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Exploiting Over-The-Air Consensus for Collision Avoidance and Formation Control in Multi-Agent Systems

Michael Epp, Fabio Molinari, Joerg Raisch

TL;DR

We address distributed formation control for $n$ agents with decoupled single-integrator dynamics $\dot{p}_i(t)=u_i(t)$, introducing Over-the-Air Consensus (OtA-Consensus) to exploit interference in wireless channels for communication efficiency. A jump-flow control strategy combines continuous dynamics with discrete updates, incorporating an auxiliary reference $\vartheta_i(t)$ and a collision-avoidance potential $\rho_{ij}(t)$. Theoretical results prove convergence under sequences of strongly connected graphs by leveraging primitive row-stochastic matrices and Lyapunov analysis. Simulations demonstrate substantial communication efficiency gains and scalability, while revealing that small asymmetries in network topology help avoid stagnation in local minima.

Abstract

This paper introduces a distributed control method for multi-agent robotic systems employing Over the Air Consensus (OtA-Consensus). Designed for agents with decoupled single-integrator dynamics, this approach aims at efficient formation achievement and collision avoidance. As a distinctive feature, it leverages OtA's ability to exploit interference in wireless channels, a property traditionally considered a drawback, thus enhancing communication efficiency among robots. An analytical proof of asymptotic convergence is established for systems with time-varying communication topologies represented by sequences of strongly connected directed graphs. Comparative evaluations demonstrate significant efficiency improvements over current state-of-the-art methods, especially in scenarios with a large number of agents.

Exploiting Over-The-Air Consensus for Collision Avoidance and Formation Control in Multi-Agent Systems

TL;DR

We address distributed formation control for agents with decoupled single-integrator dynamics , introducing Over-the-Air Consensus (OtA-Consensus) to exploit interference in wireless channels for communication efficiency. A jump-flow control strategy combines continuous dynamics with discrete updates, incorporating an auxiliary reference and a collision-avoidance potential . Theoretical results prove convergence under sequences of strongly connected graphs by leveraging primitive row-stochastic matrices and Lyapunov analysis. Simulations demonstrate substantial communication efficiency gains and scalability, while revealing that small asymmetries in network topology help avoid stagnation in local minima.

Abstract

This paper introduces a distributed control method for multi-agent robotic systems employing Over the Air Consensus (OtA-Consensus). Designed for agents with decoupled single-integrator dynamics, this approach aims at efficient formation achievement and collision avoidance. As a distinctive feature, it leverages OtA's ability to exploit interference in wireless channels, a property traditionally considered a drawback, thus enhancing communication efficiency among robots. An analytical proof of asymptotic convergence is established for systems with time-varying communication topologies represented by sequences of strongly connected directed graphs. Comparative evaluations demonstrate significant efficiency improvements over current state-of-the-art methods, especially in scenarios with a large number of agents.
Paper Structure (10 sections, 7 theorems, 52 equations, 2 figures)

This paper contains 10 sections, 7 theorems, 52 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Preliminaries
  4. Communication Model
  5. Control Strategy
  6. Flow Dynamics
  7. Jump Dynamics
  8. Convergence
  9. Simulation Results
  10. Conclusion

Key Result

Proposition 1

If $\forall i\in\mathcal{N}$, $i\in\mathcal{D}_c(0)$, then the jump-flow system has no collisions.

Figures (2)

  • Figure 1: Trajectories of six agents in space seeking a given hexagonal-shaped formation while avoiding collisions. Circles and crosses denote initial and end positions, respectively. Wider line sections indicate when agents were in danger of colliding.
  • Figure 2: Trajectories of four agents in space seeking a given square-shaped formation while avoiding collisions.

Theorems & Definitions (18)

  • Definition 1: Wireless Multiple Access Channel (WMAC)
  • Remark
  • Proposition 1: Collision Avoidance
  • proof
  • Proposition 2: Converging to the reference
  • proof
  • Definition 2
  • Definition 3
  • Theorem 1
  • proof
  • ...and 8 more