Conservative Filtering for Heterogeneous Decentralized Data Fusion in Dynamic Robotic Systems

Abstract

This paper presents a method for Bayesian multirobot peer-to-peer data fusion where any pair of autonomous robots hold non-identical, but overlapping parts of a global joint probability distribution, representing real world inference tasks (e.g., mapping, tracking). It is shown that in dynamic stochastic systems, filtering, which corresponds to marginalization of past variables, results in direct and hidden dependencies between variables not mutually monitored by the robots, which might lead to an overconfident fused estimate. The paper makes both theoretical and practical contributions by providing (i) a rigorous analysis of the origin of the dependencies and and (ii) a conservative filtering algorithm for heterogeneous data fusion in dynamic systems that can be integrated with existing fusion algorithms. This work uses factor graphs as an analysis tool and an inference engine. Each robot in the network maintains a local factor graph and communicates only relevant parts of it (a sub-graph) to its neighboring robot. We discuss the applicability to various multi-robot robotic applications and demonstrate the performance using a multi-robot multitarget tracking simulation, showing that the proposed algorithm produces conservative estimates at each robot.

Nonlinear Heterogeneous Bayesian Decentralized Data Fusion

“…Later work in [5] develops a factor graphbased framework as both the inference engine and as a tool track dependencies in the data, analyze and exploit conditional independence structure in heterogeneous fusion problems. This is then used in [9] to develop a method for conservative filtering for heterogeneous fusion in dynamic systems. Since the aforementioned body of work aimed at gaining fundamental understanding of the heterogeneous DDF problem and the nature of dependencies in the data held by the robots in the network, several assumptions were made: (i) the dynamic system transition and observation models (p(χ i k |χ i k−1 ) and p(y i k |χ i k ), respectively) are linear with additive white Gaussian noise (AWGN); and (ii) the network communication topology is described by an undirected acyclic graph.…”

“…to be explicitly tracked and removed in fusion (1) using the heterogeneousstate channel filter (HS-CF) [2]. It has been shown, that under these assumptions, the FG-DDF framework enables robots to accurately process (infer) and communicate only parts of the global joint pdf, which, by reducing communication and computation costs by more than 95% in linear-Gaussian problems [2], [5], lets heterogeneous robotic teams scale much more effectively, However, questions arise as to how robust/applicable the FG-DDF framework developed in [5] and [9] is to: nonlinear transition and observation models; real-world problems such as message dropouts; and approximations of the 'common' pdf,…”

“…A factor graph is a type of probability graphical model (PGM) [13], which has gained popularity in the robotics community since it naturally expresses the sparse information dependency structure inherent in many robotic applications [14]. Recent work used factor graphs to exploit conditional independence in heterogeneous DDF problems and suggested a new framework, FG-DDF, to analyze and solve them in linear static [5] and dynamic [9] systems.…”

“…In classical homogeneous DDF, where robots communicate and infer the same global set of rvs, methods exist to either explicitly (e.g., by using a channel filter (CF) [6]) or implicitly (e.g., covariance intersection (CI) [7], inverse covariance intersection (ICI) [8]) track such dependencies. In heterogeneous DDF, the problem becomes more acute, as in addition to the above known-unknown dependencies, there are now (hidden) unknown-unknown dependencies between non-mutual rvs that must be treated [9]. To study, analyze and solve heterogeneous DDF problems and the dependencies therein, a factor graph based framework, dubbed FG-DDF, based on the heterogeneous state CF (HS-CF) algorithm [2], was developed in [5] and then extended to linear-dynamic systems in [9].…”

“…In heterogeneous DDF, the problem becomes more acute, as in addition to the above known-unknown dependencies, there are now (hidden) unknown-unknown dependencies between non-mutual rvs that must be treated [9]. To study, analyze and solve heterogeneous DDF problems and the dependencies therein, a factor graph based framework, dubbed FG-DDF, based on the heterogeneous state CF (HS-CF) algorithm [2], was developed in [5] and then extended to linear-dynamic systems in [9]. However, some fundamental issues arise for non-linear systems -namely, the definition and meaning of common data dependencies become less clear, e.g.…”