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

2025-08-25

AI Summary

This paper addresses the tightly coupled multi-constraint problem in electromagnetic formation flying—namely, inter-satellite collision avoidance, upper bounds on relative velocity, and onboard apparent power limitations. To resolve these constraints synergistically, we propose a single-relaxation constrained cooperative control framework based on composite Control Barrier Functions (CBFs). Electromagnetic coupling dynamics are decoupled via alternating magnetic forces, and amplitude-modulated sinusoidal excitation is introduced to achieve continuous, time-averaged electromagnetic force tuning. State constraints (position and velocity) and input constraints (power) are uniformly encoded as CBF inequalities, with a slack variable incorporated to enable soft-constraint optimization. The approach enhances control freedom and real-time performance while rigorously ensuring safety. Numerical simulations demonstrate that the proposed method achieves high-precision, robust formation keeping and reconfiguration under stringent, tightly coupled multi-constraint conditions.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Satisfaction
• Intelligent Robots: Behavior Learning & Control
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Security and Privacy: Authentication, authorization, and access control
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• Decoupling electromagnetic forces between satellites using alternating fields
• Enforcing state and input constraints with control barrier functions
• Preventing collisions and power exceedance in satellite formations

Innovation

• Alternating magnetic field forces decouple electromagnetic forces
• Amplitude-modulated sinusoids control time-averaged inter-satellite forces
• Single control barrier function enforces state and input constraints