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.

翻译：二进制开关推进器常用于航天器在近距离操作期间的姿态与位置控制。然而，其离散特性对传统连续控制方法构成挑战。此类离散执行器的控制问题，要么被明确表述为混合整数优化问题，要么采用双层方法处理（即通过Delta-Sigma调制等模数转换技术将连续控制器的输出转换为二进制指令）。本文首次系统比较了这两种二进制推进器控制范式，对比了结合Delta-Sigma调制的连续模型预测控制（MPC）与直接混合整数模型预测控制（MIMPC）方法。此外，我们针对二进制驱动系统提出了一种新的MPC变体，该变体利用了Delta-Sigma调制器的状态信息。通过使用欧空局REACSA平台进行的大量仿真，对连续MPC的两种变体以及MIMPC进行了评估。结果表明，虽然所有方法在高推力区域性能相近，但MIMPC在低推力条件下实现了更优的燃料效率。带调制的连续MPC在较高推力水平下表现出不稳定性，而结合了调制器动力学的二进制信息型MPC则增强了鲁棒性，并缩小了与MIMPC之间的效率差距。从仿真与真实系统实验可以看出，MIMPC在稳定性与燃料效率方面具有显著优势，尤其适用于资源受限的任务；而连续控制方法对于计算能力有限的应用场景仍具吸引力。