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Distributed Sequential Receding Horizon Control of Multi-Agent Systems under Recurring Signal Temporal Logic

Eleftherios E. Vlahakis, Lars Lindemann, Dimos V. Dimarogonas

TL;DR

This work tackles infinite-horizon control for multi-agent systems under recurring signal temporal logic (STL) specifications, formalized as $\psi=\square_{[0,\infty)}\phi$ with a conjunctive decomposition over cliques. It introduces a receding-horizon model predictive control (MPC) framework augmented with STL-specific constraints and a backward-reachability-based terminal condition to guarantee recursive feasibility, enabling online operation. The global problem is decomposed into agent-level programs, which are coordinated by a scheduling policy to preserve feasibility; a distributed sequential MPC procedure is proposed to handle couplings while ensuring persistent satisfaction of $\psi$. A numerical example with three agents demonstrates successful surveillance under perturbations, highlights the importance of the terminal constraint, and shows favorable computational characteristics compared to a centralized baseline. The approach provides a practical pathway to scalable, online distributed control for persistent multi-agent tasks under complex STL specifications.

Abstract

We consider the synthesis problem of a multi-agent system under signal temporal logic (STL) specifications representing bounded-time tasks that need to be satisfied recurrently over an infinite horizon. Motivated by the limited approaches to handling recurring STL systematically, we tackle the infinite-horizon control problem with a receding horizon scheme equipped with additional STL constraints that introduce minimal complexity and a backward-reachability-based terminal condition that is straightforward to construct and ensures recursive feasibility. Subsequently, we decompose the global receding horizon optimization problem into agent-level programs the objectives of which are to minimize local cost functions subject to local and joint STL constraints. We propose a scheduling policy that allows individual agents to sequentially optimize their control actions while maintaining recursive feasibility. This results in a distributed strategy that can operate online as a model predictive controller. Last, we illustrate the effectiveness of our method via a multi-agent system example assigned a surveillance task.

Distributed Sequential Receding Horizon Control of Multi-Agent Systems under Recurring Signal Temporal Logic

TL;DR

This work tackles infinite-horizon control for multi-agent systems under recurring signal temporal logic (STL) specifications, formalized as with a conjunctive decomposition over cliques. It introduces a receding-horizon model predictive control (MPC) framework augmented with STL-specific constraints and a backward-reachability-based terminal condition to guarantee recursive feasibility, enabling online operation. The global problem is decomposed into agent-level programs, which are coordinated by a scheduling policy to preserve feasibility; a distributed sequential MPC procedure is proposed to handle couplings while ensuring persistent satisfaction of . A numerical example with three agents demonstrates successful surveillance under perturbations, highlights the importance of the terminal constraint, and shows favorable computational characteristics compared to a centralized baseline. The approach provides a practical pathway to scalable, online distributed control for persistent multi-agent tasks under complex STL specifications.

Abstract

We consider the synthesis problem of a multi-agent system under signal temporal logic (STL) specifications representing bounded-time tasks that need to be satisfied recurrently over an infinite horizon. Motivated by the limited approaches to handling recurring STL systematically, we tackle the infinite-horizon control problem with a receding horizon scheme equipped with additional STL constraints that introduce minimal complexity and a backward-reachability-based terminal condition that is straightforward to construct and ensures recursive feasibility. Subsequently, we decompose the global receding horizon optimization problem into agent-level programs the objectives of which are to minimize local cost functions subject to local and joint STL constraints. We propose a scheduling policy that allows individual agents to sequentially optimize their control actions while maintaining recursive feasibility. This results in a distributed strategy that can operate online as a model predictive controller. Last, we illustrate the effectiveness of our method via a multi-agent system example assigned a surveillance task.
Paper Structure (12 sections, 5 theorems, 9 equations, 3 figures)

This paper contains 12 sections, 5 theorems, 9 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. Preliminaries and Multi-Agent Setup
  3. Notation
  4. Signal Temporal Logic
  5. Multi-agent system
  6. Decomposition of STL formula $\phi$
  7. Main Results
  8. Receding horizon control
  9. Distributed receding horizon control
  10. Distributed sequential model predictive control
  11. Numerical Example
  12. Conclusion

Key Result

Theorem 1

Let the optimization problem eq:receding_horizon_relax_MAS be feasible at $t=0$. Then, it is feasible for all $t\geq 0$.

Figures (3)

  • Figure 1: Runtime for computations on an i7-1185G7 CPU at 3.00GHz. (Left) Distributed scheme. (Right) Centralized scheme.
  • Figure 2: Position and acceleration over a 13-second time horizon under the distributed receding horizon control scheme.
  • Figure 3: (Left) Nominal and perturbed trajectories. (Right) Accelerations under random perturbations in the velocity terms.

Theorems & Definitions (15)

  • Remark 1
  • Remark 2
  • Remark 3
  • Definition 1
  • Definition 2: one-Step Controllable Set
  • Remark 4
  • Theorem 1
  • proof
  • Corollary 1
  • Remark 5
  • ...and 5 more