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Where to Put Safety? Control Barrier Function Placement in Networked Control Systems

Severin Beger, Yuling Chen, Sandra Hirche

Abstract

Ensuring safe behavior is critical for modern autonomous cyber-physical systems. Control barrier functions (CBFs) are widely used to enforce safety in autonomous systems, yet their placement within networked control architectures remains largely unexplored. In this work, we investigate where to enforce safety in a networked control system in which a remote model predictive controller (MPC) communicates with the plant over a delayed network. We compare two safety strategies: i) a local myopic CBF filter applied at the plant and ii) predictive CBF constraints embedded in the remote MPC. For both architectures, we derive state-dependent disturbance tolerance bounds and show that safety placement induces a fundamental trade-off: local CBFs provide higher disturbance tolerance due to access to fresh state measurements, whereas MPC-CBF enables improved performance through anticipatory behavior, but yields stricter admissible disturbance levels. Motivated by this insight, we propose a combined architecture that integrates predictive and local safety mechanisms. The theoretical findings are illustrated in simulations on a planar three-degree-of-freedom robot performing a collision-avoidance task.

Where to Put Safety? Control Barrier Function Placement in Networked Control Systems

Abstract

Ensuring safe behavior is critical for modern autonomous cyber-physical systems. Control barrier functions (CBFs) are widely used to enforce safety in autonomous systems, yet their placement within networked control architectures remains largely unexplored. In this work, we investigate where to enforce safety in a networked control system in which a remote model predictive controller (MPC) communicates with the plant over a delayed network. We compare two safety strategies: i) a local myopic CBF filter applied at the plant and ii) predictive CBF constraints embedded in the remote MPC. For both architectures, we derive state-dependent disturbance tolerance bounds and show that safety placement induces a fundamental trade-off: local CBFs provide higher disturbance tolerance due to access to fresh state measurements, whereas MPC-CBF enables improved performance through anticipatory behavior, but yields stricter admissible disturbance levels. Motivated by this insight, we propose a combined architecture that integrates predictive and local safety mechanisms. The theoretical findings are illustrated in simulations on a planar three-degree-of-freedom robot performing a collision-avoidance task.

Paper Structure

This paper contains 9 sections, 3 theorems, 30 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Statement and Preliminaries
  3. Disturbance Tolerance of Locally and Remotely Placed CBFs
  4. Local CBF
  5. Remote MPC-CBF
  6. Disturbance Tolerance due to CBF Placement
  7. Combined Architecture: Local and Remote CBF
  8. Simulation Results
  9. Conclusion

Key Result

Lemma III.1

Consider system eq:dynamics with bounded disturbance $\lVert\bm{w}_k\rVert \leq \bar{w}$, closed with an MPC as in eq:OCP. Let $h(\cdot)$ be Lipschitz continuous with constant $L_h$ and $h(\bm{x}_0)>0$. If the fixed disturbance bound $\bar{w}$ satisfies then the local CBF eq:dCBF renders the safe set $\mathcal{C}$ as in eq:SafeSet forward invariant.

Figures (4)

  • Figure 1: Considered networked setup with potential CBF placements locally or remotely within the MPC.
  • Figure 2: Considered collision avoidance task. The robot has to avoid the obstacles while reaching for the waypoints.
  • Figure 3: End-effector paths for a single experiment in (a) the low and (b) the high disturbance case. The dots along the blue lines highlight interventions of the local CBF.
  • Figure 4: Average distance to obstacle $2$ with a maximum and minimum envelope over all runs with large disturbances.

Theorems & Definitions (6)

  • Lemma III.1: Disturbance Tolerance of Local CBF
  • proof
  • Lemma III.2: Disturbance Tolerance of Remote MPC-CBF
  • proof
  • Proposition III.3: Architectural Disturbance-Tolerance Comparison
  • proof