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Cooperative Distributed MPC via Decentralized Real-Time Optimization: Implementation Results for Robot Formations

Gösta Stomberg, Henrik Ebel, Timm Faulwasser, Peter Eberhard

TL;DR

This work tackles scalable formation control for mobile robot teams by casting formation tracking as a centralized OCP and solving it in a fully decentralized manner with ADMM and dSQP. The authors reformulate the problem as a partially separable NLP, enabling neighbor-only communication and iterative distributed optimization, while accommodating soft constraints to ensure online feasibility. Hardware experiments with four omnidirectional robots validate real-time performance, showing ADMM can produce near-optimal inputs with only a handful of iterations and that dSQP can handle nonconvex distance constraints to ensure collision avoidance, all within millisecond-scale computation times. The results demonstrate the practical viability of distributed MPC for robot formations, highlighting the approach’s potential for scalable, coordinator-free control in networked robotic systems.

Abstract

Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While the stability analysis of DMPC is quite well understood, there exist only limited implementation results for realistic applications involving distributed computation and networked communication. This article approaches formation control of mobile robots via a cooperative DMPC scheme. We discuss the implementation via decentralized optimization algorithms. To this end, we combine the alternating direction method of multipliers with decentralized sequential quadratic programming to solve the underlying optimal control problem in a decentralized fashion with nominal convergence guarantees. Our approach only requires coupled subsystems to communicate and does not rely on a central coordinator. Our experimental results showcase the efficacy of DMPC for formation control and they demonstrate the real-time feasibility of the considered algorithms.

Cooperative Distributed MPC via Decentralized Real-Time Optimization: Implementation Results for Robot Formations

TL;DR

This work tackles scalable formation control for mobile robot teams by casting formation tracking as a centralized OCP and solving it in a fully decentralized manner with ADMM and dSQP. The authors reformulate the problem as a partially separable NLP, enabling neighbor-only communication and iterative distributed optimization, while accommodating soft constraints to ensure online feasibility. Hardware experiments with four omnidirectional robots validate real-time performance, showing ADMM can produce near-optimal inputs with only a handful of iterations and that dSQP can handle nonconvex distance constraints to ensure collision avoidance, all within millisecond-scale computation times. The results demonstrate the practical viability of distributed MPC for robot formations, highlighting the approach’s potential for scalable, coordinator-free control in networked robotic systems.

Abstract

Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While the stability analysis of DMPC is quite well understood, there exist only limited implementation results for realistic applications involving distributed computation and networked communication. This article approaches formation control of mobile robots via a cooperative DMPC scheme. We discuss the implementation via decentralized optimization algorithms. To this end, we combine the alternating direction method of multipliers with decentralized sequential quadratic programming to solve the underlying optimal control problem in a decentralized fashion with nominal convergence guarantees. Our approach only requires coupled subsystems to communicate and does not rely on a central coordinator. Our experimental results showcase the efficacy of DMPC for formation control and they demonstrate the real-time feasibility of the considered algorithms.
Paper Structure (16 sections, 1 theorem, 17 equations, 8 figures, 5 tables, 3 algorithms)

This paper contains 16 sections, 1 theorem, 17 equations, 8 figures, 5 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. DMPC of Mobile Robots
  4. OCP Formulation
  5. Reformulation as Partially Separable Problem
  6. Decentralized Optimization
  7. Essentials of ADMM
  8. The Decentralized SQP Method for Nonlinear DMPC
  9. Implementation and Hardware
  10. Hardware and Experiment Environment
  11. DMPC Implementation
  12. Experimental Results
  13. Formation Control via linear-quadratic MPC and ADMM
  14. Non-convex Minimum-distance Constraints and dSQP
  15. Discussion
  16. ...and 1 more sections

Key Result

Theorem 1

Let $p^\star$ be a KKT point of nlp which, for all $i \in \mathcal{S}$, satisfies Furthermore, suppose the matrix has full row rank, i.e., $z^\star$ satisfies the linear independence constraint qualification. Furthermore, suppose the Hessian approximation ${H_i^q = \nabla_{z_iz_i}^2 L_i^q}$ is used and that ADMM is terminated in Step dsqp:while of Algorithm alg:dSQP dynamically based on eq:modS

Figures (8)

  • Figure 1: Control architectures and corresponding optimization architectures for MPC. This article discusses DMPC via decentralized optimization.
  • Figure 2: Omnidirectional mobile robot for distributed robotics experiments.
  • Figure 3: Experimental setup. The DMPC controllers run on the workstation computers and each robot is assigned one workstation to run Algorithm \ref{['alg:DMPC']}.
  • Figure 4: Block diagram for a path graph of four robots $\Sigma_i$. The controllers $\mathcal{C}_i$ of neighboring robots exchange predicted position trajectories $\bar{\boldsymbol{x}}_i$ and $\boldsymbol{w}_{ij}$.
  • Figure 5: Rectangle scenario using ADMM-based DMPC: camera images and rectangular path (dashed line), robot one trajectory (solid blue line), and current formation (solid orange line).
  • ...and 3 more figures

Theorems & Definitions (5)

  • Remark 1: Compensation of computational delay
  • Remark 2: Soft-constrained optimal control problem
  • Remark 3: Local dSQP convergence
  • Theorem 1: dSQP convergence Stomberg2022a
  • Remark 4: Hessian approximation