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Published August 2020 | public
Journal Article

Multirobot Coordination With Counting Temporal Logics

Abstract

In many multirobot applications, planning trajectories in a way to guarantee that the collective behavior of the robots satisfies a certain high-level specification is crucial. Motivated by this problem, we introduce counting temporal logics —formal languages that enable concise expression of multirobot task specifications over possibly infinite horizons in this article. We first introduce a general logic called counting linear temporal logic plus (cLTL+), and propose an optimization-based method that generates individual trajectories such that satisfaction of a given cLTL+ formula is guaranteed when these trajectories are synchronously executed. We then introduce a fragment of cLTL+, called counting linear temporal logic (cLTL), and show that a solution to a planning problem with cLTL constraints can be obtained more efficiently if all robots have identical dynamics. In the second part of this article, we relax the synchrony assumption and discuss how to generate trajectories that can be asynchronously executed, while preserving the satisfaction of the desired cLTL+ specification. In particular, we show that when the asynchrony between robots is bounded, the method presented in this article can be modified to generate robust trajectories. We demonstrate these ideas with an experiment and provide numerical results that showcase the scalability of the method.

Additional Information

© 2019 IEEE. Manuscript received July 13, 2019; accepted November 21, 2019. Date of publication December 20, 2019; date of current version August 5, 2020. This article was recommended for publication by Associate Editor A. Franchi and Editor P. Robuffo Giordano upon evaluation of the reviewers' comments. This work was supported in part by the National Science Foundation under Grant CNS-1239037, Grant CNS-1446298, and Grant ECCS-1553873, and in part by the Defense Advanced Research Projects Agency under Grant N66001-14-1-4045.

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023