Finite-time attitude synchronization with distributed discontinuous protocols

TL;DR

This paper introduces distributed discontinuous controllers for finite-time attitude synchronization of rigid bodies, ensuring convergence using non-smooth analysis and Filippov solutions, with verified simulations.

Contribution

It proposes novel distributed discontinuous control protocols for finite-time attitude synchronization using vectorized signum functions.

Findings

Almost global convergence achieved

Finite-time convergence conditions established

Simulation verifies control performance

Abstract

The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper.