Multi-robot teams must coordinate to operate effectively. When a team operates in an uncoordinated manner, and agents choose actions that are only individually optimal, the team's outcome can suffer. However, in many domains, coordination requires costly communication. We explore the value of coordination in a broad class of differentiable motion-planning problems. In particular, we model coordinated behavior as a spectrum: at one extreme, agents jointly optimize a common team objective, and at the other, agents make unilaterally optimal decisions given their individual decision variables, i.e., they operate at Nash equilibria. We then demonstrate that reasoning about coordination in differentiable motion-planning problems reduces to reasoning about the second-order properties of agents' objectives, and we provide algorithms that use this second-order reasoning to determine at which times a team of agents should coordinate.

翻译：多机器人团队必须协调才能高效运作。当团队以非协调方式运作，且智能体仅选择个体最优行动时，团队整体表现可能受损。然而，在许多领域中，协调需要付出高昂的通信代价。我们在广泛的可微分运动规划问题类别中探讨协调的价值。具体而言，我们将协调行为建模为一个连续谱：在一端，智能体联合优化共同的团队目标；在另一端，智能体根据其个体决策变量做出单边最优决策，即它们在纳什均衡点运作。随后我们证明，在可微分运动规划问题中推理协调问题可简化为对智能体目标函数二阶性质的分析，并提出了利用这种二阶推理来确定多智能体团队应在何时进行协调的算法。