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FORMULA: FORmation MPC with neUral barrier Learning for safety Assurance

Qintong Xie, Weishu Zhan, Peter Chin

Abstract

Multi-robot systems (MRS) are essential for large-scale applications such as disaster response, material transport, and warehouse logistics, yet ensuring robust, safety-aware formation control in cluttered and dynamic environments remains a major challenge. Existing model predictive control (MPC) approaches suffer from limitations in scalability and provable safety, while control barrier functions (CBFs), though principled for safety enforcement, are difficult to handcraft for large-scale nonlinear systems. This paper presents FORMULA, a safe distributed, learning-enhanced predictive control framework that integrates MPC with Control Lyapunov Functions (CLFs) for stability and neural network-based CBFs for decentralized safety, eliminating manual safety constraint design. This scheme maintains formation integrity during obstacle avoidance, resolves deadlocks in dense configurations, and reduces online computational load. Simulation results demonstrate that FORMULA enables scalable, safety-aware, formation-preserving navigation for multi-robot teams in complex environments.

FORMULA: FORmation MPC with neUral barrier Learning for safety Assurance

Abstract

Multi-robot systems (MRS) are essential for large-scale applications such as disaster response, material transport, and warehouse logistics, yet ensuring robust, safety-aware formation control in cluttered and dynamic environments remains a major challenge. Existing model predictive control (MPC) approaches suffer from limitations in scalability and provable safety, while control barrier functions (CBFs), though principled for safety enforcement, are difficult to handcraft for large-scale nonlinear systems. This paper presents FORMULA, a safe distributed, learning-enhanced predictive control framework that integrates MPC with Control Lyapunov Functions (CLFs) for stability and neural network-based CBFs for decentralized safety, eliminating manual safety constraint design. This scheme maintains formation integrity during obstacle avoidance, resolves deadlocks in dense configurations, and reduces online computational load. Simulation results demonstrate that FORMULA enables scalable, safety-aware, formation-preserving navigation for multi-robot teams in complex environments.

Paper Structure

This paper contains 15 sections, 1 theorem, 25 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Mobile Robot Model
  4. Problem Statement and Safety Notions
  5. Safe Formation Controller Design
  6. MPC With CLF Constraints
  7. Neural Network-Based Control Barrier Function
  8. Deadlock Resolution
  9. Experiments and Results
  10. Simulation Environment
  11. Baseline Algorithms
  12. Implementation Details
  13. Metrics
  14. Deadlock Resolution in Practice
  15. Conclusion and Future Work

Key Result

Lemma 1

If the optimal MPC-CLF cost $J_{\mathrm{CLF},i}(\hat{\boldsymbol{u}}_i^\ast)$ converges to zero for robot $i$, then the CLF constraint becomes inactive, and the closed-loop dynamics eq:control_affine--eq:nominaldynamics drive the formation error $\boldsymbol{e}_{\mathcal{N}_i}$ to zero, guaranteeing

Figures (4)

  • Figure 1: Cooperative formation and safety-aware navigation for multiple mobile robots.
  • Figure 2: Overview of the proposed FORMULA framework. Left: each robot runs a distributed MPC-CLF optimizer for formation stability and a NN--CBF module for safety, with an event-triggered deadlock-resolution mechanism. Right: one of the multi-robot simulation environments.
  • Figure 3: Formation control in obstacle-dense environments. (a) Planar trajectories of the leader (red) and followers (magenta, blue, green, cyan) among randomly placed obstacles (gray circles). (b) Formation tracking error $\|\boldsymbol{e}_{\mathcal{N}_i}\|$ over time for all followers, showing a temporary increase during obstacle negotiation followed by convergence as the formation re-stabilizes.
  • Figure 4: Deadlock resolution in FORMULA. Colored trajectories show four robots safely crossing at an intersection near the origin. The event-triggered mechanism perturbs the nominal states $\hat{\boldsymbol{x}}_i$ when $E_i<0$, breaking potential deadlocks while maintaining safety and formation coherence.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4: CBF ames2016control
  • Definition 5: Decentralized safety
  • Definition 6: minniti2021adaptive
  • Lemma 1
  • proof