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Control of Decommissioned Satellites and Space Debris Using CubeSats with Ion Electrospray Engines

Felix Biertümpfel, Peter Seiler, Paulo Lozano, Harald Pfifer

arXiv:2608.30215v1eess.SY

TL;DR

Increasing LEO debris and stricter deorbiting requirements create a need for effective control of decommissioned satellites. This paper proposes robust μ-synthesis attitude control using attached CubeSats with staged iESE thrusters, demonstrating stabilization and basic attitude maneuvers in nonlinear simulations despite modeled uncertainties.

  • Problem

    Attitude control of attached CubeSat–debris systems is challenging because torque authority is limited and debris dynamics, flexible appendages, residual fuel, damage, and docking positions are uncertain.

  • Method

    The paper designs a μ-synthesis attitude controller for a combined satellite–CubeSat system, explicitly modeling dynamic uncertainty and external disturbance torques.

  • Results

    0.6 deg maximum absolute tracking error was obtained during a nominal slew completed in 1228 s using 2.8 · 10^-4 kg of fuel.

  • Takeaways & Limitations

    Coordinated CubeSats using only their staged iESE main thrusters can stabilize debris and perform basic attitude maneuvers needed for later orbital mitigation operations.

Abstract

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The emergence of the New Space era has led to a rapidly increasing number of satellites in Low Earth Orbit (LEO). Consequently, more stringent deorbiting requirements have recently been imposed to avoid the Kessler syndrome in LEO. This has resulted in the proposal of new concepts for space debris removal, including attaching CubeSats to space debris as a promising mitigation strategy. The initial phase of this strategy involves stabilizing and controlling the debris' attitude. This paper proposes an attitude control design for decommissioned satellites using attached CubeSats with staged ion electrospray engines (iESE). The compact design of iESE combined with staging provides increased reliability and mission durations. The large uncertainty in the dynamics of the combined system, i.e. satellite and attached CubeSats, poses a significant challenge to the control design. The approach taken here uses the robust control framework, specifically $μ$-synthesis, to tackle this challenge. The feasibility of the approach is demonstrated on a decommissioned satellite with multiple flexile appendages.

I. Introduction

The paper proposes attaching CubeSats equipped with staged ion electrospray engines to decommissioned satellites or debris for coordinated attitude and orbit control. This approach addresses increasingly stringent debris-mitigation requirements while using robust control to manage uncertain combined-system dynamics.

  • Approximately 40% of retired LEO satellites failed to fulfill the 25-year deorbiting requirement, motivating stricter mitigation requirements.
  • CubeSats offer a cost-effective alternative to large, complex motherships for active space-debris removal.
  • The proposed concept attaches a swarm of CubeSats to debris and uses coordinated iESE thrust for stabilization, attitude control, and orbit control.
  • Throttable, jitter-free, fuel-efficient iESEs provide both thrust and torque, avoiding reaction wheels and enabling staged redundancy.
  • The control architecture is used for deorbiting and may also support satellite lifetime extension when fuel depletion limits existing control functions.
  • The paper models a representative sub-1000 kg decommissioned satellite and designs a μ-framework attitude controller that explicitly accounts for model uncertainty.

II. Space Debris Attitude Control Problem

The combined debris–CubeSat system requires precise attitude control despite limited torque authority and uncertain satellite, appendage, and docking dynamics. The paper models a flexible satellite and coordinated CubeSat swarm as the basis for robust control.

  • II. Space Debris Attitude Control Problem: The mission uses rideshare deployment into LEO, followed by swarm rendezvous, final approach, and docking with the target debris.
  • II. Space Debris Attitude Control Problem: Limited torque authority and uncertain combined-system dynamics make precise attitude control a central challenge for later debris-mitigation phases.
  • II. Space Debris Attitude Control Problem: The target is modeled as a nearly circular 685 km LEO satellite with a rigid center body and two symmetrical flexible solar arrays.
  • II. Space Debris Attitude Control Problem: Each solar array is modeled as a cantilever beam with three flexible modes and dimensions of 2 m by 2.5 m.
  • II. Space Debris Attitude Control Problem: The flexible-mode model uses damping factor ζ = 0.005 and natural frequencies of 5.6, 19.3, and 35.4 rad/s.
  • II. Space Debris Attitude Control Problem: Because the satellite is decommissioned, solar-array modal parameters are treated as constant but uncertain and depend generally on array angle.

