
Multimodal Perception and Secure State Estimation for Robotic Mobility Platforms
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Enables readers to understand important new trends in multimodal perception for mobile robotics
This book provides a novel perspective on secure state estimation and multimodal perception for robotic mobility platforms such as autonomous vehicles. It thoroughly evaluates filter-based secure dynamic pose estimation approaches for autonomous vehicles over multiple attack signals and shows that they outperform conventional Kalman filtered results.
As a modern learning resource, it contains extensive simulative and experimental results that have been successfully implemented on various models and real platforms. To aid in reader comprehension, detailed and illustrative examples on algorithm implementation and performance evaluation are also presented. Written by four qualified authors in the field, sample topics covered in the book include:
* Secure state estimation that focuses on system robustness under cyber-attacks
* Multi-sensor fusion that helps improve system performance based on the complementary characteristics of different sensors
* A geometric pose estimation framework to incorporate measurements and constraints into a unified fusion scheme, which has been validated using public and self-collected data
* How to achieve real-time road-constrained and heading-assisted pose estimation
This book will appeal to graduate-level students and professionals in the fields of ground vehicle pose estimation and perception who are looking for modern and updated insight into key concepts related to the field of robotic mobility platforms.
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Persons
Xinghua Liu is a Professor with Xi'an University of Technology. His research interests are secure state estimation and control, cyber-physical systems, and artificial Intelligence.
Rui Jiang is a Staff Algorithm Engineer at the OmniVision Technologies Inc., and an Adjunct Lecturer with the National University of Singapore. His research interests are intelligent sensing, and perception for robotic systems.
Badong Chen is a Professor with Xi'an Jiaotong University. His research interests are signal processing, machine learning, artificial intelligence, neural engineering, and robotics.
Shuzhi Sam Ge is a Professor with the National University of Singapore and an honorary Director of Institute for Future, Qingdao University, China. His research interests are adaptive control, robotics, and artificial Intelligence.
Content
About the Authors xii
Preface xiv
1 Introduction 1
1.1 Background and Motivation 1
1.2 Multimodal Pose Estimation for Vehicle Navigation 2
1.2.1 Multi-Senor Pose Estimation 2
1.2.2 Pose Estimation with Constraints 4
1.2.3 Research Focus in Multimodal Pose Estimation 5
1.3 Secure Estimation 7
1.3.1 Secure State Estimation under Cyber Attacks 7
1.3.2 Secure Pose Estimation for Autonomous Vehicles 8
1.4 Contributions and Organization 9
Part I Multimodal Perception in Vehicle Pose Estimation 13
2 Heading Reference-Assisted Pose Estimation 15
2.1 Preliminaries 16
2.1.1 Stereo Visual Odometry 16
2.1.2 Heading Reference Sensors 17
2.1.3 Graph Optimization on a Manifold 17
2.2 Abstraction Model of Measurement with a Heading Reference 19
2.2.1 Loosely Coupled Model 19
2.2.2 Tightly Coupled Model 20
2.2.3 Structure of the Abstraction Model 22
2.2.4 Vertex Removal in the Abstraction Model 22
2.3 Heading Reference-Assisted Pose Estimation (HRPE) 24
2.3.1 Initialization 24
2.3.2 Graph Optimization 24
2.3.3 Maintenance of the Dynamic Graph 26
2.4 Simulation Studies 26
2.4.1 Accuracy with Respect to Heading Measurement Error 28
2.4.2 Accuracy with Respect to Sliding Window Size 28
2.4.3 Time Consumption with Respect to Sliding Window Size 28
2.5 Experimental Results 31
2.5.1 Experimental Platform 31
2.5.2 Pose Estimation Performance 33
2.5.3 Real-Time Performance 34
2.6 Conclusion 36
3 Road-Constrained Localization Using Cloud Models 37
3.1 Preliminaries 38
