Decentralized Estimation under Communication Constraints

The decentralized cooperative exploration problem necessarily involves communication among agents, while the spatial separation inherent in this task places fundamental limits on the amount of data that can be transmitted. However, the impact of limited communication on the exploration process has not been fully characterized. No known exploration algorithm realistically models the tradeo between rapid expansion (which allows more rapid exploration of the map) and maintaining close relative proximity among agents (which facilitates communication). This work is a first step toward characterizing the impact of limited communication on this cooperative estimation task by considering a static version of the problem. The mathematical properties of the information form of the Kalman filter are leveraged in the development of two approximate algorithms for selecting highly informative portions of the information matrix for transmission. One algorithm, a fully polynomial time approximation scheme, provides provably good results in computationally tractable time for problem instances of a particular structure. The other, a heuristic-based method applicable to instances of arbitrary matrix structure, performs very well in simulation for randomly-generated problems of realistic dimension.

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