Tightly-Coupled Estimation and Guidance for Robust Low-Thrust Rendezvous via Adaptive Homotopy

Abstract

Minimum-fuel low-thrust rendezvous guidance yields bang-bang control structures highly sensitive to estimation errors, sensor anomalies, and solver regularization, making aggressive closed-loop execution brittle for uncooperative proximity operations. This paper proposes a tightly-coupled estimation and guidance architecture where navigation confidence directly modulates the homotopy parameter of a receding-horizon indirect optimal control solver. Relative motion is modeled in the Clohessy-Wiltshire frame. The translational state is estimated via a linear Kalman filter augmented by a Multiple Tuning Factors (MTF) covariance inflation mechanism that suppresses suspicious innovation directions. A composite score from the normalized innovation and MTF activity is mapped online to the homotopy parameter, allowing the controller to relax toward a smoother, conservative regime when confidence degrades, and recover fuel-efficient bang-bang control as sensing improves. Numerical results under severe measurement degradation show fixed bang-bang guidance remains brittle; both plain-KF and MTF-KF fixed-epsilon controllers yield large terminal miss distances. Conversely, the proposed MTF-adaptive homotopy controller reduces terminal miss by roughly two orders of magnitude, from hundreds of meters to sub-meter levels, requiring only a moderate increase in control effort versus the open-loop fuel-optimal benchmark. A comparison indicates adaptive homotopy is the dominant robustness mechanism, while MTF provides additional accuracy and efficiency improvements. The receding-horizon implementation exhibits consistently fast and reliable solution times, supporting the practical online viability of the proposed method.