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arxiv: 2603.19796 · v3 · submitted 2026-03-20 · 📡 eess.SY · cs.RO· cs.SY

Mixed-Integer vs. Continuous Model Predictive Control for Binary Thrusters: A Comparative Study

Franek Stark , Jakob Middelberg , Shubham Vyas This is my paper

Pith reviewed 2026-05-15 08:42 UTC · model grok-4.3

classification 📡 eess.SY cs.ROcs.SY
keywords binary thrustersmodel predictive controlmixed integer MPCDelta-Sigma modulationspacecraft attitude controlfuel efficiencystability
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The pith

Mixed-integer MPC for binary thrusters achieves better fuel efficiency and stability than continuous MPC with modulation in low-thrust spacecraft maneuvers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper systematically compares continuous model predictive control, which relies on modulation to produce binary thruster commands, against direct mixed-integer model predictive control for handling on/off thrusters in spacecraft proximity operations. It also tests a variant of the continuous approach that incorporates information from the modulator into the prediction model. The comparison, conducted via simulations and experiments on ESA's REACSA platform, reveals that while performance is comparable at high thrust demands, the mixed-integer method excels in fuel savings during low-thrust conditions and maintains stability where the continuous method can become unstable. The findings highlight trade-offs between computational demands and control performance for resource-constrained space missions.

Core claim

The central claim is that MIMPC offers complete stability and superior fuel efficiency benefits compared to continuous MPC approaches for binary actuated systems, particularly in low-thrust regimes relevant to proximity operations. Continuous MPC with Delta-Sigma modulation exhibits instabilities at higher thrust levels, but a binary-informed MPC variant that accounts for modulator dynamics reduces this gap and improves robustness. These results are supported by extensive simulations and real-system experiments on the REACSA platform.

What carries the argument

Mixed-Integer Model Predictive Control (MIMPC), which formulates the optimization problem to directly select binary on/off thruster commands, in contrast to continuous MPC whose output is post-processed by Delta-Sigma modulation to generate binary signals.

If this is right

  • MIMPC achieves superior fuel efficiency in low-thrust conditions.
  • Continuous MPC with modulation can show instabilities at higher thrust levels.
  • Binary informed MPC improves robustness and reduces the efficiency gap to MIMPC.
  • Continuous control methods remain attractive for computationally limited applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The fuel savings from MIMPC could allow longer mission durations or reduced propellant mass in orbital proximity tasks.
  • Future work might explore hybrid solvers that switch between methods based on thrust demand to balance computation and performance.
  • Similar comparisons could apply to other discrete control problems such as in robotics with on/off actuators.

Load-bearing premise

The simulations and experiments on the REACSA platform fully capture the dominant dynamics, disturbances, and hardware effects of binary thrusters in real orbital operations.

What would settle it

Observing either equivalent fuel efficiency between MIMPC and continuous methods in additional low-thrust tests or unexpected instability in MIMPC during high-thrust maneuvers would challenge the reported advantages.

read the original abstract

Binary on/off thrusters are commonly used for spacecraft attitude and position control during proximity operations. However, their discrete nature poses challenges for conventional continuous control methods. The control of these discrete actuators is either explicitly formulated as a mixed-integer optimization problem or handled in a two-layer approach, where a continuous controller's output is converted to binary commands using analog-to digital modulation techniques such as Delta-Sigma-modulation. This paper provides the first systematic comparison between these two paradigms for binary thruster control, contrasting continuous Model Predictive Control (MPC) with Delta-Sigma modulation against direct Mixed-Integer MPC (MIMPC) approaches. Furthermore, we propose a new variant of MPC for binary actuated systems, which is informed using the state of the Delta-Sigma Modulator. The two variations for the continuous MPC along with the MIMPC are evaluated through extensive simulations using ESA's REACSA platform. Results demonstrate that while all approaches perform similarly in high-thrust regimes, MIMPC achieves superior fuel efficiency in low-thrust conditions. Continuous MPC with modulation shows instabilities at higher thrust levels, while binary informed MPC, which incorporates modulator dynamics, improves robustness and reduces the efficiency gap to the MIMPC. It can be seen from the simulated and real-system experiments that MIMPC offers complete stability and fuel efficiency benefits, particularly for resource-constrained missions, while continuous control methods remain attractive for computationally limited applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript conducts a systematic comparison of continuous Model Predictive Control (MPC) with Delta-Sigma modulation against direct Mixed-Integer MPC (MIMPC) for spacecraft attitude and position control using binary on/off thrusters. It introduces a binary-informed MPC variant that augments the prediction model with modulator state. Evaluations via extensive simulations and hardware-in-the-loop experiments on ESA's REACSA platform show that all methods perform similarly at high thrust, but MIMPC yields superior fuel efficiency at low thrust, while continuous MPC exhibits instabilities at higher levels and the informed variant improves robustness and narrows the efficiency gap.

