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Disentangled Control of Multi-Agent Systems

Ruoyu Lin, Gennaro Notomista, Magnus Egerstedt

TL;DR

The paper addresses decentralized multi-agent control with entangled dynamics and time-varying objectives across arbitrary graph topologies. It introduces a unified disentangled control framework built on time-varying Lyapunov and barrier function theory, including nonsmooth extensions, and two central constructs: Shared-Entangled NS-TV-CLFs and Private-Entangled NS-TV-CLFs, along with a constraint-allocation optimization that enables decentralized, real-time synthesis even under piecewise-constant graphs. Theoretical results guarantee convergence to desired objectives under time-varying conditions and diverse topology, while empirical demonstrations verify effectiveness in time-varying leader-follower formation, decentralized coverage with time-varying densities without approximations, and safe multi-robot navigation in dense environments. Overall, the framework offers scalable, multi-objective, and topology-agnostic control suitable for real-world multi-agent robotics and related domains, with potential extensions to broader decentralized decision-making problems.

Abstract

This paper develops a general framework for multi-agent control synthesis, which applies to a wide range of problems with convergence guarantees, regardless of the complexity of the underlying graph topology and the explicit time dependence of the objective function. The proposed framework systematically addresses a particularly challenging problem in multi-agent systems, i.e., decentralization of entangled dynamics among different agents, and it naturally supports multi-objective robotics and real-time implementations. To demonstrate its generality and effectiveness, the framework is implemented across three experiments, namely time-varying leader-follower formation control, decentralized coverage control for time-varying density functions without any approximations, which is a long-standing open problem, and safe formation navigation in dense environments.

Disentangled Control of Multi-Agent Systems

TL;DR

The paper addresses decentralized multi-agent control with entangled dynamics and time-varying objectives across arbitrary graph topologies. It introduces a unified disentangled control framework built on time-varying Lyapunov and barrier function theory, including nonsmooth extensions, and two central constructs: Shared-Entangled NS-TV-CLFs and Private-Entangled NS-TV-CLFs, along with a constraint-allocation optimization that enables decentralized, real-time synthesis even under piecewise-constant graphs. Theoretical results guarantee convergence to desired objectives under time-varying conditions and diverse topology, while empirical demonstrations verify effectiveness in time-varying leader-follower formation, decentralized coverage with time-varying densities without approximations, and safe multi-robot navigation in dense environments. Overall, the framework offers scalable, multi-objective, and topology-agnostic control suitable for real-world multi-agent robotics and related domains, with potential extensions to broader decentralized decision-making problems.

Abstract

This paper develops a general framework for multi-agent control synthesis, which applies to a wide range of problems with convergence guarantees, regardless of the complexity of the underlying graph topology and the explicit time dependence of the objective function. The proposed framework systematically addresses a particularly challenging problem in multi-agent systems, i.e., decentralization of entangled dynamics among different agents, and it naturally supports multi-objective robotics and real-time implementations. To demonstrate its generality and effectiveness, the framework is implemented across three experiments, namely time-varying leader-follower formation control, decentralized coverage control for time-varying density functions without any approximations, which is a long-standing open problem, and safe formation navigation in dense environments.

Paper Structure

This paper contains 10 sections, 7 theorems, 70 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Control Lyapunov Functions
  4. Disentangled Control
  5. Applications and Experiments
  6. Time-Varying Leader-Follower Formation Control
  7. Decentralized Coverage Control for Time-Varying Density Functions
  8. Safe Formation Navigation in a Dense Environment
  9. Conclusions
  10. Limitations of Related Works

Key Result

Lemma 3.1

(Lemma 5.2 in lin2025heterogeneous) If $V(x,t)$ is a TV-CLF and $V(x(0),0) < a < \infty$ per Definition def:TVCLF, then $\lim_{t \to \infty} V(x(t),t) = 0$ along the trajectory $x(t) = \Phi_{f+gu}(x(0),t)$ under any time-varying state-feedback controller $u(x,t)$ such that ${L}_X V(x(t),t) + \frac{\

Figures (9)

  • Figure 1: (a) Illustration of the attractivity of TV-CBF; (b) Illustration of a special case of TV-CBF which has the same functionality as TV-CLF, where $\mathcal{C} (t) = \{x \in \mathbb{R}^n \,|\, V(x,t) = 0\}$, $\forall t \geq 0$.
  • Figure 2: Illustration of the control synthesis framework \ref{['eqn:disentangledOptimization']}, where the edge $(i.j)$ is undirected while $(j,k)$ is directed.
  • Figure 3: Snapshots of the simulation of decentralized time-varying leader-follower formation control in Section \ref{['Section:subsec_exp1']}. The twelve follower robots are represented by the pink dots, while the leader robot is represented by the blue dot. The green lines represent the undirected edges of the corresponding PE graph, and the blue dashed line represents the trajectory traveled by the leader robot. The full video of this simulation is available online at https://youtu.be/DyY8JiIXzAc.
  • Figure 4: The evolution of the total PE-TV-CLF of the follower robots defined in Section \ref{['Section:subsec_exp1']} with respect to time steps.
  • Figure 5: The evolution of the PE-TV-CLF for each follower robot defined in Section \ref{['Section:subsec_exp1']} with respect to time steps.
  • ...and 4 more figures

Theorems & Definitions (24)

  • Definition 3.1
  • Lemma 3.1
  • proof
  • Definition 3.2
  • Lemma 3.2
  • proof
  • Remark 3.1
  • Lemma 3.3
  • proof
  • Definition 3.3
  • ...and 14 more