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Distributed Safe Navigation of Multi-Agent Systems using Control Barrier Function-Based Optimal Controllers

Pol Mestres, Carlos Nieto-Granda, Jorge Cortés

TL;DR

This work addresses safe, formation-preserving navigation for a team of robots under obstacle and inter-robot collision constraints. It develops a distributed controller based on control barrier functions (CBFs) that encode safety as affine control-input constraints within a state-dependent network optimization, augmented with constraint-mismatch variables and a regularized objective to enable fully decentralized updates. The authors prove safety and convergence to the regularized optimum under a timescale separation and validate the approach through extensive simulations and hardware experiments with differential-drive robots, demonstrating safe navigation and formation maintenance in complex environments. The results offer a scalable, provably safe framework for multi-robot navigation with practical implications for autonomous exploration, swarming, and coordinated delivery in real-world settings.

Abstract

This paper proposes a distributed controller synthesis framework for safe navigation of multi-agent systems. We leverage control barrier functions to formulate collision avoidance with obstacles and teammates as constraints on the control input for a state-dependent network optimization problem that encodes team formation and the navigation task. Our algorithmic solution is valid for general nonlinear control dynamics and optimization problems. The resulting controller is distributed, satisfies the safety constraints at all times, and is asymptotically optimal. We illustrate its performance in a team of differential-drive robots in a variety of complex environments, both in simulation and in hardware.

Distributed Safe Navigation of Multi-Agent Systems using Control Barrier Function-Based Optimal Controllers

TL;DR

This work addresses safe, formation-preserving navigation for a team of robots under obstacle and inter-robot collision constraints. It develops a distributed controller based on control barrier functions (CBFs) that encode safety as affine control-input constraints within a state-dependent network optimization, augmented with constraint-mismatch variables and a regularized objective to enable fully decentralized updates. The authors prove safety and convergence to the regularized optimum under a timescale separation and validate the approach through extensive simulations and hardware experiments with differential-drive robots, demonstrating safe navigation and formation maintenance in complex environments. The results offer a scalable, provably safe framework for multi-robot navigation with practical implications for autonomous exploration, swarming, and coordinated delivery in real-world settings.

Abstract

This paper proposes a distributed controller synthesis framework for safe navigation of multi-agent systems. We leverage control barrier functions to formulate collision avoidance with obstacles and teammates as constraints on the control input for a state-dependent network optimization problem that encodes team formation and the navigation task. Our algorithmic solution is valid for general nonlinear control dynamics and optimization problems. The resulting controller is distributed, satisfies the safety constraints at all times, and is asymptotically optimal. We illustrate its performance in a team of differential-drive robots in a variety of complex environments, both in simulation and in hardware.
Paper Structure (9 sections, 3 theorems, 26 equations, 5 figures)

This paper contains 9 sections, 3 theorems, 26 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Statement
  4. Distributed Controller Design
  5. Analysis of the Solution: Distributed Character, Safety, and Stability
  6. Experimental validation
  7. Parameter Tuning
  8. Experiments
  9. Conclusions

Key Result

Proposition II.1

(Equivalence between the two formulations): Let $\mathcal{F}^*$ be the solution set of eq:distr-opt-pb-y. Then, $u^*=\Pi_u{\color{blue}}(\mathcal{F}^*)$ is the optimizer of eq:separable-distr-opt-pb.

Figures (5)

  • Figure 1: Block diagram of \ref{['eq:alg-sp-plant']}. The blue block updates the variables $\gamma$, $z$ and $\lambda$ using the projected saddle-point dynamics of the regularized version of \ref{['eq:cbf-distr-opt-pb-y']}. In parallel, the plant is updated using the controller $\bar{u}$.
  • Figure 2: Snapshots of the first simulation environment with color coded trajectories for the different robots. The intensity of the color decreases with time. In the last snapshot, the red x's indicate the three different waypoints for the leader of the team (in magenta). The environment has dimensions $20$m $\times$$30$m.
  • Figure 3: Evolution in the first simulation environment, cf. Figure . (left): Distance to the desired formation position over time for the different followers. (right): Distance to the different obstacles over time for the leader.
  • Figure 4: Snapshots of the second simulation environment with color coded trajectories for the different robots. The intensity of the color increases with time. In the last snapshot, the red x's indicate the four different waypoints for the leader of the team. The environment has dimensions $20$m $\times$$50$m.
  • Figure 5: Snapshots of the hardware experiment with color coded trajectories for the different robots. The intensity of the color increases with time. In the last snapshot, the red x's indicate the two different waypoints for the leader of the team. The environment has dimensions $4$m $\times$$9$m.

Theorems & Definitions (13)

  • Proposition II.1
  • Remark V.1
  • proof
  • Remark V.2
  • proof
  • Proposition V.3
  • proof
  • Remark V.4
  • proof
  • Remark V.5
  • ...and 3 more