Mean Field Game-Based Interactive Trajectory Planning Using Physics-Inspired Unified Potential Fields

2025-09-09

AI Summary

Addressing the challenge of jointly ensuring safety, efficiency, and scalability in multi-vehicle interactive trajectory planning for autonomous driving—while avoiding high computational overhead or reliance on external safety modules—this paper proposes a style-aware unified potential field framework. The method integrates driving-style-dependent reward and risk potential fields within a mean-field game formulation; leveraging variational principles, it analytically derives Nash equilibrium policies that naturally accommodate heterogeneous behaviors (e.g., conservative, aggressive, cooperative). By modeling vehicle dynamics via physics-informed stochastic differential equations and employing an exponentially convergent equilibrium solver, the framework guarantees collision avoidance without auxiliary safety layers. Evaluated in lane-changing and overtaking scenarios, the generated trajectories exhibit superior smoothness, efficiency, and adherence to safety margins, while demonstrating significantly improved adaptability and computational efficiency compared to conventional optimization- and game-theoretic approaches.

Technology Category

• Humans and AI: Human-Aware Planning and Behavior Prediction
• Multiagent Systems: Multiagent Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Interactive trajectory planning in autonomous driving must balance safety, efficiency, and scalability under heterogeneous driving behaviors. Existing methods often face high computational cost or rely on external safety critics. To address this, we propose an Interaction-Enriched Unified Potential Field (IUPF) framework that fuses style-dependent benefit and risk fields through a physics-inspired variational model, grounded in mean field game theory. The approach captures conservative, aggressive, and cooperative behaviors without additional safety modules, and employs stochastic differential equations to guarantee Nash equilibrium with exponential convergence. Simulations on lane changing and overtaking scenarios show that IUPF ensures safe distances, generates smooth and efficient trajectories, and outperforms traditional optimization and game-theoretic baselines in both adaptability and computational efficiency.

Problem

• Balancing safety, efficiency, scalability in autonomous trajectory planning
• Addressing high computational costs and external safety dependencies
• Modeling heterogeneous driving behaviors without additional safety modules

Innovation

• Physics-inspired unified potential fields
• Stochastic differential equations for Nash equilibrium
• Style-dependent benefit and risk fusion