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Risk-Budgeted Control Framework for Balanced Performance and Safety in Autonomous Vehicles

Pei Yu Chang, Vishnu Renganathan, Qadeer Ahmed

TL;DR

This work tackles the challenge of certifying safety for autonomous driving under localization and obstacle uncertainty while preserving performance under real-time constraints. It introduces a risk-budgeted monitor that governs switching between a relaxed CBF-based controller and a conservative CVaR-CBF within an MPC framework, using stochastic safe sets and tail-risk guarantees. The key contributions are formalizing a sliding-window risk-budget monitor, developing FT-C-CBF and QT-C-CBF switching mechanisms, and validating the approach through extensive Monte Carlo simulations showing high safety and good tracking with moderate computation. The results demonstrate that bounded tail risk can be achieved without overly conservative behavior, enabling practical, safety-assured autonomous navigation in uncertain environments.

Abstract

This paper presents a risk-budgeted monitor with a control framework that certifies safety for autonomous driving. In this process, a sliding window is proposed to monitor for insufficient barrier residuals or nonzero tail risk, ensuring system safety. When the safety margin deteriorates, it triggers switching the safety constraint from a performance-based relaxed-control barrier function (R-CBF) to a conservative conditional value at risk (CVaR-CBF) to address the safety concern. This switching is governed by two real-time triggers: Feasibility-Triggered (FT) and Quality-Triggered (QT) conditions. In the FT condition, if the R-CBF constraint becomes infeasible or yields a suboptimal solution, the risk monitor triggers the use of the CVaR constraints for the controller. In the QT condition, the risk monitor observes the safety margin of the R-CBF solution at every step, regardless of feasibility. If it falls below the safety margin, the safety filter switches to the CVaR-CBF constraints. The proposed framework is evaluated using a model predictive controller (MPC) for autonomous driving in the presence of autonomous vehicle (AV) localization noise and obstacle position uncertainties. Multiple AV-pedestrian interaction scenarios are considered, with 1,500 Monte Carlo runs conducted for all scenarios. In the most challenging setting with pedestrian detection uncertainty of 5 m, the proposed framework achieves a 94-96% success rate of not colliding with the pedestrians over 300 trials while maintaining the lowest mean cross-track error (CTE = 3.2-3.6 m) to the reference path. The reduced CTE indicates faster trajectory recovery after obstacle avoidance, demonstrating a balance between safety and performance.

Risk-Budgeted Control Framework for Balanced Performance and Safety in Autonomous Vehicles

TL;DR

This work tackles the challenge of certifying safety for autonomous driving under localization and obstacle uncertainty while preserving performance under real-time constraints. It introduces a risk-budgeted monitor that governs switching between a relaxed CBF-based controller and a conservative CVaR-CBF within an MPC framework, using stochastic safe sets and tail-risk guarantees. The key contributions are formalizing a sliding-window risk-budget monitor, developing FT-C-CBF and QT-C-CBF switching mechanisms, and validating the approach through extensive Monte Carlo simulations showing high safety and good tracking with moderate computation. The results demonstrate that bounded tail risk can be achieved without overly conservative behavior, enabling practical, safety-assured autonomous navigation in uncertain environments.

Abstract

This paper presents a risk-budgeted monitor with a control framework that certifies safety for autonomous driving. In this process, a sliding window is proposed to monitor for insufficient barrier residuals or nonzero tail risk, ensuring system safety. When the safety margin deteriorates, it triggers switching the safety constraint from a performance-based relaxed-control barrier function (R-CBF) to a conservative conditional value at risk (CVaR-CBF) to address the safety concern. This switching is governed by two real-time triggers: Feasibility-Triggered (FT) and Quality-Triggered (QT) conditions. In the FT condition, if the R-CBF constraint becomes infeasible or yields a suboptimal solution, the risk monitor triggers the use of the CVaR constraints for the controller. In the QT condition, the risk monitor observes the safety margin of the R-CBF solution at every step, regardless of feasibility. If it falls below the safety margin, the safety filter switches to the CVaR-CBF constraints. The proposed framework is evaluated using a model predictive controller (MPC) for autonomous driving in the presence of autonomous vehicle (AV) localization noise and obstacle position uncertainties. Multiple AV-pedestrian interaction scenarios are considered, with 1,500 Monte Carlo runs conducted for all scenarios. In the most challenging setting with pedestrian detection uncertainty of 5 m, the proposed framework achieves a 94-96% success rate of not colliding with the pedestrians over 300 trials while maintaining the lowest mean cross-track error (CTE = 3.2-3.6 m) to the reference path. The reduced CTE indicates faster trajectory recovery after obstacle avoidance, demonstrating a balance between safety and performance.

Paper Structure

This paper contains 22 sections, 2 theorems, 30 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Relaxed CBF (R-CBF)
  5. Stochastic Safe Sets
  6. Risk-Aware Safety Critical Control Formulation
  7. Probability Constraints
  8. Risk-Budget Monitor
  9. Bad Step detection
  10. Sliding Window Risk-Budgeted Monitor
  11. Risk-Switch for Probabilistic Safety
  12. Feasibility-Triggered CVaR-CBF (FT-C-CBF)
  13. Quality-Triggered CVaR-CBF (QT-C-CBF)
  14. Simulations
  15. Experimental Setup
  16. ...and 7 more sections

Key Result

Lemma 1

Let the weights $w_j := \mu^{W-1-j}$ for $j=0, \dots, W-1$. Since $\mu \in (0, 1)$, these weights are monotonically increasing: $0 < w_0 < w_1 < \dots < w_{W-1}$. Let $V$ be the set of sequences $\{v_j\}_{j=0}^{W-1}$ with the worst case $M$ entries equal to $-\overline{\nu}$ and $W-M$ entries equal

Figures (3)

  • Figure 1: Proposed framework with MPC nominal control and a risk–budget monitor for safety–driven controller switching.
  • Figure 2: Success rate versus mean cross–track error (CTE) relative to the reference trajectory across 1,500 runs.
  • Figure 3: (a) AV trajectory comparison for R-CBF, RC-CBF, FT-C-CBF, and QT-C-CBF under $\sigma_v=0.1, \sigma_o=5$ with three pedestrians. (b) Stochastic safe set: sampling-based barrier values $h(x)$ with sample mean (solid) and sampled range (shaded); shading appears when CVaR control is active. (c) Deterministic safe set: $h(x)$ evaluated at true states of vehicle and pedestrians without sampling, highlighting clearance relative to $h(x)=0$.

Theorems & Definitions (5)

  • Remark 1
  • Lemma 1: Rearrangement Lemma
  • proof
  • Theorem 1: Window-Level Safety Certificate
  • proof