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Combining Graph Attention Networks and Distributed Optimization for Multi-Robot Mixed-Integer Convex Programming

Viet-Anh Le, Panagiotis Kounatidis, Andreas A. Malikopoulos

TL;DR

This work addresses real-time multi-robot navigation by solving a parametric $MICP$ with collision-avoidance constraints. It combines a heterogeneous graph attention network to predict optimal binary decisions for robot-robot and robot-obstacle edges with a distributed proximal ADMM to solve the resulting convex subproblems online. The approach leverages offline supervised learning and online distributed optimization, achieving high prediction accuracy and substantial speedups on larger multi-agent systems, while maintaining safety constraints. The framework demonstrates real-time feasibility on a robotic testbed and shows robustness and scalability in simulation, highlighting its potential for complex, large-scale multi-agent planning tasks.

Abstract

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.

Combining Graph Attention Networks and Distributed Optimization for Multi-Robot Mixed-Integer Convex Programming

TL;DR

This work addresses real-time multi-robot navigation by solving a parametric with collision-avoidance constraints. It combines a heterogeneous graph attention network to predict optimal binary decisions for robot-robot and robot-obstacle edges with a distributed proximal ADMM to solve the resulting convex subproblems online. The approach leverages offline supervised learning and online distributed optimization, achieving high prediction accuracy and substantial speedups on larger multi-agent systems, while maintaining safety constraints. The framework demonstrates real-time feasibility on a robotic testbed and shows robustness and scalability in simulation, highlighting its potential for complex, large-scale multi-agent planning tasks.

Abstract

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.

Paper Structure

This paper contains 14 sections, 24 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Multi-Robot Navigation
  4. Parametrized MICP Formulation
  5. Learning with Heterogeneous Graph Attention Networks
  6. Graph Attention Layers
  7. Heterogeneous Graph Attention Networks
  8. Data Generation and Training
  9. Distributed Convex Optimization with Proximal Alternating Direction Method of Multipliers (ADMM)
  10. Results and Discussions
  11. Experiment Setup
  12. Experimental Validation
  13. Simulation Studies
  14. Conclusions

Figures (6)

  • Figure 1: Multi-robot navigation problem with stationary obstacles.
  • Figure 2: Illustration of a heterogeneous graph for our problem. The robots and obstacles are represented as nodes, while the edges include robot-robot, robot-obstacle, and obstacle-obstacle connections.
  • Figure 3: Architecture of the neural network for learning optimal binaries.
  • Figure 4: The architecture of our experiment setup.
  • Figure 5: Trajectories of the robots and snapshots from an experiment with three robots and three obstacles.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Definition 3