Distributed Optimization Methods for Multi-Robot Systems: Part I -- A Tutorial

Distributed optimization provides a framework for deriving distributed algorithms for a variety of multi-robot problems. This tutorial constitutes the first part of a two-part series on distributed optimization applied to multi-robot problems, which seeks to advance the application of distributed optimization in robotics. In this tutorial, we demonstrate that many canonical multi-robot problems can be cast within the distributed optimization framework, such as multi-robot simultaneous localization and planning (SLAM), multi-robot target tracking, and multi-robot task assignment problems. We identify three broad categories of distributed optimization algorithms: distributed first-order methods, distributed sequential convex programming, and the alternating direction method of multipliers (ADMM). We describe the basic structure of each category and provide representative algorithms within each category. We then work through a simulation case study of multiple drones collaboratively tracking a ground vehicle. We compare solutions to this problem using a number of different distributed optimization algorithms. In addition, we implement a distributed optimization algorithm in hardware on a network of Rasberry Pis communicating with XBee modules to illustrate robustness to the challenges of real-world communication networks.