In this paper, a sampling-based stochastic model predictive control (SMPC) algorithm is proposed for discrete-time linear systems subject to both parametric uncertainties and additive disturbances. One of the main drivers for the development of the proposed control strategy is the need for reliable and robust guidance and control strategies for automated rendezvous and proximity operations between spacecraft. To this end, the proposed control algorithm is validated on a floating spacecraft experimental testbed, proving that this solution is effectively implementable in real time. Parametric uncertainties due to the mass variations during operations, linearization errors, and disturbances due to external space environment are simultaneously considered. The approach enables to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided. Moreover, the offline sampling approach in the control design phase shifts all the intensive computations to the offline phase, thus greatly reducing the online computational cost, which usually constitutes the main limitation for the adoption of SMPC schemes, especially for low-cost on-board hardware. Numerical simulations and experiments show that the approach provides probabilistic guarantees on the success of the mission, even in rather uncertain and noisy situations, while improving the spacecraft performance in terms of fuel consumption.

中文翻译：

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离线采样SMPC框架及其在自主空间机动中的应用

针对离散时间线性系统的参数不确定性和加性扰动，提出了一种基于样本的随机模型预测控制算法。提出的控制策略发展的主要驱动力之一是需要可靠和强大的制导和​​控制策略，以用于航天器之间的自动会合和近距操作。为此，所提出的控制算法在浮动航天器试验试验台上得到了验证，证明了该解决方案可以实时有效地实施。同时考虑了由于操作过程中的质量变化，线性化误差以及由于外部空间环境引起的干扰所引起的参数不确定性。当提供不确定变量的界限时，该方法能够适当地收紧约束，以确保鲁棒的递归可行性。此外，控制设计阶段的离线采样方法将所有密集计算转移到离线阶段，从而大大降低了在线计算成本，这通常是采用SMPC方案的主要限制，特别是对于低成本机载硬件。数值模拟和实验表明，该方法即使在相当不确定和嘈杂的情况下，也能为飞行任务的成功提供概率保证，同时在燃料消耗方面改善了航天器的性能。在控制设计阶段，离线采样方法将所有密集的计算转移到离线阶段，从而大大降低了在线计算成本，这通常是采用SMPC方案的主要限制，特别是对于低成本车载硬件。数值模拟和实验表明，该方法即使在相当不确定和嘈杂的情况下，也能为飞行任务的成功提供概率保证，同时在燃料消耗方面改善了航天器的性能。控制设计阶段的离线采样方法将所有密集的计算转移到离线阶段，从而大大降低了在线计算成本，这通常是采用SMPC方案的主要限制，特别是对于低成本车载硬件。数值模拟和实验表明，该方法即使在相当不确定和嘈杂的情况下，也能为飞行任务的成功提供概率保证，同时在燃料消耗方面改善了航天器的性能。