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

• 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
• DOI: 10.1109/TAC.2022.3176797

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.