Unified Static–Dynamic Risk Modeling and Mean-Field-Game-Based Trajectory Optimization for Autonomous Racing

Autonomous racing requires fast, anticipatory, and interaction-aware trajectory planning, where the ego vehicle must interpret complex track geometries while reasoning about the future behavior of multiple competitive agents. Existing approaches typically treat static and dynamic obstacles separately or rely heavily on global perception, limiting their robustness and scalability in realistic multi-agent racing environments. This work presents a unified prediction–planning framework that jointly addresses static and dynamic challenges through three key mechanisms. First, a grid-based track discretization and static risk field are constructed to model proximity to boundaries and fixed obstacles through smooth spatial potentials, enabling efficient safety-aware path shaping. Second, an interaction-aware prediction module based on Mean Field Games (MFG) captures the collective, density-driven behavior of surrounding vehicles, providing anticipatory and rational multi-agent motion forecasts. Third, these components are integrated into a hierarchical trajectory optimizer using piecewise-jerk quadratic programming (PJPO) for path and speed planning, followed by spline smoothing to ensure continuity and dynamic feasibility. Extensive evaluations across nine racetrack segments and diverse dynamic obstacle configurations demonstrate that the proposed planner achieves superior collision avoidance, smoother trajectories, and improved lap times compared to MPC, RRT*, and A*+Profiling baselines. The results confirm the framework’s strong generalization to both static and multi-agent dynamic environments, highlighting its suitability for real-time, high-speed autonomous racing.