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Scaling Robust Optimization for Multi-Agent Robotic Systems: A Distributed Perspective

Arshiya Taj Abdul, Augustinos D. Saravanos, Evangelos A. Theodorou

TL;DR

This work tackles scalable robust trajectory optimization for multi‑agent robotic systems under both exogenous deterministic and stochastic disturbances. It fuses robust optimization with distribution steering and a distributed ADMM architecture, delivering tractable constraint approximations and convergence guarantees for large networks. The authors derive exact and surrogate reformulations for semi‑infinite robust constraints, notably robust linear mean, norm‑of‑mean, chance, and covariance constraints, and prove meaningful reductions in computational complexity compared to centralized SDP approaches. Simulation results confirm robust performance in obstacle rich environments and demonstrate scalability to hundreds of agents, underscoring the practical impact for safe, robust multi‑robot coordination. The framework paves the way for further integration with nonlinear dynamics and data‑driven uncertainty learning in distributed robotic systems.

Abstract

This paper presents a novel distributed robust optimization scheme for steering distributions of multi-agent systems under stochastic and deterministic uncertainty. Robust optimization is a subfield of optimization which aims to discover an optimal solution that remains robustly feasible for all possible realizations of the problem parameters within a given uncertainty set. Such approaches would naturally constitute an ideal candidate for multi-robot control, where in addition to stochastic noise, there might be exogenous deterministic disturbances. Nevertheless, as these methods are usually associated with significantly high computational demands, their application to multi-agent robotics has remained limited. The scope of this work is to propose a scalable robust optimization framework that effectively addresses both types of uncertainties, while retaining computational efficiency and scalability. In this direction, we provide tractable approximations for robust constraints that are relevant in multi-robot settings. Subsequently, we demonstrate how computations can be distributed through an Alternating Direction Method of Multipliers (ADMM) approach towards achieving scalability and communication efficiency. All improvements are also theoretically justified by establishing and comparing the resulting computational complexities. Simulation results highlight the performance of the proposed algorithm in effectively handling both stochastic and deterministic uncertainty in multi-robot systems. The scalability of the method is also emphasized by showcasing tasks with up to hundreds of agents. The results of this work indicate the promise of blending robust optimization, distribution steering and distributed optimization towards achieving scalable, safe and robust multi-robot control.

Scaling Robust Optimization for Multi-Agent Robotic Systems: A Distributed Perspective

TL;DR

This work tackles scalable robust trajectory optimization for multi‑agent robotic systems under both exogenous deterministic and stochastic disturbances. It fuses robust optimization with distribution steering and a distributed ADMM architecture, delivering tractable constraint approximations and convergence guarantees for large networks. The authors derive exact and surrogate reformulations for semi‑infinite robust constraints, notably robust linear mean, norm‑of‑mean, chance, and covariance constraints, and prove meaningful reductions in computational complexity compared to centralized SDP approaches. Simulation results confirm robust performance in obstacle rich environments and demonstrate scalability to hundreds of agents, underscoring the practical impact for safe, robust multi‑robot coordination. The framework paves the way for further integration with nonlinear dynamics and data‑driven uncertainty learning in distributed robotic systems.

Abstract

This paper presents a novel distributed robust optimization scheme for steering distributions of multi-agent systems under stochastic and deterministic uncertainty. Robust optimization is a subfield of optimization which aims to discover an optimal solution that remains robustly feasible for all possible realizations of the problem parameters within a given uncertainty set. Such approaches would naturally constitute an ideal candidate for multi-robot control, where in addition to stochastic noise, there might be exogenous deterministic disturbances. Nevertheless, as these methods are usually associated with significantly high computational demands, their application to multi-agent robotics has remained limited. The scope of this work is to propose a scalable robust optimization framework that effectively addresses both types of uncertainties, while retaining computational efficiency and scalability. In this direction, we provide tractable approximations for robust constraints that are relevant in multi-robot settings. Subsequently, we demonstrate how computations can be distributed through an Alternating Direction Method of Multipliers (ADMM) approach towards achieving scalability and communication efficiency. All improvements are also theoretically justified by establishing and comparing the resulting computational complexities. Simulation results highlight the performance of the proposed algorithm in effectively handling both stochastic and deterministic uncertainty in multi-robot systems. The scalability of the method is also emphasized by showcasing tasks with up to hundreds of agents. The results of this work indicate the promise of blending robust optimization, distribution steering and distributed optimization towards achieving scalable, safe and robust multi-robot control.
Paper Structure (60 sections, 6 theorems, 132 equations, 12 figures, 1 table)

This paper contains 60 sections, 6 theorems, 132 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Notation
  4. Problem Setup
  5. Dynamics
  6. Characterizations of Uncertainty
  7. Exogenous deterministic uncertainty
  8. Stochastic uncertainty
  9. Control Policies
  10. Robust Constraints
  11. Robust linear mean constraints
  12. Robust nonconvex norm-of-mean constraints
  13. Robust linear chance constraints
  14. Robust covariance constraints
  15. Problem Formulation
  16. ...and 45 more sections

Key Result

Proposition 1

The maximum value of ${\bm a}_i ^\mathrm{T} \mathbb{E}[{\bm x}^i]$ when the uncertainty vector ${\bm \zeta}^i$ lies in the set $\pazocal{U}_i$ is given by

Figures (12)

  • Figure 1: Two agents scenario with obstacle: Performance comparison between robust and non-robust case with terminal mean and obstacle constraints.
  • Figure 2: Twenty agents scenario with circle formation task and 21 obstacles: (a) Robust mean trajectories, (b)-(e) Snapshots of the robust mean trajectories of agents, (f) Distance plot showing the minimum distance of each agent from its nearest neighbor at each time step.
  • Figure 3: Four agents scenario-1 with non-convex obstacles: (a) Robust mean trajectories, (b)-(d) Snapshots of the robust mean trajectories of agents.
  • Figure 4: Four agents scenario-2 with non-convex obstacles: (a) Robust Mean Trajectories, (b)-(d) Snapshots of the robust mean trajectories of agents.
  • Figure 5: Performance analysis of robust chance constraints and Covariance Constraints - Scenario 1: (a) Mean trajectories of agents in deterministic case, (b) Trajectories of agents in deterministic case without the robust chance constraints, (c) Trajectories of agents in mixed case with robust chance constraints, (d) Trajectories of agents in mixed case with robust chance constraints and terminal covariance constraints.
  • ...and 7 more figures

Theorems & Definitions (11)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • Corollary 1
  • Proposition 5
  • ...and 1 more