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Decentralized Control of Multi-Agent Systems Under Acyclic Spatio-Temporal Task Dependencies

Gregorio Marchesini, Siyuan Liu, Lars Lindemann, Dimos V. Dimarogonas

TL;DR

A novel distributed sampled-data control method tailored for heterogeneous multi-agent systems under a global spatio-temporal task with acyclic dependencies, which provides an algorithmic approach to define a distributed sampled-data controller prioritizing the fulfilment of collaborative tasks as the primary objective.

Abstract

We introduce a novel distributed sampled-data control method tailored for heterogeneous multi-agent systems under a global spatio-temporal task with acyclic dependencies. Specifically, we consider the global task as a conjunction of independent and collaborative tasks, defined over the absolute and relative states of agent pairs. Task dependencies in this form are then represented by a task graph, which we assume to be acyclic. From the given task graph, we provide an algorithmic approach to define a distributed sampled-data controller prioritizing the fulfilment of collaborative tasks as the primary objective, while fulfilling independent tasks unless they conflict with collaborative ones. Moreover, communication maintenance among collaborating agents is seamlessly enforced within the proposed control framework. A numerical simulation is provided to showcase the potential of our control framework.

Decentralized Control of Multi-Agent Systems Under Acyclic Spatio-Temporal Task Dependencies

TL;DR

A novel distributed sampled-data control method tailored for heterogeneous multi-agent systems under a global spatio-temporal task with acyclic dependencies, which provides an algorithmic approach to define a distributed sampled-data controller prioritizing the fulfilment of collaborative tasks as the primary objective.

Abstract

We introduce a novel distributed sampled-data control method tailored for heterogeneous multi-agent systems under a global spatio-temporal task with acyclic dependencies. Specifically, we consider the global task as a conjunction of independent and collaborative tasks, defined over the absolute and relative states of agent pairs. Task dependencies in this form are then represented by a task graph, which we assume to be acyclic. From the given task graph, we provide an algorithmic approach to define a distributed sampled-data controller prioritizing the fulfilment of collaborative tasks as the primary objective, while fulfilling independent tasks unless they conflict with collaborative ones. Moreover, communication maintenance among collaborating agents is seamlessly enforced within the proposed control framework. A numerical simulation is provided to showcase the potential of our control framework.
Paper Structure (14 sections, 5 theorems, 21 equations, 2 figures, 2 algorithms)

This paper contains 14 sections, 5 theorems, 21 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and problem formulation
  3. Signal Temporal Logic and Task Graph
  4. Sampled-Data Control
  5. Problem Formulation
  6. Sampled-data time-varying CBFs
  7. sdCBF for STL tasks
  8. Decentralized Control Solution
  9. Decentralized Control for STL satisfaction
  10. Token passing algorithm
  11. Margin function computation
  12. Control reduction factor computation
  13. Simulations
  14. Conclusions

Key Result

Lemma 1

Assume $b(\bm{x},t)$ is an sdCBF as per Def. sdcbf definition for a sampling interval $\delta t>0$ and let $\bm{x}^0 = \bm{x}(t^0)\in \mathcal{C}(t^0)$. If eq:multi agent dynamics is subject to a p.w.c input trajectory $\bm{u}(t)\in \prod_i\mathcal{U}_i^{\delta t}$ such that condition eq: sdcbf cond

Figures (2)

  • Figure 1: Two heterogeneous agents (a drone and a ground vehicle with differential drive dynamic) within their respective communication radius
  • Figure 2: (a) Margin functions $\bm{\nu}^{\phi}_{ij}(\bm{e}_{ij}^k,t^k)$,$\bm{\nu}^{\phi}_{i}(\bm{x}_{i}^k,t^k)$ for each barrier $b_{ij}^{\phi}(\bm{e}_{ij},t), b_{i}^{\phi}(\bm{x}_{i},t)$. (b) Barrier functions $b_{ij}^{\phi}(\bm{e}^k_{ij},t^k),b_{i}^{\phi}(\bm{x}^k_{i},t^k)$ associated with tasks $\phi_{ij},\phi_i$. (c) Control reduction factor $\gamma_i^k$. (d) MAS simulation. The arrows represent directions of motion. Blue and green circles represent obstacles and agents respectively (e) Time required to compute $\gamma_i^k$ sequentially for each $i\in \mathcal{V}$ at each $k$ (Alg. \ref{['alg:control reduction alg']}).

Theorems & Definitions (16)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Lemma 1
  • proof
  • Remark 1
  • Proposition 1
  • proof
  • Remark 2
  • ...and 6 more