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Mesh Stability Guaranteed Rigid Body Networks Using Control and Topology Co-Design

Zihao Song, Shirantha Welikala, Panos J. Antsaklis, Hai Lin

TL;DR

This work addresses the challenge of merging and splitting rigid body networks while preserving scalability, distributed/compositional control, and mesh stability. It develops a dissipativity-based framework that combines a centralized $LMI$-based control/topology co-design with a Sylvester-criterion-inspired decentralization, yielding per-agent LMIs that enable decentralized execution during topology changes. The approach introduces $X$-EID dissipativity, scalable mesh stability ($sMS$), and a two-layer outer/inner-loop controller for 3D rigid body dynamics, along with local synthesis that guarantees dissipativity. Validation through a purpose-built simulator demonstrates improved stability, compositionality, and robustness during merging/splitting compared with a state-of-the-art consensus method, highlighting practical impact for reconfigurable multi-agent systems.

Abstract

Merging and splitting are of great significance for rigid body networks in making such networks reconfigurable. The main challenges lie in simultaneously ensuring the compositionality of the distributed controllers and the mesh stability of the entire network. To this end, we propose a decentralized control and topology co-design method for rigid body networks, which enables flexible joining and leaving of rigid bodies without the need to redesign the controllers for the entire network after such maneuvers. We first provide a centralized linear matrix inequality (LMI)-based control and topology co-design optimization of the rigid body networks with a formal mesh stability guarantee. Then, these centralized mesh stability constraints are made decentralized by a proposed alternative set of sufficient conditions. Using these decentralized mesh stability constraints and Sylvester's criterion-based decentralization techniques, the said centralized LMI problem is equivalently broken down into a set of smaller decentralized LMI problems that can be solved at each rigid body, enabling flexible merging/splitting of rigid bodies. Finally, the effectiveness of the proposed co-design method is illustrated based on a specifically developed simulator and a comparison study with respect to a state-of-the-art method.

Mesh Stability Guaranteed Rigid Body Networks Using Control and Topology Co-Design

TL;DR

This work addresses the challenge of merging and splitting rigid body networks while preserving scalability, distributed/compositional control, and mesh stability. It develops a dissipativity-based framework that combines a centralized -based control/topology co-design with a Sylvester-criterion-inspired decentralization, yielding per-agent LMIs that enable decentralized execution during topology changes. The approach introduces -EID dissipativity, scalable mesh stability (), and a two-layer outer/inner-loop controller for 3D rigid body dynamics, along with local synthesis that guarantees dissipativity. Validation through a purpose-built simulator demonstrates improved stability, compositionality, and robustness during merging/splitting compared with a state-of-the-art consensus method, highlighting practical impact for reconfigurable multi-agent systems.

Abstract

Merging and splitting are of great significance for rigid body networks in making such networks reconfigurable. The main challenges lie in simultaneously ensuring the compositionality of the distributed controllers and the mesh stability of the entire network. To this end, we propose a decentralized control and topology co-design method for rigid body networks, which enables flexible joining and leaving of rigid bodies without the need to redesign the controllers for the entire network after such maneuvers. We first provide a centralized linear matrix inequality (LMI)-based control and topology co-design optimization of the rigid body networks with a formal mesh stability guarantee. Then, these centralized mesh stability constraints are made decentralized by a proposed alternative set of sufficient conditions. Using these decentralized mesh stability constraints and Sylvester's criterion-based decentralization techniques, the said centralized LMI problem is equivalently broken down into a set of smaller decentralized LMI problems that can be solved at each rigid body, enabling flexible merging/splitting of rigid bodies. Finally, the effectiveness of the proposed co-design method is illustrated based on a specifically developed simulator and a comparison study with respect to a state-of-the-art method.
Paper Structure (15 sections, 8 theorems, 47 equations, 7 figures)

This paper contains 15 sections, 8 theorems, 47 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Dissipativity Theory
  4. Network Configuration
  5. X-EID-Based Topology Synthesis and Decentralization
  6. Mesh Stability
  7. Error Dynamics Modeling and Problem Formulation
  8. Error Dynamics Modeling
  9. Problem Formulation
  10. Main Results
  11. Centralized Control and Topology Co-design
  12. Local Control Synthesis
  13. Decentralized Co-design for Merging and Splitting
  14. Simulation Examples
  15. Conclusion

Key Result

Proposition 1

WelikalaP52022 The networked system $\Sigma$ in Eq:GeneralSystem_closedLoop can be made $L_2$-stable with the finite $L_2$-gain $\gamma$ by solving the following LMI problem to get the interconnection matrix $M$ in Eq:NSC2Interconnection: where $\textbf{X}^{12}:= \text{diag}([(X_i^{11})^{-1}X_i^{12}]_{i\in\mathcal{I}_N})$ (we assume $X_i^{11}>0$) and $\textbf{X}^{21}:= (\textbf{X}^{12})^\top$ wit

Figures (7)

  • Figure 1: Network configuration: (a) A generic networked system $\Sigma$; (b) Formation error dynamics as a networked system $\tilde{\Sigma}$.
  • Figure 2: Configuration of the rigid body networks. Each agent is assumed to know the leader's information.
  • Figure 3: The error dynamics and control architecture for the $i\textsuperscript{th}$ agent in the rigid body network.
  • Figure 4: Initially assumed communication topology.
  • Figure 5: Results observed by our proposed decentralized co-design with $9$ followers: (a) position tracking; (b) position tracking errors; (c) translational velocity tracking; (d) translational velocity tracking errors; (e) orientation tracking errors; (f) angular velocity tracking errors.
  • ...and 2 more figures

Theorems & Definitions (21)

  • Definition 1
  • Proposition 1
  • Proposition 2
  • Definition 2
  • Remark 1
  • Proposition 3
  • Remark 2
  • Proposition 4
  • Remark 3
  • Remark 4
  • ...and 11 more