This paper develops a Distributed Differentiable Dynamic Game (D3G) framework, which can efficiently solve the forward and inverse problems in multi-robot coordination. We formulate multi-robot coordination as a dynamic game, where the behavior of a robot is dictated by its own dynamics and objective that also depends on others' behavior. In the forward problem, D3G enables all robots collaboratively to seek the Nash equilibrium of the game in a distributed manner, by developing a distributed shooting-based Nash solver. In the inverse problem, where each robot aims to find (learn) its objective (and dynamics) parameters to mimic given coordination demonstrations, D3G proposes a differentiation solver based on Differential Pontryagin's Maximum Principle, which allows each robot to update its parameters in a distributed and coordinated manner. We test the D3G in simulation with two types of robots given different task configurations. The results demonstrate the effectiveness of D3G for solving both forward and inverse problems in comparison with existing methods.

翻译：本文提出了一种分布式可微动态博弈（D3G）框架，该框架能够高效求解多机器人协调中的正向与逆向问题。我们将多机器人协调建模为动态博弈，其中每个机器人的行为由其自身的动力学模型和目标函数决定，而该目标函数又依赖于其他机器人的行为。在正向问题中，D3G通过开发基于分布式打靶法的纳什均衡求解器，使所有机器人能够以分布式方式协同求解博弈的纳什均衡。在逆向问题中，当每个机器人需要寻找（学习）其目标函数（及动力学）参数以模仿给定的协调演示时，D3G基于微分庞特里亚金最大值原理提出了一种微分求解器，使每个机器人能够以分布式且协调的方式更新其参数。我们在仿真中针对两种类型的机器人及不同任务配置对D3G进行了测试。结果表明，与现有方法相比，D3G在求解正向与逆向问题方面均具有有效性。