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

TL;DR

This paper introduces an adaptive guidance method for low-thrust rendezvous that adjusts control strategies based on navigation confidence, significantly improving robustness and accuracy in degraded sensing conditions.

Contribution

It proposes a novel tightly-coupled estimation and guidance architecture using adaptive homotopy modulation based on navigation confidence, enhancing robustness and fuel efficiency.

Findings

Adaptive homotopy reduces terminal miss distance by two orders of magnitude.

The MTF mechanism improves estimation accuracy and control robustness.

The method maintains fast, reliable online solution times.

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.