A core challenge of multi-robot interactions is collision avoidance among robots with potentially conflicting objectives. We propose a game-theoretic method for collision avoidance based on rotating hyperplane constraints. These constraints ensure collision avoidance by defining separating hyperplanes that rotate around a keep-out zone centered on certain robots. Since it is challenging to select the parameters that define a hyperplane without introducing infeasibilities, we propose to learn them from an expert trajectory i.e., one collected by recording human operators. To do so, we solve for the parameters whose corresponding equilibrium trajectory best matches the expert trajectory. We validate our method by learning hyperplane parameters from noisy expert trajectories and demonstrate the generalizability of the learned parameters to scenarios with more robots and previously unseen initial conditions.

翻译：多机器人交互中的一个核心挑战是解决目标冲突的机器人之间的碰撞避免问题。我们提出了一种基于旋转超平面约束的博弈论碰撞避免方法。通过在以特定机器人为中心的禁入区域周围定义旋转分离超平面，这些约束实现了碰撞避免。由于难以在避免引入不可行性的情况下选择定义超平面的参数，我们提出从专家轨迹（即通过记录人类操作员行为收集的轨迹）中学习这些参数。为此，我们求解使得对应平衡轨迹与专家轨迹最匹配的参数。通过从含噪专家轨迹中学习超平面参数，我们验证了该方法，并展示了所学参数在包含更多机器人及未知初始条件的场景中的泛化能力。