Reliable Robot Localization

Simon Rohou is an Associate Professor at ENSTA Bretagne -Lab-STICC (Brest, France).Luc Jaulin is Full Professor of Robotics at ENSTA Bretagne-Lab-STICC.Lyudmila Mihaylova is Professor of Signal Processing and Control with the Department of Automatic Control and Systems Engineering at the University of Sheffield (UK).Fabrice Le Bars is an Associate Professor at ENSTA Bretagne-Lab-STICC.Sandor M. Veres holds a chair in Autonomous Control Systems, and leads the Robotics and Autonomous Systems Research Group at the Department of Automatic Control and Systems Engineering at the University of Sheffield.

• Preface xiNotations xiiiAbbreviations xviiIntroduction xixPart 1. Interval Tools 1Introduction to Part 1 3Chapter 1. Static Set-membership State Estimation 51.1. Introduction 51.2. Interval analysis 81.2.1. Once upon a time 81.2.2. Intervals 101.2.3. Inclusion functions 141.2.4. Pessimism and wrapping effect 161.3. Constraint propagation 191.3.1. Constraint networks 191.3.2. Contractors 211.3.3. Application to static range-only robot localization 241.4. Set-inversion via interval analysis 251.4.1. Subpaving 251.4.2. SIVIA algorithm for set-inversion 281.4.3. Illustration involving contractions 291.4.4. Kernel characterization of an interval function 331.5. Discussions 351.5.1. From sensors to reliable results 361.5.2. Numerical libraries 371.5.3. Reliable tool for proof purposes 381.6. Conclusion 38Chapter 2. Constraints Over Sets of Trajectories 412.1. Towards dynamic state estimation 412.1.1. Overall motivations 412.1.2. The approach presented in this book 432.2. Tubes 442.2.1. Definitions 442.2.2. Tube analysis 452.2.3. Contractors 482.3. Implementation 502.3.1. Data structure 522.3.2. Build a tube from real datasets 542.3.3. Tubex, dedicated tube library 572.4. Application: dead-reckoning of a mobile robot 572.4.1. Test case 582.4.2. Constraint network 582.4.3. Resolution 592.5. Discussions 602.5.1. Limits 602.5.2. Extract the most probable trajectory from a tube 612.5.3. Application to path planning 622.6. Conclusion 63Part 2. Constraints-related Contributions 65Introduction to Part 2 67Chapter 3. Trajectories under Differential Constraints 693.1. Introduction 693.1.1. The differential problem 693.1.2. Attempts with set-membership methods 703.1.3. Contribution of this work 723.2. Differential contractor for L d/dt: ẋ(·) = v(·) 733.2.1. Definition and proof 743.2.2. Contraction of the derivative 793.2.3. Implementation 803.3. Contractor-based approach for state estimation 823.3.1. Constraint network of state equations 843.3.2. Fixed-point propagations 853.3.3. Theoretical example of interest ẋ = −sin(x) 873.4. Robotic applications 903.4.1. Causal kinematic chain 903.4.2. Higher-order differential constraints 933.4.3. Kidnapped robot problem 933.4.4. Actual experiment with the Daurade AUV 943.5. Conclusion 99Chapter 4. Trajectories Under Evaluation Constraints 1014.1. Introduction 1014.1.1. Contribution of this work 1014.1.2. Motivations to deal with time uncertainties 1024.2. Generic contractor for trajectory evaluation 1054.2.1. Tube contractor for the constraint Leval : z = y(t) 1054.2.2. Implementation 1114.2.3. Application to state estimation 1134.3. Robotic applications 1144.3.1. Range-only robot localization with low-cost beacons 1144.3.2. Reliable correction of a drifting clock 1214.4. Conclusion 127Part 3. Robotics-related Contributions 129Introduction to Part 3 131Chapter 5. Looped Trajectories: From Detections to Proofs 1335.1. Introduction 1335.1.1. The difference between detection and verification 1335.1.2. Proprioceptive versus exteroceptive measurements 1345.1.3. The two-dimensional case 1355.2. Proprioceptive loop detections 1355.2.1. Formalization 1365.2.2. Loop detections in a bounded-error context 1375.2.3. Approximation of the solution set T 1385.3. Proving loops in detection sets 1415.3.1. Formalism: zero verification 1415.3.2. Topological degree for zero verification 1415.3.3. Loop existence test 1455.3.4. Reliable number of loops 1495.4. Applications 1515.4.1. The Redermor mission 1525.4.2. The Daurade mission 1565.4.3. Optimality of the approach 1595.5. Conclusion 163Chapter 6. A Reliable Temporal Approach for the SLAM Problem 1656.1. Introduction 1656.1.1. Motivations 1656.1.2. SLAM formalism 1676.1.3. Inter-temporalities 1696.2. Temporal SLAM method 1726.2.1. General assumptions 1726.2.2. Temporal resolution 1736.2.3. Lp⇒z: inter-temporal implication constraint 1746.2.4. The Cp⇒z contractor 1786.2.5. Temporal SLAM algorithm 1866.3. Underwater application: bathymetric SLAM 1906.3.1. Context 1906.3.2. Daurade’s underwater mission, October 20, 2015 1946.3.3. Daurade’s underwater mission, October 19, 2015 1996.3.4. Overview of the environment 2026.4. Discussions 2036.4.1. Relation to the state of the art 2036.4.2. About a Bayesian resolution 2056.4.3. Biased sensors 2056.4.4. Fluctuating measurements 2056.5. Conclusion 207Conclusion 211References 217Index 229