Kalman filters
• Particle filters
• Hidden Markov models
• Dynamic Bayesian networks
• Partially Observable Markov Decision Processes (POMDPs)
Kalman filter
Gaussian filter
discrete Kalman filter
Kalman filter update in 1-D
Kalman filter algorithm
EKF = extended Kalman filter
: calculates a Gaussian approximation to the true belief.
Taylor series expansion
"Linearization approximates the nonlinear function g by a linear function that is tangent to g at the mean of the Gaussian."
SLAM
Techniques for Generating Consistent Maps
• Scan matching
• EKF SLAM
• Fast-SLAM
• Probabilistic mapping with a single map and a posterior about poses Mapping + Localization
• Graph-SLAM, SEIFs
Approximations for SLAM
• Local submaps
EKF-SLAM Summary
•Quadratic in the number of landmarks: O(n2)
• Convergence results for the linear case.
• Can diverge if nonlinearities are large!
• Have been applied successfully in large-scale environments.
• Approximations reduce the computational complexity.
ch8
eg. Xavier - Localization in a topological map
ref. Probabilistic Robot Navigation in Partially Observable Environments
Reid Simmons and Sven Koenig
Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI '95), July, 1995, pp. 1080 - 1087.
Sebastian Thrun, Wolfram Burgard and Dieter Fox
MIT Press, September 2005
official: http://www.probabilistic-robotics.org
Preface xvii
Acknowledgments xix
I Basics 1
1 Introduction 3
2 Recursive State Estimation 13
3 Gaussian Filters 39
4 Nonparametric Filters 85
5 Robot Motion 117
6 Robot Perception 149
II Localization 189
7 Mobile Robot Localization: Markov and Gaussian 191
8 Mobile Robot Localization: Grid And Monte Carlo 237
III Mapping 279
9 Occupancy Grid Mapping 281
10 Simultaneous Localization and Mapping 309
11 The GraphSLAM Algorithm 337
12 The Sparse Extended Information Filter 385
13 The FastSLAM Algorithm 437
IV Planning and Control 485
14 Markov Decision Processes 487
15 Partially Observable Markov Decision Processes 513
16 Approximate POMDP Techniques 547
17 Exploration 569
Bibliography 607
Index 639
Acknowledgments xix
I Basics 1
1 Introduction 3
2 Recursive State Estimation 13
3 Gaussian Filters 39
4 Nonparametric Filters 85
5 Robot Motion 117
6 Robot Perception 149
II Localization 189
7 Mobile Robot Localization: Markov and Gaussian 191
8 Mobile Robot Localization: Grid And Monte Carlo 237
III Mapping 279
9 Occupancy Grid Mapping 281
10 Simultaneous Localization and Mapping 309
11 The GraphSLAM Algorithm 337
12 The Sparse Extended Information Filter 385
13 The FastSLAM Algorithm 437
IV Planning and Control 485
14 Markov Decision Processes 487
15 Partially Observable Markov Decision Processes 513
16 Approximate POMDP Techniques 547
17 Exploration 569
Bibliography 607
Index 639
Probability robotics is a subfield of robotics concerned with perception and control.
Introduction
introduction.pdfprobabilistic robotics
: explicit representation of uncertainty using the calculus of probability theory
perception
action
Bayes filters are a probabilistic tool for estimating the state of dynamic systems.
Bayes Filters are Familiar!
• Kalman filters
• Particle filters
• Hidden Markov models
• Dynamic Bayesian networks
• Partially Observable Markov Decision Processes (POMDPs)
Kalman filter
Gaussian filter
discrete Kalman filter
 |
 |
Kalman filter update in 1-D
correction |
prediction |
Kalman filter algorithm
EKF = extended Kalman filter
: calculates a Gaussian approximation to the true belief.
Taylor series expansion
"Linearization approximates the nonlinear function g by a linear function that is tangent to g at the mean of the Gaussian."
SLAM
 |
 |
Techniques for Generating Consistent Maps
• Scan matching
• EKF SLAM
• Fast-SLAM
• Probabilistic mapping with a single map and a posterior about poses Mapping + Localization
• Graph-SLAM, SEIFs
Approximations for SLAM
• 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]
EKF-SLAM Summary
•Quadratic in the number of landmarks: O(n2)
• Convergence results for the linear case.
• Can diverge if nonlinearities are large!
• Have been applied successfully in large-scale environments.
• Approximations reduce the computational complexity.
ch8
eg. Xavier - Localization in a topological map
ref. Probabilistic Robot Navigation in Partially Observable Environments
Reid Simmons and Sven Koenig
Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI '95), July, 1995, pp. 1080 - 1087.
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