Probabilistic Control of Heterogeneous Swarms Subject to Graph Temporal Logic Specifications: A Decentralized and Scalable Approach

We develop a probabilistic control algorithm, GTLProCo , for swarms of agents with heterogeneous dynamics and objectives, subject to high-level task specifications. The resulting algorithm not only achieves decentralized control of the swarm but also significantly improves scalability over state-of-...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 68; no. 4; pp. 2245 - 2260
Main Authors: Djeumou, Franck, Xu, Zhe, Cubuktepe, Murat, Topcu, Ufuk
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Aerospace electronics
Algorithms
Behavioral sciences
Control algorithms
Control theory
Decentralized control
Density distribution
Formal language
Heuristic algorithms
Integer programming
Linear programming
Markov analysis
Markov chains
Markov process
Markov processes
Mixed integer
Nodes
optimization methods
Probabilistic logic
Scalability
Specifications
swarm robotics
Synthesis
Task analysis
Temporal logic
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:We develop a probabilistic control algorithm, GTLProCo , for swarms of agents with heterogeneous dynamics and objectives, subject to high-level task specifications. The resulting algorithm not only achieves decentralized control of the swarm but also significantly improves scalability over state-of-the-art existing algorithms. Specifically, we study a setting in which the agents move along the nodes of a graph, and the high-level task specifications for the swarm are expressed in a recently proposed language called graph temporal logic (GTL). By constraining the distribution of the swarm over the nodes of the graph, GTL can specify a wide range of properties, including safety, progress, and response. GTLProCo , with a computational complexity agnostic to the number of agents comprising the swarm, controls the density distribution of the swarm in a decentralized and probabilistic manner. To this end, it synthesizes a time-varying Markov chain modeling the time evolution of the density distribution under the GTL constraints. We first identify a subset of GTL, namely reach-avoid specifications, for which we can reduce the synthesis of such a Markov chain to either linear or semidefinite programs. Then, in the general case, we formulate the synthesis of the Markov chain as a mixed-integer nonlinear program (MINLP). We exploit the structure of the problem to provide an efficient sequential mixed-integer linear programming scheme with trust regions to solve the MINLP. We empirically demonstrate that our sequential scheme is at least three orders of magnitude faster than off-the-shelf MINLP solvers and illustrate the effectiveness of GTLProCo in several swarm scenarios.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3176797