Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Tube-Based Safety for Anticipative Tracking in Multi-Agent Systems

Armel Koulong, Ali Pakniyat

Abstract

A tube-based safety framework is presented for robust anticipative tracking in nonlinear Brunovsky multi-agent systems subject to bounded disturbances. The architecture establishes robust safety certificates for a feedforward-augmented ancillary control policy. By rendering the state-deviation dynamics independent of the agents' internal nonlinearities, the formulation strictly circumvents the restrictive Lipschitz-bound feasibility conditions otherwise required for robust stabilization. Consequently, this structure admits an explicit, closed-form robust positively invariant (RPI) tube radius that systematically attenuates the exponential control barrier function (eCBF) tightening margins, thereby mitigating constraint conservatism while preserving formal forward invariance. Within the distributed model predictive control (MPC) layer, mapping the local tube radii through the communication graph yields a closed-form global formation error bound formulated via the minimum singular value of the augmented Laplacian. Robust inter-agent safety is enforced with minimal communication overhead, requiring only a single scalar broadcast per neighbor at initialization. Numerical simulations confirm the framework's efficacy in safely navigating heterogeneous formations through cluttered environments.

Tube-Based Safety for Anticipative Tracking in Multi-Agent Systems

Abstract

A tube-based safety framework is presented for robust anticipative tracking in nonlinear Brunovsky multi-agent systems subject to bounded disturbances. The architecture establishes robust safety certificates for a feedforward-augmented ancillary control policy. By rendering the state-deviation dynamics independent of the agents' internal nonlinearities, the formulation strictly circumvents the restrictive Lipschitz-bound feasibility conditions otherwise required for robust stabilization. Consequently, this structure admits an explicit, closed-form robust positively invariant (RPI) tube radius that systematically attenuates the exponential control barrier function (eCBF) tightening margins, thereby mitigating constraint conservatism while preserving formal forward invariance. Within the distributed model predictive control (MPC) layer, mapping the local tube radii through the communication graph yields a closed-form global formation error bound formulated via the minimum singular value of the augmented Laplacian. Robust inter-agent safety is enforced with minimal communication overhead, requiring only a single scalar broadcast per neighbor at initialization. Numerical simulations confirm the framework's efficacy in safely navigating heterogeneous formations through cluttered environments.

Paper Structure

This paper contains 18 sections, 4 theorems, 36 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Methodology
  4. Feedforward Compensation
  5. Impact on the Deviation Dynamics
  6. Leader Tube Radius
  7. Per-Agent Tube Radius under Feedforward
  8. Formation Tracking and Global Error Bound
  9. Synchronization Error and Formation Objective
  10. Connecting Local Tube Radii to Global Formation Error
  11. Tightened eCBF Functions
  12. MPC Implementation
  13. Discretization and Information Exchange
  14. Neighbor Prediction Rollout
  15. Applied Control and OCP
  16. ...and 3 more sections

Key Result

Proposition 1

Let $K^i_p$ make $A^i_p:=A_0-GK^i_p$ Hurwitz with Lyapunov pair $Q_i,P_i\succ 0$ satisfying $(A^i_p)^\top P_i+P_iA^i_p=-Q_i$. We define the effective disturbance bound: Then the ellipsoidal tube $\mathcal{Z}^i:=\{\delta x^i:(\delta x^i)^\top P_i\delta x^i \leq r_i^2\}$ is robustly positively invariant under eq:ancillary_control--eq:devdyn for: The true state deviation satisfies $\|\delta x^i(t)\

Figures (4)

  • Figure 3: The considered communication topology ${\mathcal{G}}$ and the augmented graph $\bar{\mathcal{G}}$ for the example in Section \ref{['sec:NUMERICALEXAMPLE']}.
  • Figure 4: Formation offset error and position components for leader ($i=0$) and followers ($i=1,\ldots,5$) using the tightened safety constraints of koulong2025wc
  • Figure 5: Formation offset error and position components for leader ($i=0$) and followers ($i=1,\ldots,5$)
  • Figure 6: Minimum Safety Clearance

Theorems & Definitions (13)

  • Proposition 1: Explicit Tube Radius
  • proof
  • Remark C.1: Structural difference from koulong2025wc
  • Remark C.2: Quantitative improvement over koulong2025wc
  • Remark C.3: Conservatism of worst-case tube design
  • Lemma 1: Synchronization-Error Deviation Bound
  • proof
  • Theorem 1: Global Formation Error Bound
  • proof
  • Remark C.4
  • ...and 3 more