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

06/29/2021
by   Franck Djeumou, et al.
0

We develop a probabilistic control algorithm, , 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. , 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 in several swarm scenarios.

READ FULL TEXT

Authors

page 12

page 13

page 14

12/04/2020

Decentralized State-Dependent Markov Chain Synthesis for Swarm Guidance

This paper introduces a decentralized state-dependent Markov chain synth...
11/28/2020

A Probabilistic Guidance Approach to Swarm-to-Swarm Engagement Problem

This paper introduces a probabilistic guidance approach for the swarm-to...
01/24/2020

Policy Synthesis for Factored MDPs with Graph Temporal Logic Specifications

We study the synthesis of policies for multi-agent systems to implement ...
06/10/2020

Ergodic Specifications for Flexible Swarm Control: From User Commands to Persistent Adaptation

This paper presents a formulation for swarm control and high-level task ...
05/08/2019

Bayesian Optimization for Polynomial Time Probabilistically Complete STL Trajectory Synthesis

In recent years, Signal Temporal Logic (STL) has gained traction as a pr...
03/26/2021

Control Synthesis using Signal Temporal Logic Specifications with Integral and Derivative Predicates

In many applications, the integrals and derivatives of signals carry val...
04/13/2022

Mixed-Integer Programming for Signal Temporal Logic with Fewer Binary Variables

Signal Temporal Logic (STL) provides a convenient way of encoding comple...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.