Many robotic applications involve interactions between multiple agents where an agent's decisions affect the behavior of other agents. Such behaviors can be captured by the equilibria of differential games which provide an expressive framework for modeling the agents' mutual influence. However, finding the equilibria of differential games is in general challenging as it involves solving a set of coupled optimal control problems. In this work, we propose to leverage the special structure of multi-agent interactions to generate interactive trajectories by simply solving a single optimal control problem, namely, the optimal control problem associated with minimizing the potential function of the differential game. Our key insight is that for a certain class of multi-agent interactions, the underlying differential game is indeed a potential differential game for which equilibria can be found by solving a single optimal control problem. We introduce such an optimal control problem and build on single-agent trajectory optimization methods to develop a computationally tractable and scalable algorithm for planning multi-agent interactive trajectories. We will demonstrate the performance of our algorithm in simulation and show that our algorithm outperforms the state-of-the-art game solvers. To further show the real-time capabilities of our algorithm, we will demonstrate the application of our proposed algorithm in a set of experiments involving interactive trajectories for two quadcopters.
翻译:许多机器人应用涉及多个代理商之间的互动,其中代理商的决定会影响其他代理商的行为。这种行为可以通过不同游戏的平衡性来捕捉。不同的游戏为模拟代理商的相互影响提供了一个清晰的框架。然而,找到不同游戏的平衡性通常具有挑战性,因为它涉及解决一系列相互配合的最佳控制问题。在这项工作中,我们提议利用多代理商互动的特殊结构来生成互动轨迹,方法是仅仅解决一个单一的最佳控制问题,即与尽量减少差异游戏潜在功能相关的最佳控制问题。我们的关键洞察力是,对于某类多代理商的互动来说,潜在的差异性游戏确实是一种潜在的差异性游戏,通过解决单一的最佳控制问题可以找到平衡性。我们引入了这样一个最佳控制问题,并借助单一代理商轨迹优化方法来开发一种可计算性可控和可缩放的算法,用于规划多代理方互动轨迹。我们将在模拟中展示我们算法的演算能力,并显示我们的算法超越了当前游戏解算器的状态。进一步展示了我们两个互动算法的演算能力,我们将在互动演算中展示我们所拟的两种演算法。