192 research outputs found
Set-based state estimation and fault diagnosis using constrained zonotopes and applications
This doctoral thesis develops new methods for set-based state estimation and
active fault diagnosis (AFD) of (i) nonlinear discrete-time systems, (ii)
discrete-time nonlinear systems whose trajectories satisfy nonlinear equality
constraints (called invariants), (iii) linear descriptor systems, and (iv)
joint state and parameter estimation of nonlinear descriptor systems. Set-based
estimation aims to compute tight enclosures of the possible system states in
each time step subject to unknown-but-bounded uncertainties. To address this
issue, the present doctoral thesis proposes new methods for efficiently
propagating constrained zonotopes (CZs) through nonlinear mappings. Besides,
this thesis improves the standard prediction-update framework for systems with
invariants using new algorithms for refining CZs based on nonlinear
constraints. In addition, this thesis introduces a new approach for set-based
AFD of a class of nonlinear discrete-time systems. An affine parametrization of
the reachable sets is obtained for the design of an optimal input for set-based
AFD. In addition, this thesis presents new methods based on CZs for set-valued
state estimation and AFD of linear descriptor systems. Linear static
constraints on the state variables can be directly incorporated into CZs.
Moreover, this thesis proposes a new representation for unbounded sets based on
zonotopes, which allows to develop methods for state estimation and AFD also of
unstable linear descriptor systems, without the knowledge of an enclosure of
all the trajectories of the system. This thesis also develops a new method for
set-based joint state and parameter estimation of nonlinear descriptor systems
using CZs in a unified framework. Lastly, this manuscript applies the proposed
set-based state estimation and AFD methods using CZs to unmanned aerial
vehicles, water distribution networks, and a lithium-ion cell.Comment: My PhD Thesis from Federal University of Minas Gerais, Brazil. Most
of the research work has already been published in DOIs
10.1109/CDC.2018.8618678, 10.23919/ECC.2018.8550353,
10.1016/j.automatica.2019.108614, 10.1016/j.ifacol.2020.12.2484,
10.1016/j.ifacol.2021.08.308, 10.1016/j.automatica.2021.109638,
10.1109/TCST.2021.3130534, 10.1016/j.automatica.2022.11042
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Fisher-Rao distance and pullback SPD cone distances between multivariate normal distributions
Data sets of multivariate normal distributions abound in many scientific
areas like diffusion tensor imaging, structure tensor computer vision, radar
signal processing, machine learning, just to name a few. In order to process
those normal data sets for downstream tasks like filtering, classification or
clustering, one needs to define proper notions of dissimilarities between
normals and paths joining them. The Fisher-Rao distance defined as the
Riemannian geodesic distance induced by the Fisher information metric is such a
principled metric distance which however is not known in closed-form excepts
for a few particular cases. In this work, we first report a fast and robust
method to approximate arbitrarily finely the Fisher-Rao distance between
multivariate normal distributions. Second, we introduce a class of distances
based on diffeomorphic embeddings of the normal manifold into a submanifold of
the higher-dimensional symmetric positive-definite cone corresponding to the
manifold of centered normal distributions. We show that the projective Hilbert
distance on the cone yields a metric on the embedded normal submanifold and we
pullback that cone distance with its associated straight line Hilbert cone
geodesics to obtain a distance and smooth paths between normal distributions.
Compared to the Fisher-Rao distance approximation, the pullback Hilbert cone
distance is computationally light since it requires to compute only the extreme
minimal and maximal eigenvalues of matrices. Finally, we show how to use those
distances in clustering tasks.Comment: 25 page
Applications
Volume 3 describes how resource-aware machine learning methods and techniques are used to successfully solve real-world problems. The book provides numerous specific application examples: in health and medicine for risk modelling, diagnosis, and treatment selection for diseases in electronics, steel production and milling for quality control during manufacturing processes in traffic, logistics for smart cities and for mobile communications
Localization in urban environments. A hybrid interval-probabilistic method
Ensuring safety has become a paramount concern with the increasing autonomy of vehicles and the advent of autonomous driving. One of the most fundamental tasks of increased autonomy is localization, which is essential for safe operation. To quantify safety requirements, the concept of integrity has been introduced in aviation, based on the ability of the system to provide timely and correct alerts when the safe operation of the systems can no longer be guaranteed. Therefore, it is necessary to assess the localization's uncertainty to determine the system's operability.
