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

Franek Stark, Jakob Middelberg, Shubham Vyas

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.

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

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.
Paper Structure (7 sections, 7 equations, 5 figures, 3 tables)

This paper contains 7 sections, 7 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System Description
  3. Controllers
  4. Efficiency Analysis
  5. Evaluation on the Real System
  6. Discussion
  7. Conclusion

Figures (5)

  • Figure 1: Sketch (left) of the free-floating platform (right)
  • Figure 2: Average position error after reaching and while staying at the target position (left) and time to reach the target position (right) for all compared controllers plotted over the average thrust usage. Single experiments are indicated by small dots, and the Pareto-optimal experiments for all controllers are depicted by solid lines.
  • Figure 3: Average orientation of all controllers after reaching and while doing station-keeping.
  • Figure 4: Carrying out experiments at the ORGL - Images show the transition of the platform from the starting point to the origin in reading direction
  • Figure 5: Resulting trajectory of under control of the and the binary informed . The left plot shows the whole trajectory along with the small height variations of the otherwise flat floor, which introduce disturbances. The right plots zoom into the limit cycle at the target.