# Robust Formation Control in SE(3) for Tree-Graph Structures with Prescribed Transient and Steady State Performance

## TL;DR

This paper introduces a decentralized, robust control protocol for formation management of rigid bodies in SE(3) with tree-graph sensing structures, ensuring collision avoidance, connectivity, and prescribed transient and steady state behaviors.

## Contribution

It develops a novel control method for formation control in SE(3) that guarantees robustness, decentralized implementation, and performance specifications for tree-graph structures.

## Key findings

- Control laws are decentralized and use local information.
- Guarantees collision avoidance and connectivity.
- Simulation confirms effectiveness and robustness.

## Abstract

This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose sensing graph is a static and undirected tree, in the special Euclidean group SE(3). The proposed control laws are decentralized, in the sense that each agent uses only local relative information from its neighbors to calculate its control signal, as well as robust with respect to modeling (parametric and structural) uncertainties and external disturbances. The proposed methodology guarantees the satisfaction of inter-agent distance constraints that resemble collision avoidance and connectivity maintenance properties. Moreover, certain predefined functions characterize the transient and steady state performance of the closed loop system. Finally, simulation results verify the validity and efficiency of the proposed approach.