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Collaborative Safe Formation Control for Coupled Multi-Agent Systems

Brooks A. Butler, Chi Ho Leung, Philip E. Paré

TL;DR

This work addresses safe formation control for coupled multi-agent systems under obstacle avoidance by introducing a distributed collaborative safety filter that minimally perturbs a prescribed formation controller. The method leverages high-order and collaborative control barrier functions to enforce safety constraints while agents communicate to respect multiple obstacles, encapsulated in a maximum-safety capability vector and a convergent SPRU-based protocol. The primary contributions are (i) a multi-constraint safety formulation, (ii) a max-min optimization and its LP reformulation for computing safety capability, and (iii) a convergence-guaranteed distributed algorithm that preserves forward invariance of the obstacle-safety sets under collaboration. The approach is demonstrated in a 2D virtual mass-spring formation simulation, showing safe navigation through obstacle fields and highlighting practical considerations for real-time implementation and potential extensions to more sophisticated formations.

Abstract

The safe control of multi-robot swarms is a challenging and active field of research, where common goals include maintaining group cohesion while simultaneously avoiding obstacles and inter-agent collision. Building off our previously developed theory for distributed collaborative safety-critical control for networked dynamic systems, we propose a distributed algorithm for the formation control of robot swarms given individual agent dynamics, induced formation dynamics, and local neighborhood position and velocity information within a defined sensing radius for each agent. Individual safety guarantees for each agent are obtained using rounds of communication between neighbors to restrict unsafe control actions among cooperating agents through safety conditions derived from high-order control barrier functions. We provide conditions under which a swarm is guaranteed to achieve collective safety with respect to multiple obstacles using a modified collaborative safety algorithm. We demonstrate the performance of our distributed algorithm via simulation in a simplified physics-based environment.

Collaborative Safe Formation Control for Coupled Multi-Agent Systems

TL;DR

This work addresses safe formation control for coupled multi-agent systems under obstacle avoidance by introducing a distributed collaborative safety filter that minimally perturbs a prescribed formation controller. The method leverages high-order and collaborative control barrier functions to enforce safety constraints while agents communicate to respect multiple obstacles, encapsulated in a maximum-safety capability vector and a convergent SPRU-based protocol. The primary contributions are (i) a multi-constraint safety formulation, (ii) a max-min optimization and its LP reformulation for computing safety capability, and (iii) a convergence-guaranteed distributed algorithm that preserves forward invariance of the obstacle-safety sets under collaboration. The approach is demonstrated in a 2D virtual mass-spring formation simulation, showing safe navigation through obstacle fields and highlighting practical considerations for real-time implementation and potential extensions to more sophisticated formations.

Abstract

The safe control of multi-robot swarms is a challenging and active field of research, where common goals include maintaining group cohesion while simultaneously avoiding obstacles and inter-agent collision. Building off our previously developed theory for distributed collaborative safety-critical control for networked dynamic systems, we propose a distributed algorithm for the formation control of robot swarms given individual agent dynamics, induced formation dynamics, and local neighborhood position and velocity information within a defined sensing radius for each agent. Individual safety guarantees for each agent are obtained using rounds of communication between neighbors to restrict unsafe control actions among cooperating agents through safety conditions derived from high-order control barrier functions. We provide conditions under which a swarm is guaranteed to achieve collective safety with respect to multiple obstacles using a modified collaborative safety algorithm. We demonstrate the performance of our distributed algorithm via simulation in a simplified physics-based environment.
Paper Structure (12 sections, 6 theorems, 47 equations, 2 figures, 1 algorithm)

This paper contains 12 sections, 6 theorems, 47 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation
  3. Preliminaries
  4. Safe Formation Control Problem
  5. Safe Formation Control with Collaboration
  6. Multi-Agent Collaboration Through Communication
  7. Maximum Capability Given Multiple Obstacles
  8. Collective Safety Through Distributed Collaboration
  9. Application Example
  10. Virtual Mass-Spring Formation Model
  11. Simulations
  12. Conclusions

Key Result

Lemma 1

If $h_i$ is an NBF, then $\bigcap_{r=1}^k \mathcal{C}_i^r$ is forward invariant.

Figures (2)

  • Figure 1: The trajectories of a 3-agent formation through an obstacle field, where a leader agent (blue) is given a constant control signal directing it straight through the field. Each agent implements safety filtering according to Algorithm \ref{['alg:mod_colab_safety']} and \ref{['eq:problem_statement']} to avoid obstacles while maintaining a formation behavior, according to \ref{['eq:formation_dynamics_mass_spring']} and \ref{['eq:formation_controller_mass_spring']}.
  • Figure 2: The safety-filtered control signals for each agent in the $\vec{x}$ component (left) and $\vec{y}$ component (right) of $u_i^s$, which are computed using Algorithm \ref{['alg:mod_colab_safety']} and \ref{['eq:problem_statement']}, during the traversal of the formation through the obstacle field shown in Figure \ref{['fig:obs_field_trajectory']}. Note that a constant control signal is given to agent $0$ (blue), which is included in the modified control signal.

Theorems & Definitions (14)

  • Definition 1
  • Lemma 1
  • Definition 2
  • Lemma 2
  • proof
  • Definition 3
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • ...and 4 more