Discrete State Estimators for Systems on a Lattice

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Domitilla Del Vecchio, Richard M. Murray, Erik Klavins
To appear, Automatica

We address the problem of estimating discrete variables in a class of deterministic transition systems where the continuous variables are available for measurement. This simplified scenario has practical interest, for example, in the case of decentralized multi-robot systems. In these systems, the continuous variables represent physical quantities such as the position and velocity of a robot, while discrete variables may represent the state of the logical system that is used for control and coordination. We propose a novel approach to the estimation of discrete variables using basic lattice theory that overcomes some of the severe complexity issues encountered in previous work. We show how to construct the proposed estimator for a multi-robot system performing a cooperative assignment task.