3.1.1 Scaled Measurement Equations for Visual Odometry 38
3.1.2 Cloud Models 39
3.1.3 Uniform Gaussian Distribution (UGD) 39
3.1.4 Gaussian-Gaussian Distribution (GGD) 42
3.2 Map-Assisted Ground Vehicle Localization 43
3.2.1 Measurement Representation with UGD 44
3.2.2 Shape Matching Between Map and Particles 45
3.2.3 Particle Resampling and Parameter Estimation 46
3.2.4 Framework Extension to Other Cloud Models 47
3.3 Experimental Validation on UGD 47
3.3.1 Configurations 47
3.3.2 Localization with Stereo Visual Odometry 48
3.3.3 Localization with Monocular Visual Odometry 49
3.3.4 Scale Estimation Results 52
3.3.5 Weighting Function Balancing 52
3.4 Experimental Validation on GGD 54
3.4.1 Experiments on KITTI 55
3.4.2 Experiments on the Self-Collected Dataset 61
3.5 Conclusion 63
4 GPS/Odometry/Map Fusion for Vehicle Positioning Using Potential Functions 65
4.1 Potential Wells and Potential Trenches 66
4.1.1 Potential Function Creation 67
4.1.2 Minimum Searching 71
4.2 Potential-Function-Based Fusion for Vehicle Positioning 74
4.2.1 Information Sources and Sensors 74
4.2.2 Potential Representation 76
4.2.3 Road-Switching Strategy 76
4.3 Experimental Results 78
4.3.1 Quantitative Results 78
4.3.2 Qualitative Evaluation 80
4.4 Conclusion 84
5 Multi-Sensor Geometric Pose Estimation 85
5.1 Preliminaries 86
5.1.1 Distance on Riemannian Manifolds 86
5.1.2 Probabilistic Distribution on Riemannian Manifolds 87
5.2 Geometric Pose Estimation Using Dynamic Potential Fields 88
5.2.1 State Space and Measurement Space 88
5.2.2 Dynamic Potential Fields on Manifolds 90
5.2.3 DPF-Based Information Fusion 91
5.2.4 Approximation of Geometric Pose Estimation 95
5.3 VO-Heading-Map Pose Estimation for Ground Vehicles 97
5.3.1 System Modeling 97
5.3.2 Road Constraints 98
5.3.3 Parameter Estimation on SE(3) 99
5.4 Experiments on KITTI Sequences 99
5.4.1 Overall Performance 99
5.4.2 Influence of Heading Error 102
5.4.3 Influence of Road Map Resolution 102
5.4.4 Influences of Parameters 104
5.5 Experiments on the NTU Dataset 105
5.5.1 Overall Performance 105
5.5.2 Phenomena Observed During Experiments 105
5.6 Conclusion 107
Part II Secure State Estimation for Mobile Robots 109
6 Filter-Based Secure Dynamic Pose Estimation 111
6.1 Introduction 111
6.2 RelatedWork 113
6.3 Problem Formulation 114
6.3.1 System Model 114
6.3.2 Measurement Model 116
6.3.3 Attack Model 116
6.4 Estimator Design 117
6.5 Discussion of Parameter Selection 122
6.5.1 The Probability Subject to Deception Attacks 122
6.5.2 The Bound of Signal ¿¿¿¿k 123
6.6 Experimental Validation 123
6.6.1 Pose Estimation under Attack on a Single State 125
6.6.2 Pose Estimation under Attacks on Multiple States 127
6.7 Conclusion 130
7 UKF-Based Vehicle Pose Estimation under Randomly Occurring Deception Attacks 131
7.1 Introduction 131
7.2 Related Work 133
7.3 Pose Estimation Problem for Ground Vehicles under Attack 134
7.3.1 System Model 134
7.3.2 Attack Model 136
7.4 Design of the Unscented Kalman Filter 137
7.5 Numeric Simulation 141
7.6 Experiments 144
7.6.1 General Performance 145
7.6.2 Influence of Parameters 145
7.7 Conclusion 147
8 Secure Dynamic State Estimation with a Decomposing Kalman Filter 149
8.1 Introduction 149
8.2 Problem Formulation 151
8.3 Decomposition of the Kalman Filter By Using a Local Estimate 153
8.4 A Secure Information Fusion Scheme 158
8.5 Numerical Example 161
8.6 Conclusion 162
8.7 Appendix: Proof of Theorem 8.2 162
8.8 Proof of Theorem 8.4 165
9 Secure Dynamic State Estimation for AHRS 169
9.1 Introduction 169
9.2 Related Work 170
9.2.1 Attitude Estimation 170
9.2.2 Secure State Estimation 171
9.2.3 Secure Attitude Estimation 171
9.3 Attitude Estimation Using Heading References 172
9.3.1 Attitude Estimation from Vector Observations 172
9.3.2 Secure Attitude Estimation Framework and Modeling 173
9.4 Secure Estimator Design with a Decomposing Kalman Filter 174
9.4.1 Decomposition of the Kalman Filter Using a Local Estimate 176
9.4.2 A Least-Square Interpretation for the Decomposition 177
9.4.3 Secure State Estimate 178
9.5 Simulation Validation 181
