带同伦类约束的战术博弈论决策
Tactical Game-theoretic Decision-making with Homotopy Class Constraints
AI总结：
本研究针对城市环境博弈论运动规划问题，提出带同伦类约束的战术决策框架，将驾驶建模为广义纳什均衡问题，通过混合整数方法结合同伦类划分解空间，在rounD数据集场景下实现全局最优求解且计算时间平均降低78%。
摘要：
我们提出了一种适用于城市环境下博弈论运动规划的、具备同伦感知能力的战术决策框架。我们将城市驾驶建模为广义纳什均衡问题，并采用混合整数方法来处理运动规划的组合特性。更具体地说，通过利用同伦类，我们将高维解空间划分为有限的、定义明确的子区域。每个子区域（同伦类）对应一个高层战术决策，例如智能体两两之间的通行顺序。所提出的公式通过求解一个混合整数二次规划，能够以计算上可处理的方式找到全局最优纳什均衡。每个同伦决策由一个二元变量表示，该变量会激活不同组的线性避碰约束。这种额外的同伦约束能够以更高效的方式找到解（在环岛场景中平均速度提升5倍）。我们在取自rounD数据集的场景上通过实验验证了所提出的方法。采用滚动时域方式的仿真测试表明，该框架能够获得全局最优解，同时相较于无同伦约束的实现方案，计算时间平均减少78%。
英文摘要：
We propose a tactical homotopy-aware decision-making framework for game-theoretic motion planning in urban environments. We model urban driving as a generalized Nash equilibrium problem and employ a mixed-integer approach to tame the combinatorial aspect of motion planning. More specifically, by utilizing homotopy classes, we partition the high-dimensional solution space into finite, well-defined subregions. Each subregion (homotopy) corresponds to a high-level tactical decision, such as the passing order between pairs of players. The proposed formulation allows to find global optimal Nash equilibria in a computationally tractable manner by solving a mixed-integer quadratic program. Each homotopy decision is represented by a binary variable that activates different sets of linear collision avoidance constraints. This extra homotopic constraint allows to find solutions in a more efficient way (on a roundabout scenario on average 5-times faster). We experimentally validate the proposed approach on scenarios taken from the rounD dataset. Simulation-based testing in receding horizon fashion demonstrates the capability of the framework in achieving globally optimal solutions while yielding a 78% average decrease in the computational time with respect to an implementation without the homotopic constraints.
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