A Brief Tutorial on Consensus ADMM for Distributed Optimization with Applications in Robotics

TL;DR

This tutorial explains the Consensus ADMM algorithm for distributed optimization, emphasizing its derivation and application to multi-robot trajectory planning, providing insights into its theoretical foundations and practical use cases.

Contribution

It offers a clear derivation of Consensus ADMM and demonstrates its application in multi-robot trajectory optimization, bridging theory and practice.

Findings

Consensus ADMM effectively solves distributed trajectory optimization problems.

The tutorial clarifies the connection between Consensus ADMM and augmented Lagrangian methods.

Application results show improved coordination in multi-robot systems.

Abstract

This paper presents a tutorial on the Consensus Alternating Direction Method of Multipliers (Consensus ADMM) for distributed optimization, with a specific focus on applications in multi-robot systems. In this tutorial, we derive the consensus ADMM algorithm, highlighting its connections to the augmented Lagrangian and primal-dual methods. Finally, we apply Consensus ADMM to an example problem for trajectory optimization of a multi-agent system.