9.5.1 Simulating Measurements with Attacks 182
9.5.2 Filter Performance 182
9.5.3 Influence of Parameter ¿¿¿¿ 182
9.6 Conclusion 184
10 Conclusions 185
References 189
Index 207
1
Introduction
1.1 Background and Motivation
With the rapid development of sensor technologies, and due to increased density in integrated circuits predicted by Moore's law, the autonomous vehicle has become a fruitful area blending robotics, automation, computer vision, and intelligent transportation technologies. It has been reported that traditional automobile companies and startups plan to get their autonomous driving systems ready in the 2020s [Ross, 2017].
The US Department of Transportation's National Highway Traffic Safety Administration (NHTSA) defined five levels of autonomous driving, from manual driving (level 0), to driver assistance (level 1), to fully autonomous driving (level 5) (https://www.sae.org/standards/content/j3016_202104). As an inspiring example, the Audi A8, launched in 2017, is claimed to be "the world's first production automobile conditional automated at level 3," according to Audi AG. Nevertheless, some pessimistic voices have emerged, claiming that fully autonomous cars will not be developed as quickly as expected or are even unlikely. One of the pacesetters in fully autonomous driving technologies, Waymo LLC, has received resident complaints due to conflicts in driving behaviors between humans and autonomous vehicles.
Although it is still a long way to level 5 autonomy, there is high demand for the development of autonomous vehicles so that tasks related to logistics, environmental cleanup, public security, and much more can be automated. Among all the functional blocks in autonomous vehicles, the navigation system plays an irreplaceable role since the vehicle needs to be literally "in motion" for any particular task. Multimodal perception and state estimation are two coadjutant modules for vehicle navigation. There have been extensive research outcomes on these two topics in autonomous vehicle navigation, but a few challenges still exist, motivated by which the in-depth studies in this book have been carried out:
- A modern pose estimation system contains multiple sensors to achieve accuracy and robustness. Appropriate sensor configurations, which combine the advantages of each sensor to benefit the whole estimation system, are distinct depending on the specific applications and requirements. Based on a particular sensor configuration, new theories and ideas are required for multi-sensor pose estimation, where states, measurements, and constraints are represented in a unified fusion framework.
- Due to the stealthiness of attacks, system operators usually cannot discover attacks in time, which may lead to severe economic damage and even the loss of human lives. Such incidents indicate that enhancing the security of the system is an urgent issue. Researchers have studied how we can securely estimate the state of a dynamical system from the controller's point of view based on a set of noisy and maliciously corrupted sensor measurements. In particular, researchers have focused on linear dynamical systems and have tried to understand how the system dynamics can be leveraged for security guarantees.
This book discusses the pose estimation problem for robotic mobility platforms using information from multiple sensors. The first part discusses different sensor configurations and introduces new sensor fusion algorithms and frameworks to minimize pose estimation errors. Those concepts and methods are extensively used in current state-of-the-art autonomous vehicles, and extensive experimental results have been provided to verify the algorithm performance on real robotic platforms. The second part focuses on the secure estimation problem in multi-sensor fusion, where attacks are considered and explicitly modeled in algorithm design. As this is a new topic that is at the primary stage of research, theoretical analysis and simulation results are shown in the related chapters.
