Physics-Informed Reinforcement Learning of Spatial Density Velocity Potentials for Map-Free Racing

Road traffic accidents are a leading cause of fatalities worldwide. In the US, human error causes 94% of crashes, resulting in excess of 7,000 pedestrian fatalities and $500 billion in costs annually. Autonomous Vehicles (AVs) with emergency collision avoidance systems that operate at the limits of vehicle dynamics at a high frequency, a dual constraint of nonlinear kinodynamic accuracy and computational efficiency, further enhance safety benefits during adverse weather and cybersecurity breaches, and to evade dangerous human driving when AVs and human drivers share roads. This paper parameterizes a Deep Reinforcement Learning (DRL) collision avoidance policy Out-Of-Distribution (OOD) utilizing race car overtaking, without explicit geometric mimicry reference trajectory guidance, in simulation, with a physics-informed, simulator exploit-aware reward to encode nonlinear vehicle kinodynamics. Two policies are evaluated, a default uni-direction and a reversed heading variant that navigates in the opposite direction to other cars, which both consistently outperform a Model Predictive Control and Artificial Potential Function (MPC-APF) baseline, with zero-shot transfer to proportionally scaled hardware, across three intersection collision scenarios, at 31x fewer Floating Point Operations (FLOPS) and 64x lower inference latency. The reversed heading policy outperforms the default racing overtaking policy in head-to-head collisions by 30% and the baseline by 50%, and matches the former in side collisions, where both DRL policies evade 10% greater than numerical optimal control.

Reinforcement learning has shown significant potential for autonomous racing, but it still faces challenges such as training instability, inefficient exploration, and unsafe action outputs in high-dynamic racing scenarios. This paper proposes a Trajectory guidance and Dynamics constraints Reinforcement Learning (TraD-RL) framework for autonomous racing. The proposed method incorporates expert prior knowledge into policy learning through Minimum Curvature Racing Line (MCRL) guidance, explicit vehicle dynamics constraints, and two-stage curriculum learning. MCRL provides global path and velocity references through observation augmentation and reward shaping, thereby improving exploration efficiency and racing performance. Yaw rate and sideslip angle constraints are introduced to characterize the vehicle dynamic safe operating envelope, and the corresponding stability costs are incorporated into policy optimization through Lagrangian relaxation. Moreover, the two-stage curriculum learning strategy enables a progressive transition from stable trajectory following to high-speed performance exploration. Experiments on two racetracks demonstrate that TraD-RL improves racing performance while maintaining a favorable balance between speed and dynamic stability. Further analyses of ablation, sensitivity, and robustness validate the effectiveness and stability of the proposed framework.

Accurate modeling of nonlinear vehicle dynamics is essential for high-speed autonomous racing, where controllers operate at the handling limits. Model-based methods are interpretable but rely on simplifying assumptions, while purely learned models capture nonlinearities yet often lack physical consistency, generalization, and adaptability to changing operating conditions. This paper presents DynSSM, a physics-aware state-space memory framework that combines learned temporal representations with a structured vehicle dynamics model. The proposed approach integrates state-space sequence modeling and recurrent encoders to capture long- and short-term dynamic behavior. It simultaneously adapts tire and vehicle-dynamics parameters within bounded ranges to preserve physical plausibility. A residual correction mechanism compensates for remaining unmodeled dynamics while preserving the underlying physics-based structure. DynSSM is evaluated on both simulated small-scale racing data and real-world full-scale autonomous Indy racecar data. When evaluated on an unseen real-world track, DynSSM reduces one-step prediction RMSE by up to $27.2\%$ in longitudinal velocity, $73.9\%$ in lateral velocity, and $88.8\%$ in yaw rate compared with the state-of-the-art (\sota{}) baselines. Component-wise ablation studies demonstrate the importance of temporal memory, parameter adaptation, and residual correction for predictive performance and robustness. Further, closed-loop simulations using nonlinear model predictive control demonstrate that DynSSM remains feasible across the evaluated tracks and achieves up to a 13.2% reduction in one-lap completion time compared with \sota{} baselines. These results indicate that combining temporal memory, bounded physics-guided parameter adaptation, and residual correction provides an accurate, interpretable, and control-ready dynamics model for autonomous racing.