C. External Disturbances

The attitude model includes external disturbance torques from solar radiation pressure, aerodynamics, gravity gradients, and the magnetic field. Their worst-case amplitudes are summarized in Table 1 and combined into sine-shaped disturbances for analysis.

  • C. External Disturbances: Four modeled disturbance sources are solar radiation pressure, aerodynamic torque, gravity-gradient torque, and magnetic-field torque.
  • C. External Disturbances: The individual disturbance contributions are computed using a three-dimensional spacecraft geometry and standard space-environment models.
  • C. External Disturbances: Table 1 summarizes the maximum amplitude of each disturbance torque about any axis for the modeled satellite geometry.
  • C. External Disturbances: For simplicity, the analysis assumes identical sine-shaped disturbances about each axis, with amplitudes equal to summed individual worst-case values.

D. CubeSats with Ion Electrospray Engines

The proposed CubeSat uses a staged electrospray-thruster architecture based on the STEP-1 3U design. Staging and electrospray operation provide compact, redundant, throttleable actuation for the debris-control concept.

  • D. CubeSats with Ion Electrospray Engines: The exemplary CubeSat design follows the MIT Space Propulsion Laboratory’s 3U STEP-1 electrospray-thruster demonstrator.
  • D. CubeSats with Ion Electrospray Engines: Each CubeSat is assumed to have a mass of 3.5 kg and three electrospray-thruster stages.
  • D. CubeSats with Ion Electrospray Engines: Each stage contains 32 electrospray thrusters, produces 0.64 mN total thrust, and has a specific impulse of I_sp = 1000 s.
  • D. CubeSats with Ion Electrospray Engines: Electrospray thrusters provide near-instantaneous thrust, continuous throttling, and minimal structural jitter, while firing and payload operation require approximately 10 W.

E. Combined System

The combined system consists of a decommissioned satellite with rigidly attached CubeSats whose staged iESEs provide control authority and orbital maneuver capability. Modeling assumes rigid attachment, negligible CubeSat-array dynamics, and sufficient torque and Δv for mission operations.

  • CubeSats are assumed rigidly attached to the satellite center body using docking mechanisms such as mechanical, magnetic, or electro-adhesion grippers.
  • The control torque around each axis is at least 2.8 times the worst-case disturbance torque, guaranteeing positive total control torque.
  • The combined system has a total mass of 668 kg and its rigid center-body dynamics follow standard Newton equations.
  • CubeSat solar-array effects are neglected because they do not add additional dynamics to the combined system.
  • 125 m/s maximum Δv is achievable using all stages, full fuel, and rotation to exploit CubeSats attached on all debris faces.A single iESE stage provides 6.8 m/s, while all three stages provide approximately 20 m/s without exploiting all attached CubeSats.

A. Linearized System Dynamics

The attitude-control model linearizes the nonlinear combined satellite dynamics and represents parameter variation as structured uncertainty. The uncertainty set covers mass, inertia, solar-array geometry, and flexible-mode frequency variation through an LTI shaping model.

  • Ten states describe the linearized combined-system dynamics: six rigid-motion states and four flexible-mode states.Only rotational motion is considered for the attitude-control design.
  • Four uncertainty sources are modeled: total inertia, total mass, solar-array angle, and the first solar-array bending-mode frequency.
  • CubeSat placement and mean-axis alignment produce approximately ±17% relative uncertainty in each rotational-axis inertia.CubeSats may be placed between 0% and 20% of the relative distance to the respective edge, with nominal placement at 10%.
  • The input uncertainty model represents the plant as nominal dynamics Pc plus an LTI uncertainty Δ with ∥Δ∥∞≤1 shaped by an LTI filter W.The shaping filter is fitted using 200 randomly generated models, including corner cases, and a second-order transfer matrix.
  • The uncertain plant is expressed through the upper linear fractional transformation PΔ = Fu(P, Δ), where P contains Pc and W.

