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Distributed Safety-Critical Control of Multi-Agent Systems with Time-Varying Communication Topologies

Shiyu Cheng, Luyao Niu, Bhaskar Ramasubramanian, Andrew Clark, Radha Poovendran

Abstract

Coordinating multiple autonomous agents to reach a target region while avoiding collisions and maintaining communication connectivity is a core problem in multi-agent systems. In practice, agents have a limited communication range. Thus, network links appear and disappear as agents move, making the topology state-dependent and time-varying. Existing distributed solutions to multi-agent reach-avoid problems typically assume a fixed communication topology, and thus are not applicable when encountering discontinuities raised by time-varying topologies. This paper presents a distributed optimization-based control framework that addresses these challenges through two complementary mechanisms. First, we introduce a truncation function that converts the time-varying communication graph into a smoothly state-dependent one, ensuring that constraints remain continuous as communication links are created or removed. Second, we employ auxiliary mismatch variables with two-time-scale dynamics to decouple globally coupled state-dependent constraints, yielding a singular perturbation system that each agent can solve using only local information and neighbor communication. Through singular perturbation analysis, we prove that the distributed controller guarantees collision avoidance, connectivity preservation, and convergence to the target region. We validate the proposed framework through numerical simulations involving multi-agent navigation with obstacles and time-varying communication topologies.

Distributed Safety-Critical Control of Multi-Agent Systems with Time-Varying Communication Topologies

Abstract

Coordinating multiple autonomous agents to reach a target region while avoiding collisions and maintaining communication connectivity is a core problem in multi-agent systems. In practice, agents have a limited communication range. Thus, network links appear and disappear as agents move, making the topology state-dependent and time-varying. Existing distributed solutions to multi-agent reach-avoid problems typically assume a fixed communication topology, and thus are not applicable when encountering discontinuities raised by time-varying topologies. This paper presents a distributed optimization-based control framework that addresses these challenges through two complementary mechanisms. First, we introduce a truncation function that converts the time-varying communication graph into a smoothly state-dependent one, ensuring that constraints remain continuous as communication links are created or removed. Second, we employ auxiliary mismatch variables with two-time-scale dynamics to decouple globally coupled state-dependent constraints, yielding a singular perturbation system that each agent can solve using only local information and neighbor communication. Through singular perturbation analysis, we prove that the distributed controller guarantees collision avoidance, connectivity preservation, and convergence to the target region. We validate the proposed framework through numerical simulations involving multi-agent navigation with obstacles and time-varying communication topologies.

Paper Structure

This paper contains 14 sections, 6 theorems, 47 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Notations
  5. System Model
  6. Background on Control Barrier Functions
  7. Background on Singular Perturbations
  8. Background on Projected Saddle-Point Dynamics
  9. Problem Formulation
  10. Distributed Algorithm
  11. Simulations
  12. Setup
  13. Results
  14. Conclusion

Key Result

Theorem 1

Let $\mathcal{C}\subset \mathbb{R}^n$ be a set defined as the superlevel set of a continuously differentiable function $h: \mathcal{X}\subset \mathbb{R}^n\rightarrow \mathbb{R}$. If $h$ is a CBF on $\mathcal{X}$ and $\frac{\partial h}{\partial x}(x)\neq 0$ for all $x\in \partial \mathcal{C}$, then a

Figures (2)

  • Figure 1: Trajectories of five agents and communication graphs at four selected time instants $t=0, 50, 75, 250$. Dashed curves denote agent trajectories, filled circles indicate agent positions at the selected instants, and crosses mark the final positions. Blue solid lines represent active communication edges. The green shaded region denotes the target region $\Omega_i$, and the light red circles represent obstacles.
  • Figure 2: Evolution of the algebraic connectivity $\overline{\lambda}_2$ of the binary communication graph over time. The value of $\overline{\lambda}_2$ remains strictly positive throughout the process, indicating that the connectivity of the communication graph is maintained.

Theorems & Definitions (10)

  • Definition 1: Safety
  • Definition 2: Control Barrier Function ames2019control
  • Theorem 1: ames2019control
  • Definition 3: UGAS watbled2005singular
  • Theorem 2: watbled2005singular
  • Theorem 3: cherukuri2017role
  • Theorem 4
  • Proposition 1: Problem Equivalence mestres2023distributed
  • Theorem 5
  • proof