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Online Adaptive Probabilistic Safety Certificate with Language Guidance

Zhuoyuan Wang, Xiyu Deng, Hikaru Hoshino, Yorie Nakahira

TL;DR

A language-guided adaptive probabilistic safety certificate (PSC) framework that guarantees long-term safety for stochastic systems under environmental uncertainty while accommodating diverse human preferences is proposed, demonstrating enhanced safety-performance trade-offs, adaptability to changing environments, and personalization to different user preferences.

Abstract

Achieving long-term safety in uncertain or extreme environments while accounting for human preferences remains a fundamental challenge for autonomous systems. Existing methods often trade off long-term guarantees for fast real-time control and cannot adapt to variability in human preferences or risk tolerance. To address these limitations, we propose a language-guided adaptive probabilistic safety certificate (PSC) framework that guarantees long-term safety for stochastic systems under environmental uncertainty while accommodating diverse human preferences. The proposed framework integrates natural-language inputs from users and Bayesian estimators of the environment into adaptive safety certificates that explicitly account for user preferences, system dynamics, and quantified uncertainties. Our key technical innovation leverages probabilistic invariance--a generalization of forward invariance to a probability space--to obtain myopic safety conditions with long-term safety guarantees that integrate language guidance, model information, and quantified uncertainty. We validate the framework through numerical simulations of autonomous lane-keeping with human-in-the-loop guidance under uncertain and extreme road conditions, demonstrating enhanced safety-performance trade-offs, adaptability to changing environments, and personalization to different user preferences.

Online Adaptive Probabilistic Safety Certificate with Language Guidance

TL;DR

A language-guided adaptive probabilistic safety certificate (PSC) framework that guarantees long-term safety for stochastic systems under environmental uncertainty while accommodating diverse human preferences is proposed, demonstrating enhanced safety-performance trade-offs, adaptability to changing environments, and personalization to different user preferences.

Abstract

Achieving long-term safety in uncertain or extreme environments while accounting for human preferences remains a fundamental challenge for autonomous systems. Existing methods often trade off long-term guarantees for fast real-time control and cannot adapt to variability in human preferences or risk tolerance. To address these limitations, we propose a language-guided adaptive probabilistic safety certificate (PSC) framework that guarantees long-term safety for stochastic systems under environmental uncertainty while accommodating diverse human preferences. The proposed framework integrates natural-language inputs from users and Bayesian estimators of the environment into adaptive safety certificates that explicitly account for user preferences, system dynamics, and quantified uncertainties. Our key technical innovation leverages probabilistic invariance--a generalization of forward invariance to a probability space--to obtain myopic safety conditions with long-term safety guarantees that integrate language guidance, model information, and quantified uncertainty. We validate the framework through numerical simulations of autonomous lane-keeping with human-in-the-loop guidance under uncertain and extreme road conditions, demonstrating enhanced safety-performance trade-offs, adaptability to changing environments, and personalization to different user preferences.

Paper Structure

This paper contains 21 sections, 2 theorems, 46 equations, 14 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Proposed Method
  5. Adaptive Probabilistic Safety Certificate
  6. Integration with Language Guidance
  7. Case Study: Adaptive Lane Keeping
  8. Problem Setting
  9. Long-Term Safety and Efficiency under Uncertainty
  10. Adaptation with Human Instructions
  11. Conclusion
  12. Proofs
  13. Implementation of Safety Constraints
  14. Adaptive PSC Algorithm
  15. Vehicle model
  16. ...and 6 more sections

Key Result

theorem 1

Consider the stochastic dynamics given by eq:discrete_dynamics with a nominal controller $\pi$ and a sequence of probability density functions $H_0, H_1, \dots$ for estimating $\xi$. Suppose the state and parameter estimation originate from $X_0$ and $H_0$ satisfy the following and the control action $U_k$ given by the controller $\pi_\mathrm{safe}$ satisfies eq:safety_condition_each_Zt_aug at al

Figures (14)

  • Figure 1: The proposed language-guided adaptive probabilistic safety certificate (PSC) framework.
  • Figure 2: Safety probability vs. MPC horizon $T_{\mathrm{mpc}}$.
  • Figure 3: Vehicle trajectories ($T_{\mathrm{mpc}}=10$).
  • Figure 4: Vehicle trajectories ($T_{\mathrm{mpc}}=20$).
  • Figure 5: Safety vs. efficiency trade-offs with MPC-based adaptive controls.
  • ...and 9 more figures

Theorems & Definitions (7)

  • remark 1
  • theorem 1
  • proof
  • proof
  • theorem 4
  • proof
  • remark 2