Learning Hyperplanes for Multi-Agent Collision Avoidance in Space

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.