Part 1.
basic

01.
introduction
1.1 Uncertainty in the Robotics Field
1.2 Probabilistic Robotics
1.3 Implications
1.4 Structure of this book
1.5 For the Probabilistic Robotics Lecture
1.6 References

02.
Recursive state estimation
2.1 Overview
2.2 Basic concepts of probability
2.3 Interaction with the Robot Environment
2.3.1 State
2.3.2 Environmental Interaction
2.3.3 Probabilistic generation law
2.3.4 Belief Distribution
2.4 Bayes filter
2.4.1 Bayes filter algorithm
2.4.2 Example
2.4.3 Mathematical derivation of Bayes filter
2.4.4 Markov assumptions
2.5 Expressions and Calculations
2.6 Summary
2.7 References
2.8 Practice Problems

03.
Gaussian filter
3.1 Overview
3.2 Kalman filter
3.2.1 Linear Gaussian System
3.2.2 Kalman Filter Algorithm
3.2.3 Detailed Description of the Kalman Filter
3.2.4 Mathematical proof of the Kalman filter
3.3 Extended Kalman Filter
3.3.1 The Need for Linearization
3.3.2 Linearization through Taylor expansion
3.3.3 EKF Algorithm
3.3.4 Mathematical derivation of EKF
3.3.5 Considerations for actual use
3.4 Distributed point Kalman filter
3.4.1 Linearization using distributed Kalman filter
3.4.2 UKF Algorithm
3.5 Information Filter
3.5.1 Canonical parameters
3.5.2 Information Filter Algorithm
3.5.3 Mathematical derivation of the information filter algorithm
3.5.4 Extended Information Filter Algorithm
3.5.5 Mathematical derivation of the extended information filter algorithm
3.5.6 Considerations for Actual Use
3.6 Summary
3.7 References
3.8 Practice Problems

04.
Nonparametric filter
4.1 Histogram Filter
4.1.1 Discrete Bayes Filter Algorithm
4.1.2 Continuous State
4.1.3 Mathematical derivation of histogram approximation techniques
4.1.4 Disassembly/Separation Technology
4.2 Binary Bayes filter using static states
4.3 Particle Filter
4.3.1 Basic Algorithm
4.3.2 Importance Sampling
4.3.3 Mathematical derivation of particle filters
4.3.4 Considerations and Features in Practical Use of Particle Filters
4.4 Summary
4.5 References
4.6 Practice Problems

05.
robot motion
5.1 Overview
5.2 Basic Information
5.2.1 Kinematic Environment Settings
5.2.2 Probabilistic Kinematics
5.3 Velocity motion model
5.3.1 Closed form calculations
5.3.2 Sampling Algorithm
5.3.3 Mathematical derivation of the velocity motion model
5.4 Odometry Motion Model
5.4.1 Closed form calculations
5.4.2 Sampling Algorithm
5.4.3 Mathematical Derivation of the Odometry Motion Model
5.5 Motion and Maps
5.6 Summary
5.7 References
5.8 Practice Problems

06.
Robot recognition
6.1 Overview
6.2 Map
6.3 Beam model of the laser range finder
6.3.1 Basic Measurement Algorithm
6.3.2 Tuning the Intrinsic Model Parameters
6.3.3 Mathematical derivation of the beam model
6.3.4 Considerations for Practical Use 6.3.5 Limitations of the Beam Model
6.4 Likelihood field for range finder
6.4.1 Basic Algorithms
6.4.2 Extension Algorithm
6.5 Correlation-based measurement model
6.6 Feature-based measurement model
6.6.1 Feature Extraction
6.6.2 Landmark Measurement
6.6.3 Sensor models with known response variables
6.6.4 Sampling poses
6.6.5 Additional Considerations
6.7 Considerations for actual use
6.8 Summary
6.9 References
6.10 Practice Problems


Part 2.
localization

07.
Mobile Robot Localization: Markov and Gaussian
7.1 Classification of localization issues
7.2 Markov Localization
7.3 Understanding Markov Localization through Pictures
7.4 EKF localization
7.4.1 Detailed Description
7.4.2 EKF localization algorithm
7.4.3 Mathematical Derivation of EKF Localization262
7.4.4 Practical Implementation of the Algorithm
7.5 Estimation of corresponding variables
7.5.1 EKF localization using unknown response variables
7.5.2 Mathematical derivation of maximum likelihood data association
7.6 Multiple Hypothesis Tracking
7.7 UKF Localization
7.7.1 Mathematical derivation of UKF localization
7.7.2 Detailed Description
7.8 Considerations for Practical Use
7.9 Summary
7.10 References
7.11 Practice Problems

08.
Mobile Robot Localization: Grid and Monte Carlo
8.1 Overview
8.2 Grid Localization
8.2.1 Basic Algorithm
8.2.2 Grid Resolution
8.2.3 Computational Considerations
8.2.4 Detailed Description
8.3 Monte Carlo Localization
8.3.1 Detailed Description
8.3.2 MCL Algorithm
8.3.3 Implementation
8.3.4 MCL Properties
8.3.5 Random Particle MCL: Failure Recovery
8.3.6 Modifying the Proposed Distribution
8.3.7 KLD Sampling: Adjusting the Sample Set Size
8.4 Localization in a Dynamic Environment
8.5 Considerations for Practical Use
8.6 Summary
8.7 References
8.8 Practice Problems


