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Communication-Constrained STL Task Decomposition through Convex Optimization

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

TL;DR

This work tackles the challenge of satisfying high-level STL tasks in multi-agent systems under restricted communication by decomposing global tasks into 1-hop sub-tasks aligned with the communication graph. The core method uses axis-aligned hyper-rectangles to parameterize sub-predicates and a constrained convex optimization to maximize the sub-tasks' robustness volume while ensuring entailment of the original task via Minkowski-sum based inclusions. It also formalizes potential conflicting conjunctions and provides convex constraints to avoid them, guaranteeing a conflict-free decomposed specification that preserves global task satisfaction. Simulations demonstrate rapid optimization and feasible decentralized control, highlighting practical applicability for scalable, communication-aware MAS planning and control.

Abstract

In this work, we propose a method to decompose signal temporal logic (STL) tasks for multi-agent systems subject to constraints imposed by the communication graph. Specifically, we propose to decompose tasks defined over multiple agents which require multi-hop communication, by a set of sub-tasks defined over the states of agents with 1-hop distance over the communication graph. To this end, we parameterize the predicates of the tasks to be decomposed as suitable hyper-rectangles. Then, we show that by solving a constrained convex optimization, optimal parameters maximising the volume of the predicate's super-level sets can be computed for the decomposed tasks. In addition, we provide a formal definition of conflicting conjunctions of tasks for the considered STL fragment and a formal procedure to exclude such conjunctions from the solution set of possible decompositions. The proposed approach is demonstrated through simulations.

Communication-Constrained STL Task Decomposition through Convex Optimization

TL;DR

This work tackles the challenge of satisfying high-level STL tasks in multi-agent systems under restricted communication by decomposing global tasks into 1-hop sub-tasks aligned with the communication graph. The core method uses axis-aligned hyper-rectangles to parameterize sub-predicates and a constrained convex optimization to maximize the sub-tasks' robustness volume while ensuring entailment of the original task via Minkowski-sum based inclusions. It also formalizes potential conflicting conjunctions and provides convex constraints to avoid them, guaranteeing a conflict-free decomposed specification that preserves global task satisfaction. Simulations demonstrate rapid optimization and feasible decentralized control, highlighting practical applicability for scalable, communication-aware MAS planning and control.

Abstract

In this work, we propose a method to decompose signal temporal logic (STL) tasks for multi-agent systems subject to constraints imposed by the communication graph. Specifically, we propose to decompose tasks defined over multiple agents which require multi-hop communication, by a set of sub-tasks defined over the states of agents with 1-hop distance over the communication graph. To this end, we parameterize the predicates of the tasks to be decomposed as suitable hyper-rectangles. Then, we show that by solving a constrained convex optimization, optimal parameters maximising the volume of the predicate's super-level sets can be computed for the decomposed tasks. In addition, we provide a formal definition of conflicting conjunctions of tasks for the considered STL fragment and a formal procedure to exclude such conjunctions from the solution set of possible decompositions. The proposed approach is demonstrated through simulations.
Paper Structure (13 sections, 10 theorems, 16 equations, 3 figures, 1 table)

This paper contains 13 sections, 10 theorems, 16 equations, 3 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Signal Temporal Logic
  4. Communication and Task Graphs
  5. PROBLEM FORMULATION
  6. TASK DECOMPOSITION
  7. Path decomposition of STL tasks
  8. Computing optimal parameters
  9. Dealing with conflicts
  10. Conflicting conjuncitons
  11. Resolving conflicting conjunctions
  12. SIMULATIONS
  13. CONCLUSIONS

Key Result

Proposition 1

(ziegler2012lectures) Any point $\bm{\zeta}\in\mathcal{H}(\bm{p},\bm{\nu})$ is a convex combination of the set of vertices $\mathcal{P}(\bm{p},\bm{\nu}):=\{\bm{v}\in \mathbb{R}^n | \bm{v}[s]=\bm{p}[s] + \bm{\nu}[s]/2 \; \text{or} \; \bm{v}[s]=\bm{p}[s] - \bm{\nu}[s]/2 \; \forall s=1,\ldots n \}$, wh

Figures (3)

  • Figure 1: Simple example of communication (left) and task graph (right) for a multi-agent system with 6 agents. The task and communication graph are mismatching in their case.
  • Figure 2: Example of decomposition according to \ref{['eq:path specification']}.
  • Figure 3: Trajectory evolution of the agents from time $t=0s$ to $t=15s$ (a) and from time $t=15s$ to $t=28s$ (b); Short solid arrows represent the direction of movement of the agents; green lozenges represent the starting positions of the agents, while black stars represent the final positions. Communication graph $\mathcal{G}_c$, initial task graph $\mathcal{G}_{\psi}$ and final task graph $\mathcal{G}_{\bar{\psi}}$ (c). Edges $(2,5), (3,2), (3,4), (7,4), (8,5)$, and $(7,8)$ in $\mathcal{G}_\psi$ are decomposed over the edges of $\mathcal{G}_c$ to obtain $\mathcal{G}_{\bar{\psi}}$.

Theorems & Definitions (29)

  • Example 1
  • Example 2
  • Definition 1
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • ...and 19 more