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Risk-Aware Real-Time Task Allocation for Stochastic Multi-Agent Systems under STL Specifications

Maico H. W. Engelaar, Zengjie Zhang, Eleftherios E. Vlahakis, Dimos V. Dimarogonas, Mircea Lazar, Sofie Haesaert

TL;DR

This paper addresses the control synthesis of heterogeneous stochastic linear multi-agent systems with realtime allocation of signal temporal logic (STL) specifications by decomposing specifications into subspecifications on the individual agent level.

Abstract

This paper addresses the control synthesis of heterogeneous stochastic linear multi-agent systems with real-time allocation of signal temporal logic (STL) specifications. Based on previous work, we decompose specifications into sub-specifications on the individual agent level. To leverage the efficiency of task allocation, a heuristic filter evaluates potential task allocation based on STL robustness, and subsequently, an auctioning algorithm determines the definitive allocation of specifications. Finally, a control strategy is synthesized for each agent-specification pair using tube-based model predictive control (MPC), ensuring provable probabilistic satisfaction. We demonstrate the efficacy of the proposed methods using a multi-shuttle scenario that highlights a promising extension to automated driving applications like vehicle routing.

Risk-Aware Real-Time Task Allocation for Stochastic Multi-Agent Systems under STL Specifications

TL;DR

This paper addresses the control synthesis of heterogeneous stochastic linear multi-agent systems with realtime allocation of signal temporal logic (STL) specifications by decomposing specifications into subspecifications on the individual agent level.

Abstract

This paper addresses the control synthesis of heterogeneous stochastic linear multi-agent systems with real-time allocation of signal temporal logic (STL) specifications. Based on previous work, we decompose specifications into sub-specifications on the individual agent level. To leverage the efficiency of task allocation, a heuristic filter evaluates potential task allocation based on STL robustness, and subsequently, an auctioning algorithm determines the definitive allocation of specifications. Finally, a control strategy is synthesized for each agent-specification pair using tube-based model predictive control (MPC), ensuring provable probabilistic satisfaction. We demonstrate the efficacy of the proposed methods using a multi-shuttle scenario that highlights a promising extension to automated driving applications like vehicle routing.
Paper Structure (17 sections, 2 theorems, 11 equations, 5 figures, 1 algorithm)

This paper contains 17 sections, 2 theorems, 11 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Multi-agent Systems
  4. Signal Temporal Logic & Probabilistic Satisfaction
  5. Problem Statement & Approach
  6. Risk-Aware Multi-Agent Task Allocation and Control Synthesis
  7. Decomposing Agent Dynamics
  8. Specification Decomposition
  9. Heuristic Agent-Specification Filtering
  10. Control Synthesis and Local Risk Value
  11. Task Allocation Algorithm
  12. Implementation & Theoretical Analysis
  13. Case Study
  14. Conclusion
  15. Problem Statement: Illustrative example
  16. ...and 2 more sections

Key Result

Lemma 3

Let $\mu:=(h(x)\geq \boldsymbol 0)$ be a predicate, $H:=\{x \mid h(x)\geq \boldsymbol 0\}$ be a polytope, with $x=[x_1^\intercal\;\ldots\;x_\nu^\intercal]^\intercal$, $x_i\in\mathbb{X}^{i}$, $i\in \{1,\ldots,\nu\}$, and $B_{\mathrm{in}}(H)\subseteq H$ and $B_{\mathrm{out}}(H)\supseteq H$ be the asso

Figures (5)

  • Figure 1: Decomposing and allocating tasks for vehicle routing.
  • Figure 2: Illustration of the approach at time $k$. (0) Determine for each agent-specification pair a control strategy and the local risk value. (1) Auctioning offers from agent-specification pairs. (2) Decision after auctioning.
  • Figure 3: The shuttle trajectories.
  • Figure 4: Illustration of decomposing tasks to the individual level and combining tasks with robots. Blue are robots and red are tasks.
  • Figure 5: Polytopes $H$, $B_{\mathrm{in}}(H)$, $B_{\mathrm{out}}(H)$, for Example 2-.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Lemma 3
  • proof
  • Theorem 4: Recursive feasibility
  • proof
  • Remark 1
  • Remark 2