Part 3.
Mapping

09.
Occupancy Grid Mapping
9.1 Overview
9.2 Occupancy Grid Mapping Algorithm
9.2.1 Multi-Sensor Fusion
9.3 Learning the inverse measurement model
9.3.1 Inverse transformation of the measurement model
9.3.2 Sampling in the Forward Model
9.3.3 Error function
9.3.4 Examples and Additional Considerations
9.4 Maximum posterior probability occupancy mapping
9.4.1 When dependencies are maintained
9.4.2 Occupancy Grid Mapping Using the Forward Model
9.5 Summary
9.6 References
9.7 Practice Problems

10.
Simultaneous localization and mapping
10.1 Overview
10.2 SLAM model using extended Kalman filter
10.2.1 Preparation and Assumptions 10.2.2 SLAM Model with Known Correspondence Variables
10.2.3 Mathematical derivation of EKF SLAM
10.3 EKF SLAM model using unknown response variables
10.3.1 General EKF SLAM Algorithm
10.3.2 Example
10.3.3 Feature Selection and Map Management
10.4 Summary
10.5 References
10.6 Practice Problems

11.
GraphSLAM algorithm
11.1 Overview
11.2 Intuitive Concept Explanation
11.2.1 Creating a Graph
11.2.2 Inference
11.3 GraphSLAM Algorithm
11.4 Mathematical Derivation of GraphSLAM
11.4.1 Computing the overall SLAM posterior probability
11.4.2 Calculating the negative log posterior probability
11.4.3 Taylor expansion
11.4.4 Creating an Information Form
11.4.5 Collapse the information form
11.4.6 Restoring paths and maps
11.5 Data Association in GraphSLAM
11.5.1 GraphSLAM Algorithm with Unknown Correspondence Variables
11.5.2 Mathematical derivation of the correspondence test
11.6 Considerations for Efficiency
11.7 Implementation
11.8 Other Optimization Techniques
11.9 Summary
11.10 References
11.11 Practice Problems

12.
Sparse extended information filter
12.1 Overview
12.2 Intuitive Concept Explanation
12.3 SEIF SLAM Algorithm
12.4 Mathematical Derivation of the SEIF Algorithm
12.4.1 Motion Update
12.4.2 Measurement Update
12.5 Rareness stage
12.5.1 Basic Idea
12.5.2 Rareness of SEIF
12.5.3 Mathematical derivation of the sparsification operation
12.6 Map Recovery via Amorphized Approximation
12.7 How rare is SEIF?
12.8 Incremental Data Association
12.8.1 Calculating Incremental Data Association Probabilities
12.8.2 Considerations for actual use.
12.9 Data association based on a limited-quarter algorithm
12.9.1 Recursive Search
12.9.2 Calculating the probability of association with arbitrary data
12.9.3 Equivalence Constraints
12.10 Considerations for Practical Use
12.11 Multi-Robot SLAM
12.11.1 Map Integration
12.11.2 Mathematical Derivation of Map Integration
12.11.3 Creating a Corresponding Variable
12.11.4 Example
12.12 Summary
12.13 References
12.14 Practice Problems

13.
FastSLAM algorithm
13.1 Basic Algorithm
13.2 SLAM Posterior Probability Factorization
13.2.1 Mathematical derivation of the factorized SLAM algorithm
13.3 FastSLAM using known data associations
13.4 How to improve the proposed distribution
13.4.1 Method for expanding path posterior probability by sampling new poses
13.4.2 Updating Observed Feature Estimates
13.4.3 Calculating Importance Factors
13.5 Unknown Data Associations
13.6 Map Management
13.7 FastSLAM Algorithm
13.8 Efficient Implementation
13.9 FastSLAM for Feature-Based Maps
13.9.1 Insights from Experiments
13.9.2 Loop closure
13.10 Grid-based FastSLAM
13.10.1 Algorithm
13.10.2 Insights from Experiments
13.11 Summary
13.12 References
13.13 Practice Problems


Part 4.
Planning and Control

14.
Markov Decision Process (MDP)
14.1 Motif
14.2 Uncertainty in Action Selection
14.3 Value Iteration
14.3.1 Objectives and Payoffs
14.3.2 Finding the optimal control policy for the fully observable case
14.3.3 Calculating the value function
14.4 Robot Control Applications
14.5 Summary
14.6 References
14.7 Practice Problems

