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

TL;DR

This paper introduces GTLProCo, a decentralized probabilistic control algorithm for heterogeneous swarms that ensures high-level task specifications are met efficiently, significantly improving scalability and applicability over existing methods.

Contribution

The paper presents a novel decentralized control algorithm, GTLProCo, capable of handling heterogeneous swarm dynamics under graph temporal logic constraints with improved scalability.

Findings

GTLProCo achieves decentralized control of heterogeneous swarms.

The algorithm significantly outperforms existing methods in scalability.

Effective in various swarm scenarios with high-level specifications.

Abstract

We develop a probabilistic control algorithm, $\texttt{GTLProCo}$, 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. $\texttt{GTLProCo}$, 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 semi-definite 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 $\texttt{GTLProCo}$ in several swarm scenarios.