C. Controller Synthesis

The controller is synthesized using robust mixed-sensitivity design to satisfy performance objectives across the modeled plant uncertainty. Dynamic weights encode bandwidth and roll-off requirements, while static scalings trade tracking accuracy against control effort.

  • The μ-synthesized controller is designed to achieve specified performance objectives for all uncertainties defined in the uncertain plant model.The design uses the H∞ framework, where a norm no greater than one indicates that imposed requirements are fulfilled.
  • Dynamic weights represent bandwidth and roll-off requirements, while memoryless scaling matrices provide quantitative controller tuning.
  • The control-sensitivity weight rolls off beyond 3.75 rad/s to separate controller bandwidth from the first flexible mode at 5.6 rad/s.This separation is intended to avoid exciting the flexible mode.
  • The scaling matrices Ve and Vu trade tracking accuracy against control effort using allowable attitude errors and actuator inputs.
  • γ = 1 is achieved for the full modeled uncertainty range, and balanced truncation reduces the controller order from 52 to 25.The reduced-order controller is verified with musynperf to retain the same robust performance.

IV. Controller Evaluation

The closed-loop evaluation uses a nonlinear Simulink model of the combined system and robust controller to assess two attitude maneuvers. These maneuvers represent reorientation before deorbiting and maintaining a prescribed attitude before orbital maneuvers.

  • The nonlinear closed-loop system is implemented in Matlab Simulink using SDTlib for performance analysis.
  • A slewing maneuver evaluates reorientation of the debris before deorbiting.
  • A line-of-sight tracking maneuver evaluates maintaining the debris in a prescribed attitude before orbital maneuvering.

A. Slew Maneuver

The 180° slew maneuver is completed under external disturbances, with robust simulations showing only small tracking degradation across uncertain combined-system dynamics.

  • A. Slew Maneuver: A 180° reference slew about the z axis is performed under 0.7 mNm sinusoidal disturbances on all body axes.The disturbance period equals the satellite’s 98.5-minute orbital period.
  • A. Slew Maneuver: 0.6 deg is the maximum absolute tracking error for the nominal system, occurring during a brief torque saturation midway through the slew.
  • A. Slew Maneuver: 1228 s is the completion time for the slew, requiring 2.8 · 10^-4 kg of total fuel.
  • A. Slew Maneuver: The maneuver reduces the available Δv budget for follow-up maneuvers by less than 0.1 m/s.
  • A. Slew Maneuver: Across 256 corner-case simulations, tracking performance degrades only slightly, while control-torque variation is larger and mainly reflects inertia-matrix perturbations.

B. Line-of-Sight Maneuver

The study evaluates satellite pointing over one orbit under external disturbances and compares attitude errors and commanded torques with their requirements and limits. The simulations indicate robust performance sufficient for stabilizing and reorienting space debris.

  • B. Line-of-Sight Maneuver: Pointing performance is evaluated over one orbit about all axes while tracking a zero reference under external disturbances.The assessment uses a stringent 60 arcsec pointing-error requirement to test precision tracking.
  • B. Line-of-Sight Maneuver: Figure 4 compares Φ, Θ, and Ψ pointing errors with the requirement and commanded torques with axis-specific torque limits.
  • B. Line-of-Sight Maneuver: The variation is not notable, indicating good robust performance of the control system.
  • B. Line-of-Sight Maneuver: Nonlinear simulations show that coordinated CubeSats using staged ion electrospray engines can stabilize debris and perform basic attitude maneuvers.Stabilization and reorientation are identified as crucial for orbital maneuvers supporting complex debris-mitigation tasks.
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