SGTP: Sampling-based Game-Theoretic Planning for Real-Time Multi-Vehicle Autonomous Racing

Autonomous racing demands planning algorithms that balance vehicle dynamics at the limits of handling with strategic decision-making in competitive multi-agent scenarios. Game theory provides a mathematical framework for modeling these interactions, enabling interactive trajectory planning and strategic behaviors, such as blocking. However, directly solving full dynamic games online is computationally prohibitive and challenging to integrate into robust, high-frequency autonomous software stacks. This paper proposes a hybrid architecture that integrates game-theoretic reasoning into a sampling-based motion planner, combining strategic interactions with robust trajectory generation. Building upon an $α$-potential game formulation, we utilize an offline-learned potential function to capture multi-agent interactions. During online operation, a gradient-based optimization dynamically refines interaction parameters to generate an \textit{Interaction Reference Path}. This path serves as a dynamic cost bias within a high-frequency sampling planner. We evaluate our approach in a high-fidelity simulation environment on the Yas Marina Circuit. Qualitative and quantitative results demonstrate that our approach successfully induces defensive behaviors like blocking without carrying the computational burden of full dynamic game solvers.

Autonomous racing serves as a compelling testbed for advancing autonomous vehicle systems. The 1/10-scale F1Tenth platform is widely adopted for education and research, with annual competitions held worldwide. Yet, leading solutions in these tournaments remain dominated by rule-based approaches. While learning-based methods have been proposed, they focus primarily on single-vehicle settings, leaving challenging multi-vehicle interactions largely unexplored. To address this gap, we introduce End2Race, an end-to-end learning framework designed for head-to-head autonomous racing. Using this framework, we develop a computationally efficient policy network that achieves an inference latency below 1 ms on an F1Tenth onboard computer. Extensive evaluations show that the policy generalizes to both novel tracks and unseen opponent behaviors, demonstrating high racing speeds, robust safety, and adaptive overtaking maneuvers. These results substantially outperform both prior learning-based methods and rule-based baselines. Codebase is available at https://github.com/michigan-traffic-lab/End2Race.

Autonomous systems have achieved superhuman performance in isolation or simulation, yet they remain brittle in shared, dynamic real-world spaces. This failure stems from the dominant single-agent paradigm for physical applications, where other actors are ignored or treated as environmental noise, preventing effective coordination. Here we show that multi-agent reinforcement learning provides the essential safety scaffolding required for real-world interaction. Using high-speed quadrotor racing as a high-stakes testbed, we train agents to navigate complex aerodynamic interactions and strategic maneuvering with a variable number of racers. Through league-based self-play, agents evolve sophisticated anticipatory behaviors, including proactive collision avoidance, overtaking, and handling multi-agent physical interactions, including aerodynamic downwash. Our agents outperform a champion-level human pilot in multi-player races at speeds exceeding 22 m/s, while simultaneously reducing collision rates by 50 % compared to state-of-the-art single-agent baselines. Crucially, training with diverse artificial agents enables zero-shot generalization to safer human interaction. These results suggest that the path to robust robotic co-existence lies not in isolated safety constraints, but in the rigorous demands of multi-agent interaction. Multimedia materials are available at: https://rpg.ifi.uzh.ch/marl