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

TL;DR

The paper tackles coordinated decision-making in multi-robot systems by casting it as a distributed optimization problem. It derives Consensus ADMM from an augmented Lagrangian and primal-dual perspective, enabling fully decentralized updates that enforce consensus across neighboring agents. The authors apply this framework to a distributed MPC problem for multi-drone waypoint navigation, incorporating 12-DOF drone dynamics, horizon-based optimization, and collision avoidance. The work demonstrates a scalable approach for coordinating multiple robots with communication-aware, iterative local updates that converge to global consistency.

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.