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Autonomous Driving With Perception Uncertainties: Deep-Ensemble Based Adaptive Cruise Control

Xiao Li, H. Eric Tseng, Anouck Girard, Ilya Kolmanovsky

TL;DR

An Ensemble of DNN regressors (Deep Ensemble) to provide predictions with quantified uncertainties in the context of Adaptive Cruise Control (ACC), the Deep Ensemble estimates the distance headway to the lead vehicle from RGB images, allowing the downstream controller to account for uncertainty.

Abstract

Autonomous driving depends on perception systems to understand the environment and to inform downstream decision-making. While advanced perception systems utilizing black-box Deep Neural Networks (DNNs) demonstrate human-like comprehension, their unpredictable behavior and lack of interpretability may hinder their deployment in safety critical scenarios. In this paper, we develop an Ensemble of DNN regressors (Deep Ensemble) that generates predictions with quantification of prediction uncertainties. In the scenario of Adaptive Cruise Control (ACC), we employ the Deep Ensemble to estimate distance headway to the lead vehicle from RGB images and enable the downstream controller to account for the estimation uncertainty. We develop an adaptive cruise controller that utilizes Stochastic Model Predictive Control (MPC) with chance constraints to provide a probabilistic safety guarantee. We evaluate our ACC algorithm using a high-fidelity traffic simulator and a real-world traffic dataset and demonstrate the ability of the proposed approach to effect speed tracking and car following while maintaining a safe distance headway. The out-of-distribution scenarios are also examined.

Autonomous Driving With Perception Uncertainties: Deep-Ensemble Based Adaptive Cruise Control

TL;DR

An Ensemble of DNN regressors (Deep Ensemble) to provide predictions with quantified uncertainties in the context of Adaptive Cruise Control (ACC), the Deep Ensemble estimates the distance headway to the lead vehicle from RGB images, allowing the downstream controller to account for uncertainty.

Abstract

Autonomous driving depends on perception systems to understand the environment and to inform downstream decision-making. While advanced perception systems utilizing black-box Deep Neural Networks (DNNs) demonstrate human-like comprehension, their unpredictable behavior and lack of interpretability may hinder their deployment in safety critical scenarios. In this paper, we develop an Ensemble of DNN regressors (Deep Ensemble) that generates predictions with quantification of prediction uncertainties. In the scenario of Adaptive Cruise Control (ACC), we employ the Deep Ensemble to estimate distance headway to the lead vehicle from RGB images and enable the downstream controller to account for the estimation uncertainty. We develop an adaptive cruise controller that utilizes Stochastic Model Predictive Control (MPC) with chance constraints to provide a probabilistic safety guarantee. We evaluate our ACC algorithm using a high-fidelity traffic simulator and a real-world traffic dataset and demonstrate the ability of the proposed approach to effect speed tracking and car following while maintaining a safe distance headway. The out-of-distribution scenarios are also examined.
Paper Structure (11 sections, 3 theorems, 17 equations, 9 figures)

This paper contains 11 sections, 3 theorems, 17 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Method
  4. Deep Neural Network Ensemble
  5. Adaptive Cruise Control
  6. Case Studies
  7. Deep Ensemble for Distance Headway Estimation
  8. Adaptive Cruise Control in Carla Simulation
  9. Adaptive Cruise Control with Real-World Trajectories
  10. ACC in Out-Of-Distribution Scenarios
  11. Conclusion

Key Result

Proposition 1

Given a training trajectory $\mathcal{D} = (d_k, I_{k,l},I_{k,r})_{k=1}^{M}$, assuming each data point $(d_k, I_{k,l},I_{k,r})\in D$ is independently collected, and the error is zero-mean Gaussian, i.e., $e(I_{k,l},I_{k,r})\sim\mathcal{N}\left(0, \sigma_i^2(I_{k,l},I_{k,r})\right)$, the optimal para and it is equivalent to the following optimization,

Figures (9)

  • Figure 1: A schematic diagram of the Adaptive Cruise Control (ACC) scenario: The follower (ego vehicle) keeps a safe distance headway to the lead vehicle in the front leveraging camera sensors.
  • Figure 2: Schematic diagrams of adaptive cruise controller design. (a) Each DNN differs in the CNN architecture of the image encoder, and estimates the distribution of the distance headway from input RGB images. (b) An ensemble of DNNs, with a heterogeneous set of CNN architectures as image encoders, collectively estimates the distance headway as a Gaussian mixture; then a Stochastic MPC uses estimated headway mean and variance to compute the acceleration/deceleration command for the ego vehicle.
  • Figure 3: Distance headway estimates $p_k$ (blue lines) with uncertainty quantification using 1$\sigma$, 2$\sigma$, and 3$\sigma$ intervals (purple bands) versus the actual $d_k$ (red lines). (a) The results, $p_i(I_{k,l},I_{k,r}), \sigma_i^2(I_{k,l},I_{k,r})$, $i=1,\dots,6$, of each DNN visualized in overlap. (b) Deep Ensemble estimation results. A demonstration video is available in https://bit.ly/3TCM5lC.
  • Figure 4: Histogram of vehicle driving statistics in High-D dataset: (a) longitudinal acceleration/deceleration (y-axis in log scale); (b) distance headway and (c) speed difference between lead and follower vehicles; (d) 2D histogram combining statistics in (b) and (c).
  • Figure 5: ACC simulation example in which the ego vehicle first follows the lead vehicle given its speed smaller than $v_s=20\;\rm m/s$, then, enters the speed-tracking mode after the step change in the lead vehicle speed: (a) distance headway estimation from the Deep Ensemble; (b) ACC algorithm regulating the ego out of the unsafe region; (c) speed trajectories of the lead and ego vehicles; (d) acceleration commands. The animation is available in https://bit.ly/3TFgxLZ.
  • ...and 4 more figures

Theorems & Definitions (6)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof