Simultaneous Localization and Mapping (SLAM) has been a long-standing research problem in robotics. It describes the problem of a robot mapping an unknown environment, while simultaneously localizing in it with the help of the incomplete map. This book describes a technique called Switchable Constraints.Switchable Constraints help to increase the robustness of SLAM against data association errors and in particular against false positive loop closure detections. Such false positive loop closure detections can occur when the robot erroneously assumes it re-observed a landmark it has already mapped or when the appearance of the observed surroundings is very similar to the appearance of other places in the map. Ambiguous observations and appearances are very common in human-made environments such as office floors or suburban streets, making robustness against spurious observations a key challenge in SLAM. The book summarizes the foundations of factor graph-based SLAM techniques. It explains the problem of data association errors before introducing the novel idea of Switchable Constraints. We present a mathematical derivation and probabilistic interpretation of Switchable Constraints along with evaluations on different datasets. The book shows that Switchable Constraints are applicable beyond SLAM problems and demonstrates the efficacy of this technique to improve the quality of satellite-based localization in urban environments, where multipath and non-line-of-sight situations are common error sources.
Author(s): Niko Sünderhauf
Series: Springer Tracts in Advanced Robotics, 137
Publisher: Springer
Year: 2023
Language: English
Pages: 189
City: Cham
Series Editor’s Foreword
Preface
Contents
Symbols and Notation
General Mathematical Notation
Roman Letters
Greek Letters
Special Abbreviations in Mathematical Expressions
1 Introduction
References
2 Simultaneous Localization and Mapping
2.1 S, L, and M—The Parts of SLAM
2.1.1 M for Mapping
2.1.2 L for Localization
2.1.3 S for Simultaneous
2.2 Graph Representations for SLAM
2.2.1 Dynamic Bayesian Networks
2.2.2 Factor Graphs
2.2.3 Markov Random Fields
2.3 SLAM as a Nonlinear Least Squares Optimization Problem
2.3.1 The Pose Graph SLAM Problem
2.3.2 Deriving a Nonlinear Least Squares Formulation
2.3.3 An Intuitive Analogy for the Least Squares Optimization
2.3.4 Optimization-Based SLAM—A Literature Review
2.4 Summary
References
3 Least Squares Optimization
3.1 Introduction
3.1.1 A Taxonomy of Optimization Problems
3.1.2 Least Squares Optimization Problems
3.2 Linear Least Squares Problems
3.2.1 Solving Linear Least Squares Problems
3.2.2 Examples for Linear Least Squares Problems
3.3 Nonlinear Least Squares Problems
3.3.1 Gradient Descent
3.3.2 Newton's Method
3.3.3 Gauss-Newton
3.3.4 Levenberg-Marquardt
3.3.5 Summary
3.4 Weighted Nonlinear Least Squares Problems
3.5 Least Squares Optimization for SLAM
3.5.1 A Sandbox Example
3.5.2 Why Optimization-Based SLAM Is Efficient
3.6 Least Squares Optimization in the Presence of Outliers
3.6.1 Sample Consensus Methods for Outlier Rejection
3.6.2 Robust Cost Functions
3.7 Summary
References
4 Motivation—When Optimization Fails
4.1 Data Association Errors and Their Effects On SLAM
4.2 Current Approaches for Outlier Mitigation and Avoidance
4.2.1 Outlier Avoidance on the Front-End Side
4.2.2 Outlier Mitigation on the Back-End Side
4.3 Summary
References
5 A Robust Back-End for SLAM
5.1 The Robustified Formulation for Pose Graph SLAM
5.1.1 First Steps Towards a Mathematical Formulation
5.1.2 Introducing the Switch Variables and Finding a Suitable Switch Function
5.1.3 Introducing the Switch Priors
5.1.4 Putting It All Together
5.2 Discussion
5.2.1 The Influence of sij on the Information Matrix Λij
5.2.2 Establishing the Connection to the Maximum a Posteriori Solution
5.2.3 The Influence of the Additional Variables and Constraints on The Problem Size
5.2.4 The Influence of the Additional Variables and Constraints on The Sparse Structure of the Problem
5.2.5 The Influence of the Additional Variables and Constraints on The Problem's Convergence Properties
5.3 Summary and a First Working Example
References
6 Evaluation
6.1 Error Metrics for SLAM
6.1.1 The Root-Mean-Square Error (RMSE)
6.1.2 The Relative Pose Error Metric
6.1.3 Precision-Recall Statistics
6.2 Datasets for the Evaluation
6.3 General Methodology
6.3.1 Policies for Adding Outlier Loop Closure Constraints
6.3.2 Loop Closure Displacement
6.3.3 The Switch Function
6.3.4 Used Framework and Implementation
6.4 The Influence of Ξij on the Estimation Results
6.4.1 Methodology
6.4.2 Results and Interpretation
6.5 The Robustness in the Presence of Outliers
6.5.1 Methodology
6.5.2 Results and Interpretation
6.5.3 Discussion of the Failure Cases
6.6 Runtime and Convergence Behaviour
6.6.1 Methodology
6.6.2 Results and Interpretation
6.7 Performance in the Outlier-Free Case
6.7.1 Methodology
6.7.2 Results and Interpretation
6.8 The Influence of the Switch Function Ψ
6.9 Summary of the Evaluation and First Conclusions
References
7 Applying the Robust Back-End in a Complete SLAM System on A Real-World Dataset
7.1 The Front-End
7.1.1 Visual Odometry by Image Profile Matching
7.1.2 Place Recognition Using BRIEF-Gist
7.2 Results of the Complete SLAM System on the St. Lucia Dataset
7.3 Summary
References
8 Applications Beyond SLAM—Multipath Mitigation in GNSS-Based Localization Problems Using the Robust Back-End
8.1 GNSS-Based Localization—A Gentle Introduction
8.1.1 Systematic Errors
8.1.2 Multipath Errors
8.2 Multipath Identification and Mitigation—Related Work
8.3 Modelling the GNSS-Based Localization Problem as a Factor Graph
8.3.1 The Vehicle State Vertices
8.3.2 The Pseudorange Factor
8.3.3 Additional Factors
8.3.4 Solving for the Maximum a Posteriori Solution
8.4 Towards a Problem Formulation Robust to Multipath Errors
8.4.1 The Switched Pseudorange Factor
8.4.2 The Switch Transition Factor
8.5 Multipath Mitigation in a Real-World Urban Scenario
8.5.1 The Chemnitz City Dataset
8.5.2 Methodology
8.5.3 Results
8.6 Interpretation and Summary
8.7 Outlook
References
9 An Outlook on Robust Optimization for Sensor Fusion and Calibration
9.1 Sensor Fusion by Robust Optimization
9.2 Sensor Calibration by Robust Optimization
References
10 Conclusions
10.1 What Has Been Achieved—Contributions of This Thesis
10.2 Open Questions—An Outlook on Further Work
10.2.1 Parameters of the Proposed Robust Formulation
10.2.2 Convergence Behaviour and the Dangers of Local Minima
10.2.3 Further Applications of the Robust Approach
References
11 Retrospective
11.1 Progress in Robust SLAM—From Heuristics and M-Estimators to Certifiable Robust Optimization
11.2 General Progress in SLAM
References
