[Paper Review] Potential Game-Based Decision-Making for Autonomous Driving

Mushuang Liu, Ilya Kolmanovsky+4 more|arXiv (Cornell University)|Jan 16, 2022

Energy, Environment, and Transportation Policies4 citations

TL;DR

This paper proposes finite and continuous potential game-based frameworks for autonomous driving decision-making, integrating receding horizon optimization and cost function shaping to ensure theoretical guarantees of pure-strategy Nash equilibrium existence and convergence. The approach demonstrates superior robustness against non-safety-conscious surrounding vehicles compared to reinforcement learning and control barrier functions, with zero collisions in all tested scenarios including intersection-crossing and lane-changing.

ABSTRACT

Decision-making for autonomous driving is challenging, considering the complex interactions among multiple traffic agents (e.g., autonomous vehicles (AVs), human drivers, and pedestrians) and the computational load needed to evaluate these interactions. This paper develops two general potential game based frameworks, namely, finite and continuous potential games, for decision-making in autonomous driving. The two frameworks account for the AVs' two types of action spaces, i.e., finite and continuous action spaces, respectively. We show that the developed frameworks provide theoretical guarantees, including 1) existence of pure-strategy Nash equilibria, 2) convergence of the Nash equilibrium (NE) seeking algorithms, and 3) global optimality of the derived NE (in the sense that both self- and team- interests are optimized). In addition, we provide cost function shaping approaches to constructing multi-agent potential games in autonomous driving. Moreover, two solution algorithms, including self-play dynamics (e.g., best response dynamics) and potential function optimization, are developed for each game. The developed frameworks are then applied to two different traffic scenarios, including intersection-crossing and lane-changing in highways. Statistical comparative studies, including 1) finite potential game vs. continuous potential game, and 2) best response dynamics vs. potential function optimization, are conducted to compare the performances of different solution algorithms. It is shown that both developed frameworks are practical (i.e., computationally efficient), reliable (i.e., resulting in satisfying driving performances in diverse scenarios and situations), and robust (i.e., resulting in satisfying driving performances against uncertain behaviors of the surrounding vehicles) for real-time decision-making in autonomous driving.

Motivation & Objective

• Address the challenge of multi-agent decision-making in autonomous driving under complex, real-time interactions among AVs, human-driven vehicles, and pedestrians.
• Overcome limitations in existing game-theoretic approaches, such as lack of pure-strategy Nash equilibrium existence, convergence issues, and poor scalability.
• Develop theoretically grounded frameworks that ensure existence and convergence to Nash equilibria while maintaining computational feasibility for real-time implementation.
• Enhance robustness against safety-agnostic surrounding vehicles, a critical gap in reinforcement learning and control barrier function-based methods.
• Provide practical formulations for intersection-crossing and lane-changing scenarios, validated through comprehensive statistical comparisons.

Proposed method

• Formulate finite and continuous potential games for autonomous vehicle decision-making, tailored to discrete and continuous action spaces respectively.
• Introduce a cost function shaping approach that aligns agents' objectives with common driving goals (e.g., safety, efficiency) while ensuring the game is a potential game.
• Integrate receding horizon optimization with potential game frameworks to enable real-time, dynamic decision-making.
• Design scalable Nash equilibrium seeking algorithms based on best response dynamics and potential function optimization.
• Implement and compare the frameworks using numerical simulations in intersection-crossing and lane-changing scenarios with diverse surrounding vehicle strategies.
• Use predictor-corrector collision avoidance (PCCA) as a variant of CBF for fair comparison, with bounded action space constraints.

Experimental results

Research questions

• RQ1 Can potential game frameworks be effectively applied to autonomous driving decision-making with both finite and continuous action spaces?
• RQ2 How do the proposed frameworks ensure the existence of pure-strategy Nash equilibria and convergence of equilibrium-seeking algorithms?
• RQ3 What is the robustness of the potential game approach against non-safety-conscious surrounding vehicles compared to reinforcement learning and control barrier functions?
• RQ4 How does computational efficiency of the potential game approach compare to RL and CBF-based methods in real-time driving scenarios?
• RQ5 Can the cost function shaping method generate safe, efficient, and cooperative behaviors that reflect common driving objectives?

Key findings

• The finite and continuous potential game frameworks guarantee the existence of pure-strategy Nash equilibria and convergence of equilibrium-seeking algorithms.
• In intersection-crossing scenarios, the potential game approach achieved zero collisions (0/5000) even when surrounding vehicles followed constant speed strategies, outperforming both RL (2403/5000 collisions) and CBF (2229/5000 collisions).
• The potential game approach maintained an average ego speed of 3.78 m/s under NE strategies and 3.05 m/s under constant speed strategies, demonstrating balanced performance and safety.
• The average computational time for the potential game approach was 0.05 s (max 0.10 s), well within the 0.5 s sampling time, confirming real-time feasibility.
• The potential game approach achieved the highest robustness, with no collisions under both NE and constant speed strategies, unlike RL and CBF, which failed under non-safety-conscious behaviors.
• Statistical comparisons confirmed that potential game-based decision-making is more computationally efficient and robust than RL and CBF, especially in unpredictable traffic environments.