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Combinatorial Safety-Critical Coordination of Multi-Agent Systems via Mixed-Integer Responsibility Allocation and Control Barrier Functions

Johannes Autenrieb, Mark Spiller, Hyo-Sang Shin, Namhoon Cho

TL;DR

A combinatorial coordination layer formulated as a mixed-integer linear program (MILP) that assigns collision-avoidance responsibilities among agents by explicitly distributing enforcement tasks, redundant reactions are eliminated and computational complexity is reduced.

Abstract

This paper presents a hybrid safety-critical coordination architecture for multi-agent systems operating in dense environments. While control barrier functions (CBFs) provide formal safety guarantees, decentralized implementations typically rely on ego-centric safety filtering and may lead to redundant constraint enforcement and conservative collective behavior. To address this limitation, we introduce a combinatorial coordination layer formulated as a mixed-integer linear program (MILP) that assigns collision-avoidance responsibilities among agents. By explicitly distributing enforcement tasks, redundant reactions are eliminated and computational complexity is reduced. Each agent subsequently solves a reduced local quadratic program enforcing only its assigned constraints.

Combinatorial Safety-Critical Coordination of Multi-Agent Systems via Mixed-Integer Responsibility Allocation and Control Barrier Functions

TL;DR

A combinatorial coordination layer formulated as a mixed-integer linear program (MILP) that assigns collision-avoidance responsibilities among agents by explicitly distributing enforcement tasks, redundant reactions are eliminated and computational complexity is reduced.

Abstract

This paper presents a hybrid safety-critical coordination architecture for multi-agent systems operating in dense environments. While control barrier functions (CBFs) provide formal safety guarantees, decentralized implementations typically rely on ego-centric safety filtering and may lead to redundant constraint enforcement and conservative collective behavior. To address this limitation, we introduce a combinatorial coordination layer formulated as a mixed-integer linear program (MILP) that assigns collision-avoidance responsibilities among agents. By explicitly distributing enforcement tasks, redundant reactions are eliminated and computational complexity is reduced. Each agent subsequently solves a reduced local quadratic program enforcing only its assigned constraints.
Paper Structure (6 sections, 3 theorems, 37 equations, 4 figures)

This paper contains 6 sections, 3 theorems, 37 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Setup
  4. Combinatorial Safety for Multi-Agent Systems via Mixed-Integer Optimization
  5. Results
  6. Conclusion

Key Result

Theorem 1

Given a set $S \subset \chi$, defined via the associated CBF as in Safe_set_1, any Lipschitz continuous controller $\mathbf{k}(\mathbf{x}) \in K_{S}(\mathbf{x})$ with renders the system NonlinearPlant1 forward invariant within $S$XU2015. One way to construct a controller satisfying definition_safe_controller is through a quadratic program-based safety filter, as proposed in Ames_2014: where $\ma

Figures (4)

  • Figure 1: Illustration of the control architecture with mixed-integer-based coordination and decentralized safety filters.
  • Figure 2: Agent trajectories and distance-to-goal profiles for MAS with fully decentralized QPs.
  • Figure 3: Agent trajectories and distance-to-goal profiles for MAS with MILP coordination and decentralized QPs.
  • Figure 4: Total deviation cost, average barrier value $\bar{h}$, and average local QP time $\bar{t}_{\mathrm{QP}}$.

Theorems & Definitions (7)

  • Definition 1: CBF, Ames_2017
  • Theorem 1
  • Definition 2: HOCBF, Xiao_2022hocbf
  • Theorem 2: Global safety in centralized responsibility allocation
  • proof : Proof
  • Proposition 1: Minimal additive upper bound under responsibility allocation
  • proof : Proof