In this paper, we develop a fast mixed-integer convex programming (MICP) framework for multi-robot navigation by combining graph attention networks and distributed optimization. We formulate a mixed-integer optimization problem for receding horizon motion planning of a multi-robot system, taking into account the surrounding obstacles. To address the resulting multi-agent MICP problem in real time, we propose a framework that utilizes heterogeneous graph attention networks to learn the latent mapping from problem parameters to optimal binary solutions. Furthermore, we apply a distributed proximal alternating direction method of multipliers algorithm for solving the convex continuous optimization problem. We demonstrate the effectiveness of our proposed framework through experiments conducted on a robotic testbed.

submitted to CDC 2025