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Distributed Event-Triggered Distance-Based Formation Control for Multi-Agent Systems

Evangelos Psomiadis, Panagiotis Tsiotras

Abstract

This paper addresses the problem of collaborative formation control for multi-agent systems with limited resources. We consider a team of robots tasked with achieving a desired formation from an arbitrary initial configuration. To reduce unnecessary control updates and conserve resources, we propose a distributed event-triggered formation controller. Unlike the well-studied linear formation control strategies, the proposed controller is nonlinear and relies on inter-agent distance measurements. Control updates are triggered only when the measurement error exceeds a predefined threshold, ensuring system stability while minimizing actuation effort. We also employ a distributed control barrier function to guarantee inter-agent collision avoidance. The proposed controller is validated through extensive simulations and real-world experiments involving different formations, communication topologies, scalability tests, and variations in design parameters, while also being compared against periodic triggering strategies. Results demonstrate that the event-triggered approach significantly reduces control effort while preserving formation performance.

Distributed Event-Triggered Distance-Based Formation Control for Multi-Agent Systems

Abstract

This paper addresses the problem of collaborative formation control for multi-agent systems with limited resources. We consider a team of robots tasked with achieving a desired formation from an arbitrary initial configuration. To reduce unnecessary control updates and conserve resources, we propose a distributed event-triggered formation controller. Unlike the well-studied linear formation control strategies, the proposed controller is nonlinear and relies on inter-agent distance measurements. Control updates are triggered only when the measurement error exceeds a predefined threshold, ensuring system stability while minimizing actuation effort. We also employ a distributed control barrier function to guarantee inter-agent collision avoidance. The proposed controller is validated through extensive simulations and real-world experiments involving different formations, communication topologies, scalability tests, and variations in design parameters, while also being compared against periodic triggering strategies. Results demonstrate that the event-triggered approach significantly reduces control effort while preserving formation performance.

Paper Structure

This paper contains 12 sections, 2 theorems, 30 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Notation and Preliminaries
  3. Problem Formulation
  4. Distributed Event-triggered Formation Control
  5. Stability
  6. Collision Avoidance
  7. Experiments
  8. Agent Communication Topology Variation
  9. Design Parameter Variation
  10. Scalability
  11. Discussion on Zeno Behavior
  12. Conclusions

Key Result

Theorem 1

Consider the system $\dot{\mathbf{x}} = \bar{\mathbf{u}}$ under the control law eq:distributed_ctrl, where the communication graph $G$ is connected and rigid and the desired inter-agent distances encoded in $\widetilde{\mathbf{W}}$ correspond to a formation as in eq:form_distances. Suppose that each where, $\mathbf{z}(\mathbf{x}) = \widehat{\mathbf{L}}(\mathbf{x}) \mathbf{x}$, $D_{ij}(\mathbf{x}

Figures (5)

  • Figure A1: Six GRITSBot X robots, initially arranged in a circular formation (a), achieve a V-formation (b) by employing the proposed event-triggered controller in the Robotarium Wilson2020_robotarium.
  • Figure C1: Distributed, event-triggered, distance-based formation control loop of agent $i$.
  • Figure E1: (a) Control inputs and (b) measurement errors for six agents under a complete graph.
  • Figure E2: Initial arrangement of 200 agents on a sphere (a) and their final positions (b), showing that agents near the equator have moved approximately 20 meters apart.
  • Figure E3: Average formation error for a 200-agent simulation.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Proposition 1
  • proof