Significance. If the empirical ordering holds, the work supplies actionable guidance on controller selection for binary-actuated proximity operations, quantifying the fuel-efficiency and stability advantages of MIMPC against the computational simplicity of continuous methods. Credit is due for the explicit plant models, cost-function formulations, modulator-state augmentation, tabulated fuel-consumption and settling-time metrics across thrust regimes, and the combination of simulation plus real-system experiments on a relevant platform.

minor comments (3)
  1. The abstract would benefit from a single sentence containing the key quantitative deltas (e.g., fuel-consumption reduction percentages or settling-time ratios) that are already tabulated in the results section, improving immediate accessibility for readers.
  2. Figure captions and legends should explicitly label the thrust-level cases (low/medium/high) and distinguish the three controller variants to avoid ambiguity when the plots are viewed in isolation.
  3. A brief statement on the number of Monte-Carlo runs or statistical significance of the reported fuel and stability differences would strengthen the empirical claims without altering the central narrative.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the thorough and positive review of our manuscript, including the recognition of our systematic comparison, the modulator-informed MPC variant, and the combination of simulation and hardware-in-the-loop experiments on the REACSA platform. We are pleased that the work is viewed as providing actionable guidance for controller selection in binary-actuated proximity operations. We address the report below and confirm that the minor revision will incorporate any clarifications needed.

Circularity Check

0 steps flagged

No significant circularity: empirical comparison of control architectures

full rationale

The manuscript is a direct empirical comparison of MIMPC, continuous MPC with Delta-Sigma modulation, and a binary-informed MPC variant on the REACSA platform. It supplies explicit plant models, cost-function formulations, modulator state augmentation, and tabulated fuel-consumption/settling-time metrics across thrust levels. No derivation step reduces by the paper's own equations to a fitted parameter renamed as prediction, nor does any central claim rest on a self-citation chain that is itself unverified. All performance statements are grounded in simulation and hardware-in-the-loop results under stated assumptions, making the work self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; typical MPC modeling assumptions are implicit but no explicit free parameters, invented entities, or ad-hoc axioms are stated in the provided text.

axioms (1)
  • domain assumption Accurate plant model and bounded disturbances are available for the REACSA platform
    Standard prerequisite for any MPC formulation used in the comparison.

pith-pipeline@v0.9.0 · 5561 in / 1433 out tokens · 49238 ms · 2026-05-15T08:42:55.872445+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

  1. [1]

    Aiaa, 1998

    Bong Wie.Space vehicle dynamics and control. Aiaa, 1998

    work page 1998

  2. [2]

    Afeasiblestudyonthemodelpredictivecontrolfordockingapproachofsmallspacecraft using thrusters and a control moment gyro

    KatsuyoshiTsujita. Afeasiblestudyonthemodelpredictivecontrolfordockingapproachofsmallspacecraft using thrusters and a control moment gyro. In2023 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), pages 696–701, June 2023. doi:10.1109/AIM46323.2023.10196262

    work page doi:10.1109/aim46323.2023.10196262 2023

  3. [3]

    Satpute, Christoforos Kanellakis, Ilias Tevetzidis, Jakub Haluska, Per Bodin, and George Nikolakopoulos

    Avijit Banerjee, Sumeet G. Satpute, Christoforos Kanellakis, Ilias Tevetzidis, Jakub Haluska, Per Bodin, and George Nikolakopoulos. On the Design, Modeling and Experimental Verification of a Floating Satel- lite Platform.IEEE Robotics and Automation Letters, 7(2):1364–1371, Apr. 2022. ISSN:2377-3766. doi:10.1109/LRA.2021.3140134

    work page doi:10.1109/lra.2021.3140134 2022

  4. [4]

    Spacecraft Thruster Control via Sigma–Delta Modulation.JournalofGuidance,Control,andDynamics,40(11):2928–2933,Nov.2017

    Richard Zappulla, Josep Virgili-Llop, and Marcello Romano. Spacecraft Thruster Control via Sigma–Delta Modulation.JournalofGuidance,Control,andDynamics,40(11):2928–2933,Nov.2017. ISSN:0731-5090. doi:10.2514/1.G002986

    work page doi:10.2514/1.g002986 2017

  5. [5]

    Meeting-merging-mission: A multi- robot coordinate framework for large-scale communication-limited exploration

    Anton Bredenbeck, Shubham Vyas, Martin Zwick, Dorit Borrmann, Miguel Olivares-Mendez, and Andreas Nüchter. Trajectory Optimization and Following for a Three Degrees of Freedom Overactuated Floating Platform. In2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 4084–4091, July 2022. doi:10.1109/IROS47612.2022.9981294

    work page doi:10.1109/iros47612.2022.9981294 2022

  6. [6]

    A Hybrid Model Predictive Control Approach to Attitude Control with Minimum-Impulse-Bit Thrusters

