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Distributed Optimization Methods for Multi-Robot Systems: Part II -- A Survey

Ola Shorinwa, Trevor Halsted, Javier Yu, Mac Schwager

TL;DR

This survey addresses the challenge of applying distributed optimization to multi-robot systems by classifying methods into three families: distributed first-order algorithms, distributed sequential convex programming, and ADMM-based approaches. It analyzes how these methods achieve consensus and optimization over time-varying networks, including directed graphs, with discussions of convergence, communication requirements, and online/adaptive contexts. The paper maps these algorithms to robotics problems such as localization, mapping, tracking, and planning, and highlights practical considerations, open questions, and hardware-implementation gaps. Overall, it provides a structured taxonomy, connects algorithms to concrete robotic applications, and outlines research opportunities to advance fully distributed coordination without central control. This work thus serves robotics researchers and practitioners seeking scalable, privacy-preserving, and robust distributed optimization solutions for complex multi-robot tasks.

Abstract

Although the field of distributed optimization is well-developed, relevant literature focused on the application of distributed optimization to multi-robot problems is limited. This survey constitutes the second part of a two-part series on distributed optimization applied to multi-robot problems. In this paper, we survey three main classes of distributed optimization algorithms -- distributed first-order methods, distributed sequential convex programming methods, and alternating direction method of multipliers (ADMM) methods -- focusing on fully-distributed methods that do not require coordination or computation by a central computer. We describe the fundamental structure of each category and note important variations around this structure, designed to address its associated drawbacks. Further, we provide practical implications of noteworthy assumptions made by distributed optimization algorithms, noting the classes of robotics problems suitable for these algorithms. Moreover, we identify important open research challenges in distributed optimization, specifically for robotics problems.

Distributed Optimization Methods for Multi-Robot Systems: Part II -- A Survey

TL;DR

This survey addresses the challenge of applying distributed optimization to multi-robot systems by classifying methods into three families: distributed first-order algorithms, distributed sequential convex programming, and ADMM-based approaches. It analyzes how these methods achieve consensus and optimization over time-varying networks, including directed graphs, with discussions of convergence, communication requirements, and online/adaptive contexts. The paper maps these algorithms to robotics problems such as localization, mapping, tracking, and planning, and highlights practical considerations, open questions, and hardware-implementation gaps. Overall, it provides a structured taxonomy, connects algorithms to concrete robotic applications, and outlines research opportunities to advance fully distributed coordination without central control. This work thus serves robotics researchers and practitioners seeking scalable, privacy-preserving, and robust distributed optimization solutions for complex multi-robot tasks.

Abstract

Although the field of distributed optimization is well-developed, relevant literature focused on the application of distributed optimization to multi-robot problems is limited. This survey constitutes the second part of a two-part series on distributed optimization applied to multi-robot problems. In this paper, we survey three main classes of distributed optimization algorithms -- distributed first-order methods, distributed sequential convex programming methods, and alternating direction method of multipliers (ADMM) methods -- focusing on fully-distributed methods that do not require coordination or computation by a central computer. We describe the fundamental structure of each category and note important variations around this structure, designed to address its associated drawbacks. Further, we provide practical implications of noteworthy assumptions made by distributed optimization algorithms, noting the classes of robotics problems suitable for these algorithms. Moreover, we identify important open research challenges in distributed optimization, specifically for robotics problems.
Paper Structure (25 sections, 29 equations, 1 figure, 7 algorithms)

This paper contains 25 sections, 29 equations, 1 figure, 7 algorithms.

Table of Contents

  1. Introduction
  2. Existing Surveys
  3. Contributions
  4. Organization
  5. Notation and Preliminaries
  6. Problem Formulation
  7. Distributed First-Order Algorithms
  8. Distributed (Sub)-Gradient Descent and Diffusion Algorithms
  9. Distributed Gradient Tracking Algorithms
  10. Distributed Dual Averaging
  11. Distributed Sequential Convex Programming
  12. Approximate Newton Methods
  13. Convex Surrogate Methods
  14. Alternating direction method of multipliers
  15. Distributed Optimization in Robotics and Related Applications
  16. ...and 10 more sections

Figures (1)

  • Figure 1: A motivation for distributed optimization: consider an estimation scenario in which a robot seeks to localize a target given sensor measurements. The robot can compute an optimal solution given only its observations, as represented in (a). By using distributed optimization techniques, each robot in a networked system of robots can compute the optimal solution given all robots' observations without actually sharing individual sensor models or measurements with one another, as represented in (b).

Theorems & Definitions (8)

  • Definition 1: Non-negative Matrix
  • Definition 2: Stochastic Matrix
  • Definition 3: Summable Sequence
  • Definition 4: Square-Summable Sequence
  • Definition 5: Connectivity of an Undirected Graph
  • Definition 6: Connectivity of a Directed Graph
  • Definition 7: Convergence Rate
  • Definition 8: Synchronous Algorithm