Electromagnetic Formation Flying Using Alternating Magnetic Field Forces and Control Barrier Functions for State and Input Constraints

TL;DR

This paper introduces a feedback control algorithm for electromagnetic satellite formation flying that ensures state and input constraints are satisfied by combining alternating magnetic forces, optimal control, and control barrier functions.

Contribution

It proposes a novel control method integrating alternating magnetic forces with barrier functions to handle constraints in electromagnetic satellite formation flying.

Findings

Successful numerical simulation demonstration

Effective decoupling of electromagnetic forces between satellites

Constraint satisfaction in formation control

Abstract

This article presents a feedback control algorithm for electromagnetic formation flying with constraints on the satellites' states and control inputs. The algorithm combines several key techniques. First, we use alternating magnetic field forces to decouple the electromagnetic forces between each pair of satellites in the formation. Each satellite's electromagnetic actuation system is driven by a sum of amplitude-modulated sinusoids, where amplitudes are controlled in order to prescribe the time-averaged force between each pair of satellites. Next, the desired time-averaged force is computed from a optimal control that satisfies state constraints (i.e., no collisions and an upper limit on intersatellite speeds) and input constraints (i.e., not exceeding satellite's apparent power capability). The optimal time-averaged force is computed using a single relaxed control barrier function that is obtained by composing multiple control barrier functions that are designed to enforce each state and input constraint. Finally, we demonstrate the satellite formation control method in numerical simulations.