Robotics and Autonomous Systems 57 (2009) 310–320 Contents lists available at ScienceDirect Robotics and Autonomous Systems journal homepage: www.elsevier.com/locate/robot Decentralised decision making in heterogeneous teams using anonymous optimisation George M. Mathews a,b,∗ , Hugh Durrant-Whyte a , Mikhail Prokopenko c a ARC Centre of Excellence for Autonomous Systems, The University of Sydney, Sydney NSW, Australia b CSIRO Industrial Physics, Lindfield NSW, Australia c CSIRO ICT Centre, North Ryde NSW, Australia article info Article history: Available online 19 November 2008 Keywords: Asynchronous optimisation Team decision making Multi-agent systems abstract This paper considers the scenario where multiple autonomous agents must cooperate in making decisions to minimise a continuous and differentiable team cost function. A distributed and asynchronous optimisation algorithm is presented which allows each agent to incrementally refine their decisions while intermittently communicating with the rest of the team. A convergence analysis provides quantitative requirements on the frequency agents must communicate that is prescribed by the structure of the decision problem. In general the solution method will require every agent to communicate to and have a model of every other agent in the team. To overcome this, a specific subset of systems, called Partially Separable, is defined. These systems only require each agent to have a combined summary of the rest of the team and allows each agent to communicate locally over an acyclic communication network, greatly increasing the scalability of the system. © 2008 Elsevier B.V. All rights reserved. 1. Introduction This paper is part of an on going research program into decision making and control algorithms for large distributed active sensor networks. The vision of this work is a system of interconnected robotic agents, such as a team of unmanned air and ground vehicles. This type of system has applications in environmental monitoring, searching and rescue, surveillance, bush firefighting, target tracking, mapping and exploration, etc. Utilising an autonomous system to perform these tasks allows human operators to be removed from possibly dangerous (or simply mundane) situations. The decision problems that are encountered in these types of multi-agent systems generally fall into two categories, discrete (e.g. task allocation) and continuous (e.g. motion control). This work is primarily focused on the latter. Current work in this area has mainly focused on the consensus problem [1–4], whereby multiple agents, each starting out with different local values of a common decision variable, must collaboratively reach agreement. ∗ Corresponding address: Advanced Technology Centre, BAE SYSTEMS, Sowerby Building, FPC 267, PO BOX 5, Filton, Bristol, United Kingdom. Tel.: +44 0 117 302 8149; fax: +44 0 117 302 8007. E-mail addresses: george.mathews@baesystems.com (G.M. Mathews), h.durrant-whyte@cas.edu.au (H. Durrant-Whyte), mikhail.prokopenko@csiro.au (M. Prokopenko). However, what is often overlooked in consensus theory is that some decisions are explicitly better than others (there exists a common cost function). To include this it is necessary to cast the decision problem as a distributed optimisation problem. Existing approaches to this optimisation problem are either: (1) Fully centralised [5,6] where the system as a whole is modelled and the optimal decision found using conventional algorithms. (2) Distributed or hierarchical [7] which utilise the distributed computational capacity of the multiple platforms but require a single facility to fuse information or resolve global constrains, or (3) Fully decentralised which do not require any centralised facility. The decentralised approach can be further broken down into systems that require each platform to have global information about the system and those that only require local information from a small subset [8,9]. It is the latter that is of interest here. This paper presents a general asynchronous gradient-based distributed optimisation algorithm that can be used to solve the team decision problem. However, this algorithm requires every agent to communicate to every other agent, limiting the scalability of the system. To overcome this issue a specific class of systems, called Partially Separable, is defined that enable each agent to communicate in an anonymous fashion over an acyclic communication network. The paper is organised as follows: Section 2 presents the general decentralised and asynchronous optimisation algorithm for smooth and differentiable cost functions. A convergence analysis quantitatively specifies the communication requirements 0921-8890/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.robot.2008.10.020