Fast Weighted Exponential Product Rules for Robust General Multi-Robot Data Fusion Nisar Ahmed* Jonathan Schoenberg* Mark Campbell Autonomous Systems Laboratory, Cornell University Ithaca, New York 14853 e-mail:[nra6,jrs55,mc288]@cornell.edu *both authors contributed equally to this work Abstract—This paper considers the distributed data fusion (DDF) problem for general multi-agent robotic sensor net- works in applications such as 3D mapping and target search. In particular, this paper focuses on the use of conservative fusion via the weighted exponential product (WEP) rule to combat inconsistencies that arise from double-counting common information between fusion agents. WEP fusion is ideal for fusing arbitrarily distributed estimates in ad-hoc communication network topologies, but current WEP rule variants have limited applicability to general multi-robot DDF. To address these issues, new information-theoretic WEP metrics are presented along with novel optimization algorithms for efficiently performing DDF within a recursive Bayesian estimation framework. While the proposed WEP fusion methods are generalizable to arbitrary probability distribution functions (pdfs), emphasis is placed here on widely-used Bernoulli and Gaussian mixture pdfs. Experi- mental results for multi-robot 3D mapping and target search applications show the effectiveness of the proposed methods. I. I NTRODUCTION The problem of fusing information from an ensemble of noisy data streams is critical to many existing and soon-to- be-realized robotic systems operating in uncertain dynamic environments. This is particularly true for distributed multi- robot systems requiring distributed perception for applica- tions such as collaborative mapping for exploration, target search/tracking for surveillance, and futuristic unmanned ur- ban transport systems. For sensor agents in a network to share information and perform distributed data fusion (DDF), it is most desirable to establish a scalable, flexible and robust network over which the robots can transmit and receive infor- mation. An ad-hoc and arbitrary connected network provides scalability for fusion agents to join and drop off the network, flexibility to allow agents to join at any point and robustness to ensure multiple links or agents must fail before the network becomes unconnected [5]. Implementation of DDF for general robot sensor networks thus requires conservative data fusion techniques to maintain estimates that avoid inconsistencies due to rumor propaga- tion [3]. A common conservative fusion rule for estimates with Gaussian probability distribution functions (pdfs) with unknown correlation is Covariance Intersection (CI) [11]. This rule is appropriate for certain types of problems, but it is inadequate for handling non-Gaussian distributions that arise in applications such as target search and 3D mapping. A suit- able conservative fusion rule for arbitrary pdfs with unknown correlation is the weighted exponential product (WEP) [1]. The WEP is a generalization of CI to non-Gaussian distributions [9] and different cost metrics to determine an optimal WEP fusion weight have been proposed [3, 9]. However, these existing WEP fusion approaches have drawbacks that can limit their usefulness in robotic DDF, including the theoretical nature of their cost metrics and difficult implementation for arbitrary pdfs. This paper makes the following contributions: (1) it pro- poses novel information-theoretic metrics for performing WEP fusion that address these issues and are suitable for fusing arbitrary state estimates shared via ad-hoc network communi- cation topologies in a wide range of robotic DDF applications; (2) it presents new formally consistent algorithms for online implementation of our proposed WEP fusion metrics that can be used to quickly and robustly combine information in a recursive Bayesian estimation framework, with emphasis on the Bernoulli and Gaussian mixture distribution functions used widely in robotics; (3) it demonstrates the effectiveness of our proposed WEP fusion methods for performing online collaborative 3D mapping and 2D target search with multi- robot networks in loopy communication topologies. A. DDF Preliminaries Formally, let x k ∈ R nx be an n x -dimensional state to be estimated at discrete time steps k =0, 1, ... by N independent robotic sensor agents. Assume that each robot i ∈{1, ..., N } obtains n y local sensor measurements of x k in the vector y k i with likelihood function p i (y k i |x k ). Let p i (x k |Z k i ) be the local posterior pdf for robot i given the set of all information Z k i =  Z k-1 i ,y k i  available to i before new information Z k j arrives from robot j = i, such that local fusion of y k i is given by the posterior pdf from Bayes’ rule, p i (x k |Z k i ) ∝ p i (x k-1 |Z k-1 i )p i (y k i |x k ). (1) For generality, the robot networks considered here are as- sumed to have arbitrary dynamic node-to-node communication topologies, such that: (i) N may vary; (ii) each robot is only aware of nodes it connected to; (iii) no robot ever knows the complete global network topology; (iv) no robot knows the receipt status of messages it has sent. Centralized fusion or raw data sharing can fully recover new information in  N i=1 Z k i , but such methods scale poorly with