Regulation-Aware Game-Theoretic Motion Planning for Autonomous Racing

This paper presents a regulation-aware motion planning framework for autonomous racing scenarios. Each agent solves a Regulation-Compliant Model Predictive Control problem, where racing rules - such as right-of-way and collision avoidance responsibilities - are encoded using Mixed Logical Dynamical constraints. We formalize the interaction between vehicles as a Generalized Nash Equilibrium Problem (GNEP) and approximate its solution using an Iterative Best Response scheme. Building on this, we introduce the Regulation-Aware Game-Theoretic Planner (RA-GTP), in which the attacker reasons over the defender's regulation-constrained behavior. This game-theoretic layer enables the generation of overtaking strategies that are both safe and non-conservative. Simulation results demonstrate that the RA-GTP outperforms baseline methods that assume non-interacting or rule-agnostic opponent models, leading to more effective maneuvers while consistently maintaining compliance with racing regulations.