Although dynamic games provide a rich paradigm for modeling agents' interactions, solving these games for real-world applications is often challenging. Many real-world interactive settings involve general nonlinear state and input constraints that couple agents' decisions with one another. In this work, we develop an efficient and fast planner for interactive trajectory optimization in constrained setups using a constrained game-theoretical framework. Our key insight is to leverage the special structure of agents' objective and constraint functions that are common in multi-agent interactions for fast and reliable planning. More precisely, we identify the structure of agents' cost and constraint functions under which the resulting dynamic game is an instance of a constrained dynamic potential game. Constrained dynamic potential games are a class of games for which instead of solving a set of coupled constrained optimal control problems, a constrained Nash equilibrium, i.e. a Generalized Nash equilibrium, can be found by solving a single constrained optimal control problem. This simplifies constrained interactive trajectory optimization significantly. We compare the performance of our method in a navigation setup involving four planar agents and show that our method is on average 20 times faster than the state-of-the-art. 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：尽管动态博弈为建模智能体交互提供了丰富的范式，但在实际应用中求解这些博弈往往具有挑战性。许多实际交互场景涉及耦合智能体决策的非线性状态与输入约束。本文利用约束博弈理论框架，开发了一种高效快速的交互式轨迹优化规划器，适用于受约束场景。我们的核心洞察是：利用多智能体交互中常见的智能体目标函数与约束函数的特殊结构，实现快速可靠的规划。更具体而言，我们识别了智能体代价函数与约束函数的结构，在此结构下所得到的动态博弈属于约束动态势博弈。约束动态势博弈是一类特殊博弈，其约束纳什均衡（即广义纳什均衡）可通过求解单个约束最优控制问题获得，而非求解一组耦合的约束最优控制问题。这一性质显著简化了约束交互式轨迹优化。我们在涉及四个平面智能体的导航场景中对比了该方法性能，结果表明其平均速度比现有最先进方法快20倍。我们还通过两个四旋翼无人机协作搬运刚性物体并避开两个行人的导航实验，验证了所提方法的有效性。