Sensor-Based Safety-Critical Control Using an Incremental Control Barrier Function Formulation via Reduced-Order Approximate Models

TL;DR

This work addresses safety under parametric uncertainty by introducing measurement-robust incremental control barrier functions (MRICBFs) that replace certain model components with real-time sensor measurements to ensure forward invariance of the safe set $S$. By combining a reduced-order output model with an incremental barrier condition $\sup_{\Delta u}[\dot{h}_n(y,\Delta u)-\varphi(y,\Delta t)] \ge -\alpha(h(y))$ and explicit error compensation, MRICBFs provide safety guarantees even with bounded approximation and sensor errors. The approach is validated in two simulations: a 1D SISO system with time-varying sensor biases and an overactuated hypersonic glide vehicle (GHGV-2) with multiple state constraints, where MRICBFs maintain safety while standard CBFs may fail. Results also show that applying a low-pass filter to measurements can reduce oscillations without sacrificing safety. Overall, MRICBFs remove the need for perfect model knowledge in certain uncertain scenarios and enable immediate safety assurances using sensor data.

Abstract

The existing control barrier function literature generally relies on precise mathematical models to guarantee system safety, limiting their applicability in scenarios with parametric uncertainties. While incremental control techniques have shown promise in addressing model uncertainties in flight control applications, translating these approaches to safety-critical control presents significant challenges. This paper bridges this gap by introducing measurement-robust incremental control barrier functions (MRICBFs), which leverage sensor-based reduced-order models to provide formal safety guarantees for uncertain systems. By carefully addressing the challenges of sensor accuracy and approximation errors in the incremental formulation, our approach enables substituting specific model components with real-time sensor measurements while maintaining rigorous safety guarantees. This formulation overcomes the limitations of traditional adaptive control methods that adjust system parameters over time, enabling immediate and reliable safety measures for a class of model uncertainties. The efficacy of MRICBFs is demonstrated in two simulation case studies: a simple first-order system with time-varying sensor biases and a more complex overactuated hypersonic glide vehicle with multiple state constraints.

Figures (8)

• Figure 1: System response in the scenario with time-varying sensor biases.
• Figure 2: Overview of the proposed safety-critical control framework applied to the control of a hypersonic vehicle with parametric uncertainties.
• Figure 3: Example sketch of external forces and moments acting on a hypersonic glide vehicle Autenrieb2021.
• Figure 4: Rear view sketch of the considered hypersonic glide vehicle and available control effectors during endoatmospheric operations Autenrieb2022.
• Figure 5: Closed-loop response of pitch rate control case with MRICBF for the simplified HGV dynamics.

Theorems & Definitions (13)

• Definition 1: Forward invariance and safety, Blanchini_1999Ames_2014
• Definition 2: Class $\mathcal{K}$ functions, Khalil
• Definition 3: CBF,Ames_2017
• Theorem 1
• Lemma 1
• proof
• Theorem 2
• proof
• Definition 4
• Theorem 3