In the literature, probability and set-membership theory are two predominant approaches that provide mathematical tools to assess uncertainty. Probabilistic approaches often provide accurate point-valued results but tend to underestimate the uncertainty. Set-membership approaches reliably estimate the uncertainty but can be overly pessimistic, producing inappropriately large uncertainties and no point-valued results. While underestimating the uncertainty can lead to misleading information and dangerous system failure without warnings, overly pessimistic uncertainty estimates render the system inoperative for practical purposes as warnings are fired more often.
This doctoral thesis aims to study the symbiotic relationship between set-membership-based and probabilistic localization approaches and combine them into a unified hybrid localization approach. This approach enables safe operation while not being overly pessimistic regarding the uncertainty estimation. In the scope of this work, a novel Hybrid Probabilistic- and Set-Membership-based Coarse and Refined (HyPaSCoRe) Localization method is introduced. This method localizes a robot in a building map in real-time and considers two types of hybridizations. On the one hand, set-membership approaches are used to robustify and control probabilistic approaches. On the other hand, probabilistic approaches are used to reduce the pessimism of set-membership approaches by augmenting them with further probabilistic constraints.
The method consists of three modules - visual odometry, coarse localization, and refined localization. The HyPaSCoRe Localization uses a stereo camera system, a LiDAR sensor, and GNSS data, focusing on localization in urban canyons where GNSS data can be inaccurate. The visual odometry module computes the relative motion of the vehicle. In contrast, the coarse localization module uses set-membership approaches to narrow down the feasible set of poses and provides the set of most likely poses inside the feasible set using a probabilistic approach. The refined localization module further refines the coarse localization result by reducing the pessimism of the uncertainty estimate by incorporating probabilistic constraints into the set-membership approach.
The experimental evaluation of the HyPaSCoRe shows that it maintains the integrity of the uncertainty estimation while providing accurate, most likely point-valued solutions in real-time. Introducing this new hybrid localization approach contributes to developing safe and reliable algorithms in the context of autonomous driving
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
Reactive Particle Swarm Control Architecture and Application for Scalar Field Adaptive Navigation
Adaptive navigation is a subcategory of navigation techniques that attempts to identify goal locations that satisfy specific criteria in an unknown area. In 2D scalar field adaptive navigation (SFAN), primitives navigate to or along features of interest in an unknown, possibly time-varying, planar scalar field. Features include extrema, contours, and fronts. This work solves the 2D SFAN problem using swarm robotic techniques. Robotic swarms are a subset of multi-robot systems that use decentralized control of simple interchangeable robots to perform collective actions. A subgroup of swarms is the Reactive Particle Swarm (RPS), characterized based on its simplicity, reactivity to its current environment, and flexibility of applications. Previous work in RPS lacks a unified implementation for RPS behaviors making cross-comparison and reuse challenging.
This work presents a novel 1) RPS control architecture that streamlines the development of novel RPS behaviors, 2) elliptical aggregation algorithm that meets the four tenets of elliptical aggregation, and 3) series of 2D RPS SFAN primitives, and verifies all RPS base and composite behaviors using simulated and hardware-in-the-loop case studies.
The architecture unifies the development of new RPS behaviors. The weighted summation of simple base behaviors and external command inputs form complex composite behaviors. This plug-and-play design concept allows for the rapid development of novel combinations of base behaviors, and emphasizes the topdown design of composite behaviors. A series of simulated and on-hardware case studies demonstrate the utility and flexibility of the architecture while establishing a library of verified RPS base behaviors.
The four tenets of elliptical aggregation are 1) guidelines for swarm and ellipse parameter selection to ensure successful aggregation, 2) commandable ellipse parameters, 3) simplicity for scaling in the number of robots, and 4) adaptive sizing. The elliptical attraction behavior can be leveraged for SFAN to orient the swarm to improve feature sensing and size to overcome noise thresholds. The elliptical attraction behavior and adaptive sizing variant were verified using simulated and experimental trials.
For 2D RPS SFAN primitives, the extremum seeking, contour following, and front identification behaviors and their adaptive sizing variants are verified using simulations incorporating both artificial and interpolated real-world scalar fields and hardware-in-the-loop trials. The ridge descent, trench ascent, and saddle point identification behaviors are presented in a preliminary form and are verified through simulation.
Overall this work has four main contributions, 1) a novel RPS control architecture that unifies the implementation and streamlines the development of novel RPS behaviors, 2) a novel elliptical attraction behavior, 3) novel SFAN primitives, and 4) verification of all RPS behaviors through simulation and hardware-in-theloop trials
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
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