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Incremental Bayesian Learning for Fail-Operational Control in Autonomous Driving

Lei Zheng, Rui Yang, Zengqi Peng, Wei Yan, Michael Yu Wang, Jun Ma

TL;DR

A real-time fail-operational controller that ensures the asymptotic convergence of an uncertain EV to a safe state, while preserving task efficiency in dynamic environments is presented.

Abstract

Abrupt maneuvers by surrounding vehicles (SVs) can typically lead to safety concerns and affect the task efficiency of the ego vehicle (EV), especially with model uncertainties stemming from environmental disturbances. This paper presents a real-time fail-operational controller that ensures the asymptotic convergence of an uncertain EV to a safe state, while preserving task efficiency in dynamic environments. An incremental Bayesian learning approach is developed to facilitate online learning and inference of changing environmental disturbances. Leveraging disturbance quantification and constraint transformation, we develop a stochastic fail-operational barrier based on the control barrier function (CBF). With this development, the uncertain EV is able to converge asymptotically from an unsafe state to a defined safe state with probabilistic stability. Subsequently, the stochastic fail-operational barrier is integrated into an efficient fail-operational controller based on quadratic programming (QP). This controller is tailored for the EV operating under control constraints in the presence of environmental disturbances, with both safety and efficiency objectives taken into consideration. We validate the proposed framework in connected cruise control (CCC) tasks, where SVs perform aggressive driving maneuvers. The simulation results demonstrate that our method empowers the EV to swiftly return to a safe state while upholding task efficiency in real time, even under time-varying environmental disturbances.

Incremental Bayesian Learning for Fail-Operational Control in Autonomous Driving

TL;DR

A real-time fail-operational controller that ensures the asymptotic convergence of an uncertain EV to a safe state, while preserving task efficiency in dynamic environments is presented.

Abstract

Abrupt maneuvers by surrounding vehicles (SVs) can typically lead to safety concerns and affect the task efficiency of the ego vehicle (EV), especially with model uncertainties stemming from environmental disturbances. This paper presents a real-time fail-operational controller that ensures the asymptotic convergence of an uncertain EV to a safe state, while preserving task efficiency in dynamic environments. An incremental Bayesian learning approach is developed to facilitate online learning and inference of changing environmental disturbances. Leveraging disturbance quantification and constraint transformation, we develop a stochastic fail-operational barrier based on the control barrier function (CBF). With this development, the uncertain EV is able to converge asymptotically from an unsafe state to a defined safe state with probabilistic stability. Subsequently, the stochastic fail-operational barrier is integrated into an efficient fail-operational controller based on quadratic programming (QP). This controller is tailored for the EV operating under control constraints in the presence of environmental disturbances, with both safety and efficiency objectives taken into consideration. We validate the proposed framework in connected cruise control (CCC) tasks, where SVs perform aggressive driving maneuvers. The simulation results demonstrate that our method empowers the EV to swiftly return to a safe state while upholding task efficiency in real time, even under time-varying environmental disturbances.
Paper Structure (14 sections, 2 theorems, 31 equations, 8 figures, 2 tables)

This paper contains 14 sections, 2 theorems, 31 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and problem statement
  3. Methodology
  4. Gaussian Process
  5. Incremental Learning for Enhanced GPs
  6. Stochastic Fail-Operational Barrier
  7. Real-Time Fail- Operational Controller
  8. Illustrative Example
  9. Vehicle Model
  10. Simulation Setup
  11. Results
  12. Real-Time Performance
  13. Task Performance
  14. Conclusions

Key Result

Lemma 1

(srinivas2012informationumlauft2018uncertainty) Let $\varsigma\in(0,\ 1)$ and the measurement noise $\upsilon_j$ is uniformly bounded by $\sigma_{\text{noise}}$. Then a probability $Pr$ holds where $\beta = [\beta_1, \beta_2, \cdots, \beta_n]$, $\beta_j=(2\|{\delta_j\|^2}_{k_j}+300\gamma_j ln^3(\frac{N+1}{\upsilon_j}))^{-2}$; $\gamma_j$ is the maximum information gain obtained about the GP prior

Figures (8)

  • Figure 1: The stochastic fail-operational barrier module enables the red EV to recover from an unsafe state (top subfigure) to a safe state (bottom subfigure).
  • Figure 2: The evolution of solving time of the optimization problem (\ref{['eq:opt_1']})-(\ref{['eq:opt_5']}) with two unsafe initial states. (a) Initial state $x_0 = {[ 25 \,\text{m}, 18\,\text{m/s}]}^T$, (b) Initial state $x_0 = {[ 110 \,\text{m}, 18\,\text{m/s}]}^T$.
  • Figure 3: The evolution of incremental learning and inference time with the initial state $x_0 = {[ 110 \,\text{m}, 18\,\text{m/s}]}^T$ .
  • Figure 4: The evolution of incremental learning and inference time with the initial state $x_0 = {[ 25 \,\text{m}, 18\,\text{m/s}]}^T$.
  • Figure 5: The evolution of the CBF value for the EV with two different unsafe initial states. (a) $x_0 = {[ 25 \,\text{m}, 18\,\text{m/s}]}^T$, (b) $x_0 = {[ 110 \,\text{m}, 18\,\text{m/s}]}^T$. The negative CBF can quickly converge to positive values and remain positive throughout the CCC task in the presence of environmental disturbances.
  • ...and 3 more figures

Theorems & Definitions (8)

  • Remark 1
  • Definition 1
  • Definition 2
  • Lemma 1
  • Lemma 2
  • proof
  • Remark 2
  • Remark 3