15.
Partially Observable Markov Decision Process (POMDP)
15.1 Motive
15.2 Explanation through examples
15.2.1 Preparation
15.2.2 Selecting a value
15.2.3 Sensing
15.2.4 Forecast
15.2.5 Deep Horizon and Pruning
15.3 POMDP Algorithm in Finite Worlds
15.4 Mathematical Derivation of POMDP
15.4.1 Value Iteration in Belief Space
15.4.2 Value Function Expression
15.4.3 Calculating the value function
15.5 Considerations for Practical Use
15.6 Summary
15.7 References
15.8 Practice Problems


16.
Approximation POMDP technology

16.1 Motive
16.2 QMDP
16.3 Augmented Markov Decision Process (AMDP)
16.3.1 Augmented State Space
16.3.2 AMDP Algorithm
16.3.3 Mathematical Derivation of AMDP
16.3.4 Application to mobile robot navigation
16.4 Monte Carlo POMDP
16.4.1 Method using particle sets 16.4.2 MC-POMDP algorithm
16.4.3 Mathematical Derivation of MC-POMDP
16.4.4 Considerations for Actual Use
16.5 Summary
16.6 References
16.7 Practice Problems

17.
Exploration
17.1 Overview
17.2 Basic Exploration Algorithms
17.2.1 Information Gain
17.2.2 Greedy Technology
17.2.3 Monte Carlo exploration technique
17.2.4 Multi-stage technology
17.3 Active Localization
17.4 Exploration for learning occupancy grid maps
17.4.1 Calculating Information Gain
17.4.2 Gain Propagation
17.4.3 Expansion to a multi-robot system
17.5 Exploration for SLAM
17.5.1 Entropy Decomposition of SLAM
17.5.2 Exploration of FastSLAM
17.5.3 Empirical Characteristics
17.6 Summary
17.7 References
17.8 Practice Problems

★ What this book covers ★

Probabilistic robotics is a growing new field in robotics that focuses on perception and control despite uncertainty.
Probabilistic robotics, based on mathematical statistics, makes robots more robust in real-world situations.
This book introduces a wealth of technologies and algorithms in the field of robotics.
All algorithms are based on a single, comprehensive mathematical concept.
Each chapter provides pseudocode, detailed mathematical derivations, discussions from a practitioner's perspective, extensive exercises, and implementation examples from a list of class projects.

★ Target audience for this book ★

It is intended for students, researchers, and practitioners.
Since I believe that everyone who builds robots should develop software, the contents of this book are also relevant to all roboticists.
It will also be useful to applied statisticians and anyone working with real-world sensor data outside of robotics.
It is written for a wide range of readers with diverse technical backgrounds, with the goal of making it as self-studyable as possible.
Prior knowledge of linear algebra and basic probability and statistics will be helpful in reading this book.
It includes an introduction to the basic laws of probability and generally avoids the use of advanced mathematical techniques.

★ Author's Note ★

A comprehensive introduction to the new field of robotics.
Probabilistic robotics is a subfield of robotics concerned with perception and control.
It relies on statistical techniques to represent information and make decisions.
This accommodates the uncertainty that arises in most modern robotics applications.
In recent years, probabilistic techniques have become one of the dominant paradigms for algorithm design in robotics.
This book provides a comprehensive introduction to key technologies in robotics, with a focus on algorithms.
All algorithms are based on Bayes' rule and an ad hoc extension called Bayes' filter, and a unified mathematical framework is common to probabilistic algorithms.

In writing this book, I tried to make it as technically perfect as possible.
Each chapter describes one or more key algorithms, each of which provides four things:


(1) Implementation example of pseudocode
(2) Complete mathematical derivation from first principles, making various assumptions explicit.
(3) Empirical results to help understand the algorithm presented in the book.
(4) Explanation of the strengths and weaknesses of each algorithm from a practical perspective

You can skip the mathematical derivation process if you don't need it, but if you don't read it consistently, it may be difficult to digest the contents of the book.
I hope that by studying this book diligently, you will gain a much deeper understanding of the subject than can be conveyed through superficial, non-mathematical expressions.

★ Translator's Note ★

As of 2020, artificial intelligence, machine learning, and deep learning are producing tremendous results across all fields.
It's surprising to think that just a few years ago, deep learning and machine learning were only achieving limited results in areas like computer vision, image analysis, and natural language processing.

Meanwhile, the autonomous vehicle field is also one of the representative fields utilizing artificial intelligence and deep learning.
One of the fields where artificial intelligence, machine learning, deep learning, and reinforcement learning, which come to mind when thinking about these things, can be best applied is robotics.

In robotics, too, massive amounts of data, advanced mathematics, statistics, and algorithmic techniques are being mobilized to overcome existing limitations and to enable smarter adaptation to ever-changing real-world environments.
In other words, in order to select the optimal action based on various situational understandings in a much more complex environment, it is essential to develop algorithms that can mathematically model these, logically prove them, and enable them to operate consistently.

This book richly introduces research achievements in the field of robotics based on various mathematical knowledge such as probability theory, statistics, and linear algebra.
Although the content may be somewhat difficult to understand, I believe that if you solidify the basic concepts, practice how to derive them mathematically, express them as algorithms, and learn step by step what the actual simulation results are, you will be able to achieve good results.