    Pantelis Sopasakis, Daniele Bernardini, Hans Strauch, Samir Bennani, and Alberto Bemporad. A Hybrid Model Predictive Control Approach to Attitude Control with Minimum-Impulse-Bit Thrusters. pages 2079– 2084, July 2015. doi:10.1109/ECC.2015.7330846

    work page doi:10.1109/ecc.2015.7330846 2079

  7. [7]

    All-Electric Spacecraft PrecisionPointingUsingModelPredictiveControl.JournalofGuidance,Control,andDynamics,38(1):161– 168, 2015

    Mirko Leomanni, Andrea Garulli, Antonio Giannitrapani, and Fabrizio Scortecci. All-Electric Spacecraft PrecisionPointingUsingModelPredictiveControl.JournalofGuidance,Control,andDynamics,38(1):161– 168, 2015. ISSN:0731-5090. doi:10.2514/1.G000347

    work page doi:10.2514/1.g000347 2015

  8. [8]

    Linear Model Predictive Control for a planar free-floating platform: A comparison of binary input constraint formulations

    Franek Stark, Shubham Vyas, Georg Schildbach, and Frank Kirchner. Linear Model Predictive Control for a planar free-floating platform: A comparison of binary input constraint formulations. InProceedings of 17th Symposium on Advanced Space Technologies in Robotics and Automation, volume 17, Leiden, The Netherlands, Oct. 2023. doi:10.48550/arXiv.2312.10788

    work page doi:10.48550/arxiv.2312.10788 2023

  9. [9]

    Mixed Integer Model Predictive Control for a free-floating platform with binary and continuous actuation

    Franek Stark, Shubham Vyas, Georg Schildbach, and Frank Kirchner. Mixed Integer Model Predictive Control for a free-floating platform with binary and continuous actuation. InProceedings of the 2024 {CEAS EuroGNC} conference, volume 2024, Bristol, UK, June 2024. doi:10.82124/CEAS-GNC-2024-013, https://eurognc.ceas.org/archive/EuroGNC2024/html/CEAS-GNC-2024...

    work page doi:10.82124/ceas-gnc-2024-013 2024

  10. [10]

    MartinZwick,IreneHuertas,LevinGerdes,andGuillermoOrtega. ORGL–ESA’sTestFacilityforApproach andContactoperationsinOrbitalandPlanetaryEnvironments.InProceedingsoftheInternationalSymposium onArtificialIntelligence,RoboticsandAutomationinSpace(i-SAIRAS),volume6,Madrid,Spain,June2018

    work page

  11. [11]

    REACSA: Actuated Floating Platform for Orbital Robotic ConceptTestingandControlSoftwareDevelopment

    Willem Suter, Gunter Just, and Marti Vilella. REACSA: Actuated Floating Platform for Orbital Robotic ConceptTestingandControlSoftwareDevelopment. InProceedingsof17thSymposiumonAdvancedSpace Technologies in Robotics and Automation 2023, volume 17, Scheltema, Leiden, The Netherlands, Oct. 2023

    work page 2023

  12. [12]

    Performance cost functions for a reaction-jet-controlled system during an on-off limit cycle

    Jerry Mendel. Performance cost functions for a reaction-jet-controlled system during an on-off limit cycle. IEEE Transactions on Automatic Control, 13(4):362–368, Aug. 1968. ISSN:1558-2523. Conference Name: IEEE Transactions on Automatic Control. doi:10.1109/TAC.1968.1098940

    work page doi:10.1109/tac.1968.1098940 1968

  13. [13]

    Pfetsch, Franziska Schlösser, Felipe Serrano, Yuji Shinano, Mark Turner, Stefan Vigerske, Dieter Weninger, and Lixing Xu

    SureshBolusani, MathieuBesançon, KseniaBestuzheva, AntoniaChmiela, JoãoDionísio, TimDonkiewicz, Jasper van Doornmalen, Leon Eifler, Mohammed Ghannam, Ambros Gleixner, Christoph Graczyk, Katrin Halbig, Ivo Hedtke, Alexander Hoen, Christopher Hojny, Rolf van der Hulst, Dominik Kamp, Thorsten Koch, Kevin Kofler, Jurgen Lentz, Julian Manns, Gioni Mexi, Erik M...

    work page 2024

  14. [14]

    coin-or/Clp: Release releases/1.17.10, Aug

    John Forrest, Stefan Vigerske, Ted Ralphs, Lou Hafer, jpfasano, Haroldo Gambini Santos, Jan-Willem, Matthew Saltzman, a andre, Bjarni Kristjansson, h-i gassmann, Alan King, Arevall, Bohdan Mart, Pierre Bonami, Ruan Luies, Samuel Brito, and to st. coin-or/Clp: Release releases/1.17.10, Aug. 2024. doi:10.5281/ZENODO.13347196,https://zenodo.org/doi/10.5281/z...

    work page doi:10.5281/zenodo.13347196 2024

  15. [15]

    Drake: Model-baseddesignandverificationforrobotics,2019

    RussTedrakeandDrake-Development-Team. Drake: Model-baseddesignandverificationforrobotics,2019. https://drake.mit.edu

    work page 2019