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Safety-Critical Formation Control of Non-Holonomic Multi-Robot Systems in Communication-Limited Environments

Vishrut Bohara, Siavash Farzan

TL;DR

This work tackles safe and stable formation control for non-holonomic multi-robot systems operating with severely limited communication. It introduces a decentralized estimator-based safety-critical controller that fuses a robust predecessor-velocity estimator with Control Barrier Functions to enforce collision avoidance, yielding a closed-form, non-optimized control law and proven string stability. Theoretical guarantees are established via Lyapunov analysis: global asymptotic stability for constant velocities and global uniformly ultimately boundedness under time-varying conditions, with explicit safety and convergence criteria. The approach is validated through extensive simulations and Gazebo-based experiments, demonstrating precise formation tracking, strict safety margins, and disturbance resilience without inter-robot communication. The results advance safe, scalable formation control in communication-constrained environments and enable practical deployment in real-world, safety-critical applications.

Abstract

This paper introduces a decentralized estimator-based safety-critical controller designed for formation control of non-holonomic mobile robots operating in communication-constrained environments. The proposed framework integrates a robust state estimator capable of accurately reconstructing neighboring agents' velocity vectors and orientations under varying dynamic conditions, with a decentralized formation tracking controller that leverages Control Barrier Functions (CBFs) to guarantee collision avoidance and inter-agent safety. We present a closed-form control law that ensures both stability and string stability, effectively attenuating disturbances propagating from leader to followers. The theoretical foundations of the estimator and controller are established using Lyapunov stability analysis, which confirms global asymptotic stability under constant velocities and global uniformly ultimate boundedness under time-varying conditions. Extensive numerical simulations and realistic Gazebo-based experiments validate the effectiveness, robustness, and practical applicability of the proposed method, demonstrating precise formation tracking, stringent safety maintenance, and disturbance resilience without relying on inter-robot communication.

Safety-Critical Formation Control of Non-Holonomic Multi-Robot Systems in Communication-Limited Environments

TL;DR

This work tackles safe and stable formation control for non-holonomic multi-robot systems operating with severely limited communication. It introduces a decentralized estimator-based safety-critical controller that fuses a robust predecessor-velocity estimator with Control Barrier Functions to enforce collision avoidance, yielding a closed-form, non-optimized control law and proven string stability. Theoretical guarantees are established via Lyapunov analysis: global asymptotic stability for constant velocities and global uniformly ultimately boundedness under time-varying conditions, with explicit safety and convergence criteria. The approach is validated through extensive simulations and Gazebo-based experiments, demonstrating precise formation tracking, strict safety margins, and disturbance resilience without inter-robot communication. The results advance safe, scalable formation control in communication-constrained environments and enable practical deployment in real-world, safety-critical applications.

Abstract

This paper introduces a decentralized estimator-based safety-critical controller designed for formation control of non-holonomic mobile robots operating in communication-constrained environments. The proposed framework integrates a robust state estimator capable of accurately reconstructing neighboring agents' velocity vectors and orientations under varying dynamic conditions, with a decentralized formation tracking controller that leverages Control Barrier Functions (CBFs) to guarantee collision avoidance and inter-agent safety. We present a closed-form control law that ensures both stability and string stability, effectively attenuating disturbances propagating from leader to followers. The theoretical foundations of the estimator and controller are established using Lyapunov stability analysis, which confirms global asymptotic stability under constant velocities and global uniformly ultimate boundedness under time-varying conditions. Extensive numerical simulations and realistic Gazebo-based experiments validate the effectiveness, robustness, and practical applicability of the proposed method, demonstrating precise formation tracking, stringent safety maintenance, and disturbance resilience without relying on inter-robot communication.
Paper Structure (16 sections, 74 equations, 9 figures)

This paper contains 16 sections, 74 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Problem Description
  3. Predecessor-Follower Dynamics
  4. Formation Control
  5. String Stability
  6. Estimator-based Safety Critical Controller
  7. Estimator Design
  8. Stability Analysis
  9. Safety-Critical Controller Design
  10. String Stability
  11. Results and Evaluation
  12. Estimator Analysis
  13. Formation Control with Constant Leader Velocity
  14. String Stability Performance
  15. Physics Engine-Based Experiments
  16. ...and 1 more sections

Figures (9)

  • Figure 1: Leader-Follower formation control of mobile robots in a diamond formation, illustrating inter-agent interaction edges and safety boundaries. The red dashed circles denote the safety regions for each robot, and the blue dashed arrows represent predecessor-follower interactions, where followers maintain desired distances from their predecessors without communication.
  • Figure 2: Predecessor-follower pair and associated parameters in a leader-follower formation control setting.
  • Figure 3: Block diagram of the proposed estimator-integrated safety-critical control system, illustrating the interconnection of the estimator and controller modules within the decentralized formation control framework.
  • Figure 4: Estimator performance for a two-agent system with different control profiles: (a) Linear acceleration profiles; (b) Angular velocities; (c) Position estimation errors; (d) Velocity estimation errors.
  • Figure 5: Formation control for a circular motion using the proposed framework: (a) Linear velocity profiles; (b) Acceleration profiles; (c) Angular velocities; (d) Distances maintained along the motion; (e) Position estimation errors; (f) Distance perpendicular to the motion, and (f) Overall motion of the formation.
  • ...and 4 more figures

Theorems & Definitions (4)

  • proof
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