1.2 Multimodal Pose Estimation for Vehicle Navigation
1.2.1 Multi-Senor Pose Estimation
Multi-sensor fusion is a typical solution where system dynamics, measurements, and constraints are fused consistently to increase estimation performance in terms of accuracy and robustness [Borges and Aldon, 2002, Ye et al., 2015, Teixeira et al., 2018]. Essentially, pose estimation can be considered as state estimation within a state space with a problem-dependent topological structure. Let us assume the following discrete state equation and output equation:
(1.1) (1.2)where , , denote the state, control input, and measurement, respectively; and are the state equation and output equation; and and represent process and measurement noise.
Filtering and optimization are two frequently used data fusion frameworks for pose estimation. Filtering approaches propagate state vectors with their joint probability distributions along with time. The Kalman filter models the state and noise as Gaussian, which is not suitable for non-Gaussian or multimodal distributions. The particle filter and its variants [Van Der Merwe et al., 2001, Nummiaro et al., 2003] have been proposed to deal with non-linear and non-Gaussian systems, and the computation load of updating particle states proliferates with the sample number. The optimization-based approaches retain historical measurement and estimation as a graph such that they can be used for bundle adjustment or simultaneous localization and mapping (SLAM) [Grisetti et al., 2010]. The two commonly used frameworks are elaborated here.
Filtering-Based Approaches As shown in related work [Janabi-Sharifi and Marey, 2010, Koval et al., 2015, Bloesch et al., 2017], filters provide a probabilistic solution on pose estimation, which can be divided into two steps. First, the "prediction" step predicts states without current measurement, according to the state equation
(1.3)where denotes the conditional distribution, and specifically is obtained from (1.1). Then, the probability distribution of the update can be obtained in the "correction" step, based on the output equation
(1.4)where is obtained from (1.2), and the constant denominator is
(1.5)Optimization-Based Approaches Instead of using the filtering-based approaches, some other research [Leutenegger et al., 2015, Huang et al., 2017, Parisotto et al., 2018, Wang et al., 2018a] aims to minimize the user-defined cost function such that
(1.6)where denotes the cost items to be considered; the information matrix indicates the degree of confidence in the corresponding measurement; and the error function measures the difference between the ideal and actual measurement.
1.2.2 Pose Estimation with Constraints
Constraints1 in pose estimation are helpful in increasing algorithm robustness and accuracy. For example, we may consider motion constraints (1.1), that limit the vehicle's pose change with time, and road constraints, which require the vehicle to stay on the road. Constraints in practical issues are mostly considered as soft to allow modeling errors and noise. We discuss constrained pose estimation from two perspectives.
Incorporating Constraints into Filtering Given the constraints , where is a constant vector, the augmented output equation can be obtained to incorporate the constraints into measurements [Mourikis and Roumeliotis, 2007, Simon, 2010, Boada et al., 2017, Ramezani et al., 2017, Yang et al., 2017a, Shen et al., 2017]:
(1.7)where the covariance matrix of indicates the confidence in the soft constraints. With a prediction that remains the same, the correction step can be achieved by applying the augmented output equation.
In addition, we may first obtain the estimate without constraints and then project the unconstrained estimates toward the constraint states to get the final estimate
(1.8)where is an operator indicating the difference between states and is a positive-definite weighting matrix. For linear systems under linear constraints, if , the ordinary vector subtraction is selected as , leading to analytical solutions. Numerical methods are required to generalize the projection method to non-linear systems or with non-linear constraints. For particle filters, particle weights can be adjusted to reduce the influence of estimation results that do not satisfy the constraints.
Incorporating Constraints into Optimization For hard constraints, the method of Lagrange multipliers can be used to construct the corresponding non-constrained optimization problem. For soft constraints, one naive but effective way is to add the penalty functions to the cost function , such that
(1.9)where denotes the -th constraint to be considered; indicates the degree of confidence in the -th constraint. Examples of related work can be found in [Estrada et al., 2005, Levinson et al., 2007, Lu et al., 2017, Hoang et al.,...
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