Multi-vehicle autonomous driving couples strategic interaction with hybrid (discrete-continuous) maneuver planning under shared safety constraints. We introduce IBR-GCS, an Iterative Best Response (IBR) planning approach based on the Graphs of Convex Sets (GCS) framework that models highway driving as a generalized noncooperative game. IBR-GCS integrates combinatorial maneuver reasoning, trajectory planning, and game-theoretic interaction within a unified framework. The key novelty is a vehicle-specific, strategy-dependent GCS construction. Specifically, at each best-response update, each vehicle builds its own graph conditioned on the current strategies of the other vehicles, with vertices representing lane-specific, time-varying, convex, collision-free regions and edges encoding dynamically feasible transitions. This yields a shortest-path problem in GCS for each best-response step, which admits an efficient convex relaxation that can be solved using convex optimization tools without exhaustive discrete tree search. We then apply an iterative best-response scheme in which vehicles update their trajectories sequentially and provide conditions under which the resulting inexact updates converge to an approximate generalized Nash equilibrium. Simulation results across multi-lane, multi-vehicle scenarios demonstrate that IBR-GCS produces safe trajectories and strategically consistent interactive behaviors.

翻译：多车自动驾驶将策略性交互与共享安全约束下的混合（离散-连续）机动规划相耦合。本文提出IBR-GCS——一种基于凸集图框架的迭代最优响应规划方法，该方法将高速公路驾驶建模为广义非合作博弈。IBR-GCS在统一框架中集成了组合机动推理、轨迹规划与博弈论交互。其核心创新在于构建了依赖车辆特定策略的凸集图结构：在每次最优响应更新时，每辆车根据其他车辆的当前策略构建专属图结构，其中顶点表示车道特定、时变、凸且无碰撞的区域，边编码动态可行的状态转移。这使得每个最优响应步骤可转化为凸集图中的最短路径问题，该问题存在高效凸松弛形式，可直接使用凸优化工具求解而无需穷举离散树搜索。随后采用迭代最优响应策略，使车辆顺序更新轨迹，并给出非精确更新收敛至近似广义纳什均衡的条件。在多车道、多车辆的仿真场景中，IBR-GCS能够生成安全轨迹及策略一致的交互行为。