Finite-time attitude synchronization with a discontinuous protocol

TL;DR

This paper introduces a simple discontinuous control protocol for finite-time attitude synchronization of rigid bodies using axis-angle representation, ensuring convergence under specific initial conditions.

Contribution

A novel distributed discontinuous control law based on signum functions is proposed for finite-time attitude synchronization, addressing axis-angle singularity issues.

Findings

Achieves finite-time synchronization under certain initial conditions.

Uses a signum-based control law that is simple and distributed.

Validated with a simulation example.

Abstract

A finite-time attitude synchronization problem is considered in this paper where the rotation of each rigid body is expressed using the axis-angle representation. One simple discontinuous and distributed controller using the vectorized signum function is proposed. This controller only involves the sign of the state differences of adjacent neighbors. In order to avoid the singularity introduced by the axis-angular representation, an extra constraint is added to the initial condition. It is proved that for some initial conditions, the control law achieves finite-time attitude synchronization. One simulated example is provided to verify the usage of the control protocol designed in this paper.