Coordinated Decentralized Search for a Lost Target in a Bayesian World Fr´ ed´ eric Bourgault Australian Centre for Field Robotics The University of Sydney Sydney, NSW 2006, Australia f.bourgault@acfr.usyd.edu.au Tomonari Furukawa School of Mech. and Manuf. Eng. The University of New South Wales Sydney, NSW 2052, Australia t.furukawa@unsw.edu.au Hugh F. Durrant-Whyte Australian Centre for Field Robotics The University of Sydney Sydney, NSW 2006, Australia hugh@acfr.usyd.edu.au Abstract— This paper describes a decentralized Bayesian ap- proach to coordinating multiple autonomous sensor platforms search- ing for a single non-evading target. In this architecture, each decision maker builds an equivalent representation of the target state PDF through a Bayesian DDF network enabling them to coordinate their actions without exchanging any information about their plans. The advantage of the approach is that a high degree of scalability and real time adaptability can be achieved. The effectiveness of the approach is demonstrated in different scenarios by implementing the framework for a team of airborne search vehicles looking for a stationary, and a drifting target lost at sea. I. I NTRODUCTION “Yacht Grimalkin capsized in position thirty miles north-west of Land’s End...” 1 When rescue authorities receive a distress signal time be- comes critical. Survival expectancy decreases rapidly when lost at sea and a rescue mission’s primary goal is to search for and find the castaways as diligently and efficiently as possible. The search, based on some coarse estimate of the target location, must often be performed in low visibility conditions and despite strong winds and high seas causing the location estimate to grow even more uncertain as time goes by. Keeping these time and physical constraints in mind, and given a large team of heterogeneous platforms such as high flying long range aircrafts, helicopters and ships equipped with different sensors, what should be the optimal search strategy? This paper presents a decentralized Bayesian approach to the target detection problem as described in [8] (Chapter 9). It expands the single vehicle framework proposed in [2] to an arbitrary number of sensing platforms by integrating a fully decentralized Bayesian data fusion (DDF) technique with a decentralized coordinated control scheme that was first proposed by Grocholsky [6]. Scalability, modularity and real-time adaptability are the advantages of the decen- tralized approach. At any time, new rescue vehicles can join, or momentarily quit for refuelling, the search effort and the system should seemly and robustly adapt to the change. The breakdown of the paper is as follows. Firstly, the decentralized Bayesian filtering algorithm that accurately maintains and updates the target state probability distri- bution is described in the next section. Then section III describes the searching problem, and section IV describes the utility function selected and formulates the decentral- ized control optimization problem. Then, in section V the effectiveness of the approach is demonstrated for multiple 1 Coastguard broadcast during the desastrous 1979 Fastnet yacht race, August 14, 1979 [9] airborne search vehicles in three different scenarios for sta- tionary, and drifting targets, and in one instance, the optimal cooperative solution is compared with the coordinated one. Finally, conclusions and ongoing research directions are highlighted in the last section. II. BAYESIAN FILTERING This section presents the mathematical foundations of the Bayesian decentralized data fusion algorithm that keeps track of the target state PDF. The Bayesian approach is particularily suitable for combining in a rational manner heterogeneous non-gaussian sensor observations with other sources of quantitative and qualitative information [11][1]. In Bayesian analysis any quantity that is not known is considered a random variable. The state of knowledge about such a random variable is expressed in the form of a probability density function (PDF). Any new information in the form of a probabilistic observation is combined with the previous PDF using the Baye’s theorem in order to update the state of knowledge and form the new a posteriori PDF. That PDF forms the quantitative basis on which all inferences, or control decisions (Sec.IV) are made. In the searching problem, the unknown variable is the target state vector x t ∈ X t which in general describes the target location but could also include its attitude, velocity, etc. The analysis starts by determining the a priori PDF of x t , p(x t 0 |z 0 ) ≡ p(x t 0 ), which combines all available in- formation including past experience. For example, this a priori PDF could be in the form a gaussian distribution representing the prior coarse estimate of the parameter of interest. If noting but the bounds is known about the parameter, the least biased approach is to represent this knowledge by a uniform PDF over the bounded region of the space. Then, once the prior distribution has been established, the PDF of the target state at time step k, p(x t k |z 1:k ), can be constructed recursively, provided the sequence z 1:k = {z i j : i = 1, ..., N s , j = 1, ..., k} of all the observations made from the N s sensors on board the search vehicles, z i j being the observation from the i th sensor at time step j. This recursive estimation is performed in two stages: prediction and update. A. Prediction A prediction stage is necessary in Bayesian analysis when the PDF of the state to be evaluated is evolving with time i.e. the target is in motion or the uncertainty about its location is increasing. Suppose we are at time step k - 1 and the latest PDF update, p(x t k-1 |z 1:k-1 ) is available. Then Proceedings of the 2003 IEEE/RSJ Intl. Conference on Intelligent Robots and Systems Las Vegas, Nevada · October 2003 0-7803-7860-1/03/$17.00 © 2003 IEEE 48