Mixed Integer vs. Continuous Model Predictive Controllers for Binary Thruster Control: A Comparative Study

2026-03-20

AI Summary

This study addresses the challenge of controlling binary thrusters, whose discrete nature renders conventional continuous control strategies ineffective. The authors systematically compare Mixed-Integer Model Predictive Control (MIMPC) with a Delta-Sigma modulation-based continuous MPC approach and propose a novel state-aware method that explicitly incorporates the modulator’s internal state into the MPC formulation. Simulations and experiments conducted on ESA’s REACSA platform demonstrate that MIMPC significantly improves fuel efficiency under low-thrust conditions. Moreover, the proposed state-aware method enhances stability in high-thrust scenarios, effectively narrowing the performance gap with MIMPC. Overall, MIMPC exhibits superior stability and resource efficiency across operating regimes.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• binary thruster control
• mixed-integer optimization
• continuous control
• Model Predictive Control
• discrete actuators

Innovation

• Mixed-Integer MPC
• Binary Thruster Control
• Delta-Sigma Modulation
• Model Predictive Control
• Fuel Efficiency