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Courteous MPC for Autonomous Driving with CBF-inspired Risk Assessment

Yanze Zhang, Yiwei Lyu, Sude E. Demir, Xingyu Zhou, Yupeng Yang, Junmin Wang, Wenhao Luo

TL;DR

The paper tackles safe and courteous autonomous driving in mixed traffic by extending a Control Barrier Functions (CBF)-inspired risk framework to handle noisy position and velocity observations, producing an ego-risk map to guide decisions. It develops a CVaR-based risk measure under uncertainty, constructs an ego-perceived risk map for highway scenarios, and embeds these into a Courteous Model Predictive Control (MPC) that minimizes a combined cost and risk term while enforcing probabilistic safety guarantees. The approach is validated through theoretical analysis and simulations with IDM vehicles and the NGSIM US-101 dataset, showing earlier yet safer overtaking, larger spacing around surrounding vehicles, and robust performance in realistic traffic. The work provides a principled, probabilistic safety guarantee and a practical decision-making tool that promotes courteous interactions with human drivers in autonomous driving systems.

Abstract

With more autonomous vehicles (AVs) sharing roadways with human-driven vehicles (HVs), ensuring safe and courteous maneuvers that respect HVs' behavior becomes increasingly important. To promote both safety and courtesy in AV's behavior, an extension of Control Barrier Functions (CBFs)-inspired risk evaluation framework is proposed in this paper by considering both noisy observed positions and velocities of surrounding vehicles. The perceived risk by the ego vehicle can be visualized as a risk map that reflects the understanding of the surrounding environment and thus shows the potential for facilitating safe and courteous driving. By incorporating the risk evaluation framework into the Model Predictive Control (MPC) scheme, we propose a Courteous MPC for ego AV to generate courteous behaviors that 1) reduce the overall risk imposed on other vehicles and 2) respect the hard safety constraints and the original objective for efficiency. We demonstrate the performance of the proposed Courteous MPC via theoretical analysis and simulation experiments.

Courteous MPC for Autonomous Driving with CBF-inspired Risk Assessment

TL;DR

The paper tackles safe and courteous autonomous driving in mixed traffic by extending a Control Barrier Functions (CBF)-inspired risk framework to handle noisy position and velocity observations, producing an ego-risk map to guide decisions. It develops a CVaR-based risk measure under uncertainty, constructs an ego-perceived risk map for highway scenarios, and embeds these into a Courteous Model Predictive Control (MPC) that minimizes a combined cost and risk term while enforcing probabilistic safety guarantees. The approach is validated through theoretical analysis and simulations with IDM vehicles and the NGSIM US-101 dataset, showing earlier yet safer overtaking, larger spacing around surrounding vehicles, and robust performance in realistic traffic. The work provides a principled, probabilistic safety guarantee and a practical decision-making tool that promotes courteous interactions with human drivers in autonomous driving systems.

Abstract

With more autonomous vehicles (AVs) sharing roadways with human-driven vehicles (HVs), ensuring safe and courteous maneuvers that respect HVs' behavior becomes increasingly important. To promote both safety and courtesy in AV's behavior, an extension of Control Barrier Functions (CBFs)-inspired risk evaluation framework is proposed in this paper by considering both noisy observed positions and velocities of surrounding vehicles. The perceived risk by the ego vehicle can be visualized as a risk map that reflects the understanding of the surrounding environment and thus shows the potential for facilitating safe and courteous driving. By incorporating the risk evaluation framework into the Model Predictive Control (MPC) scheme, we propose a Courteous MPC for ego AV to generate courteous behaviors that 1) reduce the overall risk imposed on other vehicles and 2) respect the hard safety constraints and the original objective for efficiency. We demonstrate the performance of the proposed Courteous MPC via theoretical analysis and simulation experiments.
Paper Structure (15 sections, 3 theorems, 16 equations, 7 figures, 1 table)

This paper contains 15 sections, 3 theorems, 16 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Control Barrier Functions
  4. Sample-Data Control Barrier Functions
  5. Kinematic Vehicle Model
  6. Problem Statement
  7. Methods
  8. Control Barrier Functions-inspired Conditional Value at Risk under Noisy Observations
  9. Ego-perceived Risk Map for Highway Decision Making
  10. Courteous Model Predictive Control
  11. Experiments and Discussion
  12. Parameter Analysis
  13. Simulation Experiment on IDM Vehicles
  14. Simulation Experiment on NGSIM Dataset
  15. Conclusions

Key Result

Lemma 1

[Summarized from ames2019control] Given a dynamical system affine defined in Eq. eq:Affine and a safe set $\mathcal{H}$ as the 0-super level set of a continuously differentiable function $h: \mathbb{R}^d \mapsto \mathbb{R}$, the function $h$ is called a control barrier function, if there exists an e where $L_f h(x) = \nabla h^{T}(x) f(x)$ and $L_g h(x) = \nabla h^{T}(x) g(x)$, respectively.

Figures (7)

  • Figure 1: On-ramp merging scenario where the human-driven vehicle (blue) is trying to merge onto the main lane occupied by the ego vehicle (red). To accommodate the human-driven vehicle (HV) in a courteous manner, the ego vehicle could consider lane-change behavior that makes space for the HV without sacrificing much on safety and efficiency.
  • Figure 2: Running example for visualizing the CBF-inspired risk map, demonstrating how risk is aggregated when considering various velocity configurations' influence on the ego-perceived risk map using Eq. \ref{['eq:risk_evaluation']}. The red vehicle represents the ego vehicle, and the blue one is the observed neighboring vehicle. The area within the dashed blue contour indicates the region where the evaluated risk is larger than $0$.
  • Figure 3: Influence of $P_{\mathrm{S}}$ on the minimum distance between the ego vehicle and neighboring IDM vehicles.
  • Figure 4: Performance comparison of the simulation experiments in the highway-env environment, depicting two different examples of overtaking behavior for each of three methods. Fig. \ref{['fig:batchmpc1']} and Fig. \ref{['fig:batchmpc2']} depict the results for Batch MPC, Fig. \ref{['fig:risk-aware mpc1']} and Fig. \ref{['fig:risk-aware mpc2']} for Risk-aware MPC, and Fig. \ref{['fig:courteous mpc1']} and Fig. \ref{['fig:courteous mpc2']} for Courteous MPC. The red ellipse in each figure highlights the ego vehicle and its overtaking target. And the value shown behind every vehicle is its speed.
  • Figure 5: Minimum distance between the ego vehicle and the neighboring IDM vehicles over time.
  • ...and 2 more figures

Theorems & Definitions (8)

  • Lemma 1
  • Lemma 2
  • Remark 1
  • Theorem 3
  • proof
  • Remark 2
  • Remark 3
  • Remark 4