14 research outputs found
Factor Graphs for Heterogeneous Bayesian Decentralized Data Fusion
This paper explores the use of factor graphs as an inference and analysis
tool for Bayesian peer-to-peer decentralized data fusion. We propose a
framework by which agents can each use local factor graphs to represent
relevant partitions of a complex global joint probability distribution, thus
allowing them to avoid reasoning over the entirety of a more complex model and
saving communication as well as computation cost. This allows heterogeneous
multi-robot systems to cooperate on a variety of real world, task oriented
missions, where scalability and modularity are key. To develop the initial
theory and analyze the limits of this approach, we focus our attention on
static linear Gaussian systems in tree-structured networks and use Channel
Filters (also represented by factor graphs) to explicitly track common
information. We discuss how this representation can be used to describe various
multi-robot applications and to design and analyze new heterogeneous data
fusion algorithms. We validate our method in simulations of a multi-agent
multi-target tracking and cooperative multi-agent mapping problems, and discuss
the computation and communication gains of this approach.Comment: 8 pages, 6 figures, 1 table, submitted to the 24th International
Conference on Information Fusio
Heterogeneous Bayesian Decentralized Data Fusion: An Empirical Study
In multi-robot applications, inference over large state spaces can often be
divided into smaller overlapping sub-problems that can then be collaboratively
solved in parallel over `separate' subsets of states. To this end, the factor
graph decentralized data fusion (FG-DDF) framework was developed to analyze and
exploit conditional independence in heterogeneous Bayesian decentralized fusion
problems, in which robots update and fuse pdfs over different locally
overlapping random states. This allows robots to efficiently use smaller
probabilistic models and sparse message passing to accurately and scalably fuse
relevant local parts of a larger global joint state pdf, while accounting for
data dependencies between robots. Whereas prior work required limiting
assumptions about network connectivity and model linearity, this paper relaxes
these to empirically explore the applicability and robustness of FG-DDF in more
general settings. We develop a new heterogeneous fusion rule which generalizes
the homogeneous covariance intersection algorithm, and test it in multi-robot
tracking and localization scenarios with non-linear motion/observation models
under communication dropout. Simulation and linear hardware experiments show
that, in practice, the FG-DDF continues to provide consistent filtered
estimates under these more practical operating conditions, while reducing
computation and communication costs by more than 95%, thus enabling the design
of scalable real-world multi-robot systems.Comment: 7 pages, 2 figures, submitted to IEEE Conference on Robotics and
Automation (ICRA 2023
Map building, localization and exploration for multi-robot systems
The idea of having robots performing the task for which they have been designed completely autonomously and interacting with the environment has been the main objective since the beginning of mobile robotics. In order to achieve such a degree of autonomy, it is indispensable for the robot to have a map of the environment and to know its location in it, in addition to being able to solve other problems such as motion control and path planning towards its goal. During the fulfillment of certain missions without a prior knowledge of its environment, the robot must use the inaccurate information provided by its on-board sensors to build a map at the same time it is located in it, arising the problem of Simultaneous Localization and Mapping (SLAM) extensively studied in mobile robotics. In recent years, there has been a growing interest in the use of robot teams due to their multiple benefits with respect to single-robot systems such as higher robustness, accuracy, efficiency and the possibility to cooperate to perform a task or to cover larger environments in less time. Robot formations also belongs to this field of cooperative robots, where they have to maintain a predefined structure while navigating in the environment. Despite their advantages, the complexity of autonomous multi-robot systems increases with the number of robots as a consequence of the larger amount of information available that must be handled, stored and transmitted through the communications network. Therefore, the development of these systems presents new difficulties when solving the aforementioned problems which, instead of being addressed individually for each robot, must be solved cooperatively to efficiently exploit all the information collected by the team. The design of algorithms in this multi-robot context should be directed to obtain greater scalability and performance to allow their online execution. This thesis is developed in the field of multi-robot systems and proposes solutions to the navigation, localization, mapping and path planning processes which form an autonomous system. The first part of contributions presented in this thesis is developed in the context of robot formations, which require greater team cooperation and synchronization, although they can be extended to systems without this navigation constraint. We propose localization, map refinement and exploration techniques under the assumption that the formation is provided with a map of the environment, possibly partial and inaccurate, wherein it has to carry out its commanded mission. In a second part, we propose a multi-robot SLAM approach without any assumption about the prior knowledge of a map nor the relationships between robots in which we make use of state of the art methodologies to efficiently manage the resources available in the system. The performance and efficiency of the proposed robot formation and multi-robot SLAM systems have been demonstrated through their implementation and testing both in simulations and with real robots
Nonlinear bayesian filtering with applications to estimation and navigation
In principle, general approaches to optimal nonlinear filtering can be described
in a unified way from the recursive Bayesian approach. The central idea to this recur-
sive Bayesian estimation is to determine the probability density function of the state
vector of the nonlinear systems conditioned on the available measurements. However,
the optimal exact solution to this Bayesian filtering problem is intractable since it
requires an infinite dimensional process. For practical nonlinear filtering applications
approximate solutions are required. Recently efficient and accurate approximate non-
linear filters as alternatives to the extended Kalman filter are proposed for recursive
nonlinear estimation of the states and parameters of dynamical systems. First, as
sampling-based nonlinear filters, the sigma point filters, the unscented Kalman fil-
ter and the divided difference filter are investigated. Secondly, a direct numerical
nonlinear filter is introduced where the state conditional probability density is calcu-
lated by applying fast numerical solvers to the Fokker-Planck equation in continuous-
discrete system models. As simulation-based nonlinear filters, a universally effective
algorithm, called the sequential Monte Carlo filter, that recursively utilizes a set of
weighted samples to approximate the distributions of the state variables or param-
eters, is investigated for dealing with nonlinear and non-Gaussian systems. Recentparticle filtering algorithms, which are developed independently in various engineer-
ing fields, are investigated in a unified way. Furthermore, a new type of particle
filter is proposed by integrating the divided difference filter with a particle filtering
framework, leading to the divided difference particle filter. Sub-optimality of the ap-
proximate nonlinear filters due to unknown system uncertainties can be compensated
by using an adaptive filtering method that estimates both the state and system error
statistics. For accurate identification of the time-varying parameters of dynamic sys-
tems, new adaptive nonlinear filters that integrate the presented nonlinear filtering
algorithms with noise estimation algorithms are derived.
For qualitative and quantitative performance analysis among the proposed non-
linear filters, systematic methods for measuring the nonlinearities, biasness, and op-
timality of the proposed nonlinear filters are introduced. The proposed nonlinear
optimal and sub-optimal filtering algorithms with applications to spacecraft orbit es-
timation and autonomous navigation are investigated. Simulation results indicate
that the advantages of the proposed nonlinear filters make these attractive alterna-
tives to the extended Kalman filter
Regularized model learning in EDAs for continuous and multi-objective optimization
Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using
two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods
Gaussian belief propagation for real-time decentralised inference
For embodied agents to interact intelligently with their surroundings, they require perception systems that construct persistent 3D representations of their environments. These representations must be rich; capturing 3D geometry, semantics, physical properties, affordances and much more. Constructing the environment representation from sensory observations is done via Bayesian probabilistic inference and in practical systems, inference must take place within the power, compactness and simplicity constraints of real products. Efficient inference within these constraints however remains computationally challenging and current systems often require heavy computational resources while delivering a fraction of the desired capabilities.
Decentralised algorithms based on local message passing with in-place processing and storage offer a promising solution to current inference bottlenecks. They are well suited to take advantage of recent rapid developments in distributed asynchronous processing hardware to achieve efficient, scalable and low-power performance.
In this thesis, we argue for Gaussian belief propagation (GBP) as a strong algorithmic framework for distributed, generic and incremental probabilistic estimation. GBP operates by passing messages between the nodes on a factor graph and can converge with arbitrary asynchronous message schedules. We envisage the factor graph being the fundamental master environment representation, and GBP the flexible inference tool to compute local in-place probabilistic estimates. In large real-time systems, GBP will act as the `glue' between specialised modules, with attention based processing bringing about local convergence in the graph in a just-in-time manner.
This thesis contains several technical and theoretical contributions in the application of GBP to practical real-time inference problems in vision and robotics. Additionally, we implement GBP on novel graph processor hardware and demonstrate breakthrough speeds for bundle adjustment problems. Lastly, we present a prototype system for incrementally creating hierarchical abstract scene graphs by combining neural networks and probabilistic inference via GBP.Open Acces
Factor, structured factor and vine copula models for multivariate social science data
The development of multivariate models with parsimonious dependence is of great interest in a wide range of applications. Two broad frameworks have been considered for parsimonious dependence modelling, namely the latent variable (factor) and copula frameworks. Within these two broad frameworks, we propose several factor models based on copulas for modelling parsimonious dependence structures in multivariate social science data.
We develop factor copula models for mixed continuous and discrete responses where the dependence among the observed variables is explained via a few factors. These are conditional independence models; the observed variables are conditionally independent given the factors.
We also propose the bi-factor and second-order copula models for item response data that can be split into non-overlapping groups, where each group of items has homogeneous dependence. These proposed models fall under the structured factor copula class. Our general models subsume the Gaussian bi-factor and second-order models as special cases and are suitable for capturing different dependencies between and within different groups of observed variables.
Using the vine copula framework, we extend the factor copula models in order to capture any residual dependence. We propose combined factor/truncated vine copula models for item response data. These are conditional dependence models given very few factors. The proposed models can be viewed as a truncated regular vine copula models that involve both observed and latent variables. They allow for flexible construction based on a sequence of bivariate copulas that can provide different tail, asymmetric and non-linear dependence properties.
All the proposed copula models are applied to real datasets and are compared with other relevant benchmark models showing substantial improvement and performance both conceptually and in fit to data