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Distributed constraint optimization for teams of mobile sensing agents

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Abstract

Coordinating a mobile sensor team (MST) to cover targets is a challenging problem in many multiagent applications. Such applications are inherently dynamic due to changes in the environment, technology failures, and incomplete knowledge of the agents. Agents must adaptively respond by changing their locations to continually optimize the coverage of targets. We propose distributed constraint optimization problems (DCOP)_MST, a new model for representing MST problems that is based on DCOP. In DCOP_MST, agents maintain variables for their physical positions, while each target is represented by a constraint that reflects the quality of coverage of that target. In contrast to conventional, static DCOPs, DCOP_MST not only permits dynamism but exploits it by restricting variable domains to nearby locations; consequently, variable domains and constraints change as the agents move through the environment. DCOP_MST confers three major advantages. It directly represents the multiple forms of dynamism inherent in MSTs. It also provides a compact representation that can be solved efficiently with local search algorithms, with information and communication locality based on physical locality as typically occurs in MST applications. Finally, DCOP_MST facilitates organization of the team into multiple sub-teams that can specialize in different roles and coordinate their activity through dynamic events. We demonstrate how a search-and-detection team responsible for finding new targets and a surveillance sub-team tasked with coverage of known targets can effectively work together to improve performance while using the DCOP_MST framework to coordinate. We propose different algorithms to meet the specific needs of each sub-team and several methods for cooperation between sub-teams. For the search-and-detection team, we develop an algorithm based on the DSA that forces intensive exploration for new targets. For the surveillance sub-team, we adapt several incomplete DCOP algorithms, including MGM, DSA, DBA, and Max-sum, which requires us to develop an efficient method for agents to find the value assignment in their local environment that is optimal in minimizing the maximum unmet coverage requirement over all targets. The disadvantage of dynamic domains based on physical locality is that adaptations of standard local search algorithms tend to become trapped in local optima where targets beyond the immediate range of the agents go uncovered. To address this shortcoming we develop exploration methods to be used with the local search algorithms. Our algorithms are extensively evaluated in a simulation environment. We use a reputation model to determine the individual credibility of agents and consider both additive and submodular joint credibility functions for determining coverage of targets by multiple agents. The performance is measured on two objectives: minimizing the maximum remaining coverage requirement, and minimizing the sum of remaining coverage requirements. Our results show that DSA and MGM with the exploration heuristics outperform the other incomplete algorithms across a wide range of settings. Furthermore, organizing the team into two sub-teams leads to significant gains in performance, and performance continues to improve with greater cooperation between the sub-teams.

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Notes

  1. In this paper we assume that each agent resides on a mobile sensor and we use the terms agent and sensor interchangeably.

  2. We leave the problem of handling inconsistent information caused by malicious activity for future work.

  3. This is a reasonable assumption considering that GPS receivers are used.

  4. For simplicity of presentation and without loss of generality we assume that each agent holds a single variable

  5. In Sect. 5 we present experimental results showing that our approach is also effective for the objective of minimizing the sum of remaining coverage requirements.

  6. In our proof we assume that there are no plateaus (continuous areas with the same \( ER \) value) and that the number of points of the same (highest) value can be found efficiently. If plateaus do exist, the proof is still valid; however, there is a need to use geometric computation in order to evaluate areas instead of points.

  7. In contrast to the assumptions made, in case the initial possible position set or target set are too large and the method cannot be completed in reasonable time, the method can be stopped and one of the positions in \(pos\_set\) can be selected. However, in this case local optimality is not guaranteed.

  8. If not, agents would need to inform all other agents when they change position so that they can update their set of neighbors accordingly.

  9. The details of Max-sum are beyond the scope of this paper. The reader is referred to the following papers for a description of the algorithm [11, 54].

  10. importance(\(p\)) in line 5 is the true importance of point \(p\) sensed by the agent.

    Fig. 10
    figure 10

    DSA_SAT

    Full size image

  11. In contrast to SPORAS, the initial credibility is not zero since in MSTs we are not concerned with agents using different pseudonyms.

  12. We omit the maximum remaining coverage here because the effect is not notable until all targets are located.

  13. Notice that the MGM_PDMR method reduces to MGM_MST when the domains are fixed and therefore is not evaluated in this experiment.

  14. Beginning with this experiment, we present only the results for the \(F_{ sum}\) method. The results in the experiments using \(F_{ cprob}\) were consistently similar with less apparent differences between the algorithms.

  15. We do not present error bars in this graph because they make the figure unreadable due to the similarity of the results.

  16. In the rest of the figures the error bounds were omitted due to the density of the graphs.

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Acknowledgments

This research has been supported by AFOSR FA9550-08-1-0356.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beersheba, Israel

    Roie Zivan, Harel Yedidsion & Steven Okamoto

  2. Robotics Institute, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA , 15213, USA

    Robin Glinton & Katia Sycara

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  1. Roie Zivan
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Correspondence to Roie Zivan.

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Zivan, R., Yedidsion, H., Okamoto, S. et al. Distributed constraint optimization for teams of mobile sensing agents. Auton Agent Multi-Agent Syst 29, 495–536 (2015). https://doi.org/10.1007/s10458-014-9255-3

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