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

TL;DR

This paper introduces a decentralized control and topology co-design approach for rigid body networks that guarantees mesh stability during reconfiguration, enabling flexible merging and splitting without redesigning controllers.

Contribution

It presents a novel decentralized LMI-based co-design method with formal mesh stability guarantees for reconfigurable rigid body networks.

Findings

Decentralized LMI problems can be solved at each rigid body independently.

The method ensures mesh stability during flexible merging and splitting.

Simulation results demonstrate the effectiveness of the proposed approach.

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.