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：二元开关推进器常用于航天器在近距离操作过程中的姿态与位置控制。然而，其离散特性对传统连续控制方法构成了挑战。这些离散执行器的控制要么被明确表述为混合整数优化问题，要么通过双层方法处理——即利用Delta-Sigma调制等模数转换技术将连续控制器的输出转换为二元指令。本文首次系统比较了这两种二元推进器控制范式，对比了采用Delta-Sigma调制的连续模型预测控制（MPC）与直接混合整数MPC（MIMPC）方法。此外，我们针对二元驱动系统提出了一种新型MPC变体，该变体利用Delta-Sigma调制器状态进行信息更新。通过使用ESA的REACSA平台进行的广泛仿真，评估了连续MPC的两种变体与MIMPC的性能。结果表明：在所有方法在高推力区间表现相似的情况下，MIMPC在低推力条件下实现了更优的燃料效率。采用调制的连续MPC在较高推力水平下表现出不稳定性，而融合调制器动力学的二元信息增强型MPC则提升了鲁棒性，并缩小了与MIMPC的效率差距。从仿真与真实系统实验可见，MIMPC在资源受限型任务中具有完全的稳定性和燃油效率优势，而连续控制方法在计算能力受限的应用场景中仍具吸引力。