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A Tutorial on Distributed Optimization for Cooperative Robotics: from Setups and Algorithms to Toolboxes and Research Directions

Andrea Testa, Guido Carnevale, Giuseppe Notarstefano

TL;DR

This paper models cooperative robotics through two rich distributed optimization frameworks: constraint-coupled and aggregative optimization, enabling scalable, decentralized decision-making without central coordinators. It surveys and develops algorithms (dual and primal decompositions, projected tracking, distributed Frank-Wolfe, and dual-consensus ADMM) with convergence guarantees under standard communication and convexity assumptions, and demonstrates practical ROS 2–based toolboxes (DISROPT, ChoiRbot, CrazyChoir) and real experiments. The work binds theory to practice by detailing three representative constraint-coupled use cases (task allocation, battery charging, pickup-and-delivery) and two aggregative use cases (target surveillance, soft-constraint resource allocation), complemented by extensive simulations and physical experiments on heterogeneous robot networks. The article also identifies future directions in nonconvex, mixed-integer, imperfect communication, unknown-function, online, and stochastic settings, aiming to broaden applicability to realistic robotic deployments and dynamic environments.

Abstract

Several interesting problems in multi-robot systems can be cast in the framework of distributed optimization. Examples include multi-robot task allocation, vehicle routing, target protection, and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this paper, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss its implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots.

A Tutorial on Distributed Optimization for Cooperative Robotics: from Setups and Algorithms to Toolboxes and Research Directions

TL;DR

This paper models cooperative robotics through two rich distributed optimization frameworks: constraint-coupled and aggregative optimization, enabling scalable, decentralized decision-making without central coordinators. It surveys and develops algorithms (dual and primal decompositions, projected tracking, distributed Frank-Wolfe, and dual-consensus ADMM) with convergence guarantees under standard communication and convexity assumptions, and demonstrates practical ROS 2–based toolboxes (DISROPT, ChoiRbot, CrazyChoir) and real experiments. The work binds theory to practice by detailing three representative constraint-coupled use cases (task allocation, battery charging, pickup-and-delivery) and two aggregative use cases (target surveillance, soft-constraint resource allocation), complemented by extensive simulations and physical experiments on heterogeneous robot networks. The article also identifies future directions in nonconvex, mixed-integer, imperfect communication, unknown-function, online, and stochastic settings, aiming to broaden applicability to realistic robotic deployments and dynamic environments.

Abstract

Several interesting problems in multi-robot systems can be cast in the framework of distributed optimization. Examples include multi-robot task allocation, vehicle routing, target protection, and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this paper, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss its implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots.
Paper Structure (40 sections, 5 theorems, 51 equations, 15 figures, 5 algorithms)

This paper contains 40 sections, 5 theorems, 51 equations, 15 figures, 5 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Optimization in Robotic Applications
  4. Toolboxes for Cooperative Robotics
  5. Related Tutorial and Survey Papers
  6. Organization
  7. Notation
  8. Distributed Multi-Robot Setup: from Theoretical Modeling to ROS 2 Implementation
  9. Theoretical Modeling
  10. Hardware-Software Implementation: a ROS-2 perspective
  11. Consensus Optimization and Partition-Based Optimization
  12. Consensus Optimization
  13. Partition-Based Optimization
  14. Constraint-Coupled Optimization Setup for Cooperative Robotics
  15. Multi-Robot Constraint-Coupled 1: Multi-Robot Task Allocation
  16. ...and 25 more sections

Key Result

Theorem 6.7

Consider Distributed Dual Decomposition as given in Algorithm alg:dual_decomp. Let Assumptions ass:dualdec_convex-ass:dualdec_network hold. Let $\mu^\star$ denote an optimal solution to eq:constr_coupled_dual and let $X_{}^\star$ denote the set of minimizers of eq:constr_coupled. Also, let $x_{}^{t}

Figures (15)

  • Figure 1: Example of a robotic network. A team of heterogeneous robots cooperatively solves an optimization problem, leveraging the ROS 2 infrastructure. Local planning and actuation follow the result of the optimization.
  • Figure 2: Example of constraint-coupled setup. The two local decision variables $x_{1}^{}\in X_{1}$ and $x_{2}^{}\in X_{2}$ are coupled by a linear coupling constraint $A_1 x_{1}^{}+ A_2 x_{2}^{}\leq b$. The gray area represents the feasible set. The tuple $(c_1,c_2)$ represents the components of the linear cost. The cost direction is represented as a red arrow.
  • Figure 3: Task assignment problem. Robots are represented by circles, while tasks are represented by squares. An arrow from $i$ to $k$ means that robot $i$ can perform task $k$, incurring a cost $c_{ik}$.
  • Figure 4: Example PDVRP scenario with two pickup and two delivery requests. Robots are initially located at the "start" and must end at the terminal node. On the left, dashed, grey lines denote all the possible paths robot can travel. Right: black lines denote the optimal paths for the two robots.
  • Figure 5: Example of the target surveillance problem. Robots are represented as blue big circles, while the target is represented as a flag. The small blue circle represents the robots' barycenter. Red circles represent adversaries. Each robot wants to move towards a certain adversary, while the barycenter is steered near the target (white arrows).
  • ...and 10 more figures

Theorems & Definitions (7)

  • Remark 6.1
  • Theorem 6.7: falsone2017dual
  • Remark 6.8
  • Theorem 6.13: camisa2021distributed
  • Theorem 7.4: carnevale2021distributed
  • Theorem 7.8: wang2022distributed
  • Theorem 7.11: grontas2022distributed