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：摘要：在空间近距离操作中，二进制开关式喷气推进器常用于航天器姿态与位置控制，但其离散特性对传统连续控制方法构成挑战。这类离散执行器的控制可通过两种范式实现：显式构建混合整数优化问题求解，或采用双层框架通过模数转换技术（如Delta-Sigma调制）将连续控制器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，重点对比了结合Delta-Sigma调制的连续模型预测控制（MPC）与直接混合整数MPC（MIMPC）方法。此外，我们提出一种针对二进制驱动系统的新型MPC变体，该变体利用Delta-Sigma调制器状态进行信息增强。通过利用欧空局REACSA平台进行大量仿真实验，评估了两种连续MPC变体与MIMPC的性能。结果表明：在高推力工况下各方法性能相近，但MIMPC在低推力条件下具有更优的燃料效率；采用调制策略的连续MPC在高推力水平下表现出不稳定性，而融入调制器动力学的二元信息增强MPC提升了鲁棒性并缩小了与MIMPC的效率差距。仿真与实物实验表明：尽管连续控制方法仍适用于计算资源受限场景，但MIMPC能提供完全稳定性和燃料效率优势，尤其适用于资源约束型任务。