In interactive multi-agent settings, decision-making and planning are challenging mainly due to the agents' interconnected objectives. Dynamic game theory offers a formal framework for analyzing such intricacies. Yet, solving constrained dynamic games and determining the interaction outcome in the form of generalized Nash Equilibria (GNE) pose computational challenges due to the need for solving constrained coupled optimal control problems. In this paper, we address this challenge by proposing to leverage the special structure of many real-world multi-agent interactions. More specifically, our key idea is to leverage constrained dynamic potential games, which are games for which GNE can be found by solving a single constrained optimal control problem associated with minimizing the potential function. We argue that constrained dynamic potential games can effectively facilitate interactive decision-making in many multi-agent interactions. We will identify structures in realistic multi-agent interactive scenarios that can be transformed into weighted constrained potential dynamic games (WCPDGs). We will show that the GNE of the resulting WCPDG can be obtained by solving a single constrained optimal control problem. We will demonstrate the effectiveness of the proposed method through various simulation studies and show that we achieve significant improvements in solve time compared to state-of-the-art game solvers. We further provide experimental validation of our proposed method in a navigation setup involving two quadrotors carrying a rigid object while avoiding collisions with two humans.

翻译：在交互式多智能体环境中，决策与规划面临的主要挑战源于智能体间相互关联的目标。动态博弈理论为分析此类复杂交互提供了形式化框架。然而，求解约束动态博弈并以广义纳什均衡（GNE）形式确定交互结果，由于需要求解约束耦合最优控制问题而存在计算挑战。本文通过利用现实世界多智能体交互的特殊结构来应对这一挑战。具体而言，我们的核心思想是借助约束动态势博弈——这类博弈的GNE可通过求解与最小化势函数相关的单个约束最优控制问题获得。我们认为约束动态势博弈能有效促进多智能体交互中的决策过程。我们将识别现实多智能体交互场景中可转化为加权约束势动态博弈（WCPDG）的结构特征，并证明所得WCPDG的GNE可通过求解单个约束最优控制问题获得。通过多项仿真研究，我们将验证所提方法的有效性，并证明相较于最先进的博弈求解器，本方法在求解时间上取得显著提升。我们进一步在双四旋翼无人机协同搬运刚性物体并规避两名行人的导航场景中，对所提方法进行了实验验证。