Scalable Factor Graph-Based Heterogeneous Bayesian DDF for Dynamic Systems

TL;DR

This work introduces FG-DDF, a factor-graph-based framework for scalable heterogeneous Bayesian decentralized data fusion in dynamic multi-robot systems. By exploiting conditional independence, robots reason over local subgraphs and fuse data on common variables, reducing communication and computation while preserving conservativeness through a conservative filtering/deflation strategy. The approach supports explicit (HS-CF) and implicit (HS-CI) common-data handling, and it is validated via simulations and hardware experiments under realistic conditions, including cycles, dropouts, and non-linear dynamics. The results demonstrate consistent, conservative estimates and robustness, highlighting the method's practicality for large-scale cooperative sensing and localization tasks.

Abstract

Heterogeneous Bayesian decentralized data fusion captures the set of problems in which two robots must combine two probability density functions over non-equal, but overlapping sets of random variables. In the context of multi-robot dynamic systems, this enables robots to take a "divide and conquer" approach to reason and share data over complementary tasks instead of over the full joint state space. For example, in a target tracking application, this allows robots to track different subsets of targets and share data on only common targets. This paper presents a framework by which robots can each use a local factor graph 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 costs. From a theoretical point of view, this paper makes contributions by casting the heterogeneous decentralized fusion problem in terms of a factor graph, analyzing the challenges that arise due to dynamic filtering, and then developing a new conservative filtering algorithm that ensures statistical correctness. From a practical point of view, we show how this framework can be used to represent different multi-robot applications and then test it with simulations and hardware experiments to validate and demonstrate its statistical conservativeness, applicability, and robustness to real-world challenges.

Figures (13)

• Figure 1: Neighborhood graph perspective: factor graph representing robot $i$' local pdf with hidden local variables of neighboring robots $m$ and $j$. Dashed nodes and grey factors are hidden from robot $i$. (a) graph before marginalization of time step 1, demonstrating conditional independence structure (b) fully connected graph after marginalization.
• Figure 2: Shift in approach from requiring all robots to reason over the full global graph, irrespective of their smaller local tasks (a), to each robot reasons over its local smaller graph, representing its task (b).
• Figure 3: DDF in factor graphs: a) full (centralized) factor graph showing the local variable sets of robots $i$ and $j$ and the common variables set. b) showing the local factor graphs over each robot's variables of interest. c) is the common graph describing the factors common to both robots. d-e) demonstrates the fusion operation; the message sent from $j$ with new information over the common variables (d) is then integrated into $i$'s local graph with a simple factor addition (e).
• Figure 4: Example of hidden dependency due to filtering, demonstrated on robot $i$'s local graph and neighborhood variables, unimportant factors for the example are not shown. Dashed lines and gray factors are hidden from agent $i$. (a) Graph before marginalization step. (b) Naive marginalization creates hidden dependencies. (c)-(d) The proposed approach to avoid hidden dependencies. We use the notation $f(\chi_{C,2}^{ij}|\chi_{C,1}^{ij})$ to express and emphasize conditional dependency between variables frey_extending_2002.
• Figure 5: (a) Visible dependencies with full graph perspective. (b) graph after accounting for hidden dependencies and filtering; (c) addition of measurement factors and dependencies at time step 2, red dense factor breaks conditional independence assumption required for heterogeneous fusion. (d)-(e) our proposed method to regain conditional independence by factorizing into smaller local factors.