# Intrinsic Reduced Attitude Formation with Ring Inter-Agent Graph

## TL;DR

This paper presents a novel approach for reduced attitude formation control in multi-agent systems using feedback based on relative attitudes, demonstrating convergence to specific formations depending on group size parity.

## Contribution

It introduces a sign-reversal of a classic consensus protocol for formation control under various graph topologies, revealing new formation behaviors.

## Key findings

- Convergence to antipodal points for even group sizes.
- Equidistant distribution on a great circle for odd group sizes.
- Almost global convergence under undirected ring topology.

## Abstract

This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using feedback based on relative attitude information. Under both undirected and directed cycle graph topologies, it is shown that reversing the sign of a classic consensus protocol yields asymptotical convergence to formations whose shape depends on the parity of the group size. Specifically, in the case of even parity the reduced attitudes converge asymptotically to a pair of antipodal points and distribute equidistantly on a great circle in the case of odd parity. Moreover, when the inter-agent graph is an undirected ring, the desired formation is shown to be achieved from almost all initial states.