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Hierarchical Voronoi graphs : spatial representation and reasoning for mobile robots

Author: Jan Oliver Wallgrün
Publisher: Heidelberg ; London : Springer, ©2010.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This book investigates the application of hierarchical Voronoi graphs for the internal spatial memory of a mobile robot, focusing on the robot mapping problem of deriving the correct representation  Read more...

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Document Type: Book
All Authors / Contributors: Jan Oliver Wallgrün
ISBN: 9783642103025 3642103022 3642103456 9783642103452
OCLC Number: 502406561
Description: xxiii, 218 pages : illustrations (some color) ; 24 cm
Contents: 1. Introduction --
1.1. The Robot Mapping Problem --
1.2. The Spatial Representation Perspective --
1.3. The Uncertainty Handling Perspective --
1.4. Combining Representation and Uncertainty Handling --
1.5. Route Graphs Based on Generalized Voronoi Diagrams --
1.6. Theses, Goals, and Contributions of This Book --
1.7. Outline of This Book --
2. Robot Mapping --
2.1. A Spatial Model for What? --
2.1.1. Navigation --
2.1.2. Systematic Exploration --
2.1.3. Communication --
2.2. Correctness, Consistency, and Criteria --
2.2.1. Extractability and Maintainability --
2.2.2. Information Adequacy --
2.2.3. Efficiency and Scalability --
2.3. Spatial Representation and Organization --
2.3.1. Basic Spatial Representation Approaches --
2.3.2. Coordinate-Based Representations --
2.3.3. Relational Representations --
2.3.4. Organizational Forms --
2.4. Uncertainty Handling Approaches --
2.4.1. Incremental Approaches --
2.4.2. Multi-pass Approaches --
2.5. Conclusions --
3. Voronoi-Based Spatial Representations --
3.1. Voronoi Diagram and Generalized Voronoi Diagram --
3.2. Generalized Voronoi Graph and Embedded Generalized Voronoi Graph --
3.3. Annotated Generalized Voronoi Graphs --
3.4. Hierarchical Annotated Voronoi Graphs --
3.5. Partial and Local Voronoi Graphs --
3.6. An Instance of the HAGVG --
3.7. Stability Problems of Voronoi-Based Representations --
3.8. Strengths and Weaknesses of the Representation --
4. Simplification and Hierarchical Voronoi Graph Construction --
4.1. Relevance Measures for Voronoi Nodes --
4.2. Computation of Relevance Values --
4.3. Voronoi Graph Simplification --
4.4. HAGVG Construction --
4.5. Admitting Incomplete Information --
4.6. Improving the Efficiency of the Relevance Computation --
4.7. Incremental Computation --
4.8. Application Scenarios --
4.8.1. Incremental HAGVG Construction --
4.8.2. Removal of Unstable Parts --
4.8.3. Automatic Route Graph Generation from Vector Data --
5. Voronoi Graph Matching for Data Association --
5.1. The Data Association Problem --
5.1.1. Data Associations and the Interpretation Tree --
5.1.2. Data Association Approaches --
5.2. AGVG Matching Based on Ordered Tree Edit Distance --
5.2.1. Ordered Tree Matching Based on Edit Distance --
5.2.2. Overall Edit Distance --
5.2.3. Modeling Removal and Addition Costs --
5.2.4. Optimizations --
5.2.5. Complexity --
5.3. Incorporating Constraints --
5.3.1. Unary Constraints Based on Pose Estimates and Node Similarity --
5.3.2. Binary Constraints Based on Relative Distance --
5.3.3. Ternary Angle Constraints --
5.4. Map Merging Based on a Computed Data Association --
6. Global Mapping: Minimal Route Graphs Under Spatial Constraints --
6.1. Theoretical Problem --
6.2. Branch and Bound Search for Minimal Model Finding --
6.2.1. Search Through the Interpretation Tree --
6.2.2. Best-First Branch and Bound Search Based on Solution Size --
6.2.3. Expand and Update Operations --
6.2.4. Two Variants of the Minimal Model Finding Problem --
6.3. Pruning Based on Spatial Constraints --
6.3.1. Checking Planarity --
6.3.2. Checking Spatial Consistency --
6.3.3. Incorporation into the Search Algorithm --
6.4. Combining Minimal Route Graph Mapping and AGVG Representations --
7. Experimental Evaluation --
7.1. Relevance Assessment and HAGVG Construction --
7.1.1. Efficiency of the Relevance Computation Algorithms --
7.1.2. Combining the HAGVG Construction Methods with a Grid-Based FastSLAM Approach --
7.2. Evaluation of the Voronoi-Based Data Association --
7.3. Evaluation of the Minimal Route Graph Approach --
7.3.1. Solution Quality --
7.3.2. Pruning Efficiency --
7.3.3. Absolute vs. Relative Direction Information --
7.3.4. Overall Computational Costs --
7.3.5. Application to Real AGVG Data --
7.4. A Complete Multi-hypothesis Mapping System --
7.4.1. Local Metric Mapping and Local AGVG Computation --
7.4.2. Data Association for Node Tracking and History Generation --
7.4.3. Global Mapping and Post-processing --
7.4.4. Experiments --
7.4.5. Discussion --
8. Conclusions and Outlook --
8.1. Summary and Conclusions --
8.1.1. Extraction and HAGVG Construction --
8.1.2. Data Association and Matching --
8.1.3. Minimal Route Graph Model Finding --
8.1.4. Complete Mapping Approaches --
8.2. Outlook --
8.2.1. Extensions of the Work Described in Chaps. 3 --
8.2.2. Combining Voronoi Graphs and Uncertainty Handling --
8.2.3. Challenges for Voronoi-Based Representation Approaches --
8.2.4. Challenges for Qualitative Spatial Reasoning --
8.2.5. The Future: Towards Spatially Competent Mobile Robots --
Appendix A. Mapping as Probabilistic State Estimation --
1. The Recursive Bayes Filter --
2. Parametric Filters --
2.1. Kalman Filter --
2.2. Extended Kalman Filter --
3. Nonparametric Filters --
3.1. Particle Filter --
3.2. Rao-Blackwellized Particle Filter and FastSLAM --
Appendix B. Qualitative Spatial Reasoning --
1. Qualitative Constraint Calculi --
2. Weak vs. Strong Operations --
3. Constraint Networks and Consistency --
4. Checking Consistency.
Responsibility: Jan Oliver Wallgrün.

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