发表机构
Laboratoire Jacques-Louis Lions（雅克-路易·利翁斯实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究对比四类MPC算法，基于CWH模型揭示长时域下快速MPC发散的原因，验证Tube MPC的鲁棒性与安全性，实现无外部库的核心例程，支持其作为星上实时航天器交会制导控制器。
AI 中文摘要
本报告研究并比较了四类用于自主航天器交会制导的模型预测控制（MPC）算法：线性MPC、Tube MPC、快速/嵌入式MPC以及逐次凸化（SCvx）。采用Clohessy-Wiltshire-Hill（CWH）相对运动模型，我们证明了底层动力学的边际稳定性会导致凝聚海森矩阵的条件数随预测时域急剧增大，这解释了为何基于梯度的求解器（如快速MPC）在长时域压力测试下会发散，而精确线性代数求解器（带Cholesky分解的ADMM）则不受影响。Tube MPC在五种标准交会机动（平移、R-bar、V-bar、自然运动环绕、螺旋运动）中采用单一固定控制器配置进行验证，并直接从代价权重矩阵推导得到了可证明正确的双侧最坏情况跟踪误差界。该框架还通过在线重新计算线性化扩展至跟踪任意非闭式参考轨迹，且全程保持安全保证。最后，为评估其在实际飞行软件中的可行性，核心数值例程（Cholesky分解和Riccati方程求解器）从基本原理出发重新实现，未使用外部库，并针对标准科学计算工具进行了机器精度验证。综合而言，这些结果支持Tube MPC成为用于星上实时航天器交会制导的鲁棒且计算可行的控制器。
英文摘要
This report studies and compares four families of Model Predictive Control (MPC) algorithms for autonomous spacecraft rendezvous guidance: Linear MPC, Tube MPC, Fast/Embedded MPC, and Successive Convexification (SCvx). Using the Clohessy-Wiltshire-Hill (CWH) relative-motion model, we show that the marginal stability of the underlying dynamics causes the condition number of the condensed Hessian to grow sharply with the prediction horizon, which explains why gradient-based solvers such as Fast MPC diverge under long-horizon stress tests while exact linear-algebra solvers (ADMM with Cholesky factorisation) remain unaffected. Tube MPC is validated across five standard rendezvous manoeuvres (Translation, R-bar, V-bar, Natural Motion Circumnavigation, and Corkscrew) using a single fixed controller configuration, and a two-sided, provably correct bound is derived to bracket the worst-case tracking error directly from the cost weight matrices. The framework is further extended to track an arbitrary, non-closed-form reference trajectory through online-recomputed linearisation, with the safety guarantee holding throughout. Finally, to assess feasibility for real flight software, the core numerical routines (Cholesky factorisation and the Riccati equation solver) are re-implemented from first principles, without external libraries, and validated against standard scientific computing tools to machine precision. Taken together, these results support Tube MPC as a robust and computationally realistic controller for onboard, real-time spacecraft rendezvous guidance.
Comments55 pages, 6 figures. Summer research internship report, Laboratoire Jacques-Louis Lions, Sorbonne Université
