CIKAN: Constraint Informed Kolmogorov-Arnold Networks for Autonomous Spacecraft Rendezvous using Time Shift Governor

TL;DR

The study tackles constraint enforcement in spacecraft rendezvous by learning the optimal time-shift mapping for a Time Shift Governor (TSG). It introduces Constraint-Informed Kolmogorov-Arnold Networks (CIKAN) to approximate the TSG mapping $\pi^{\ast}$, leveraging Kolmogorov-Arnold Networks and log-transform loss for improved learning of small shifts. Empirical results in highly elliptic orbit rendezvous show that CIKAN-based TSG achieves competitive accuracy with lower model complexity and faster inference than MLP-based CINNs, while satisfying LoS, thrust, and velocity constraints and reducing Delta V. The findings indicate that integrating constrained control with KAN-based predictors can enhance online performance and fuel efficiency in space missions, with future work needed on convergence guarantees and broader scenario generalization.

Abstract

The paper considers a Constrained-Informed Neural Network (CINN) approximation for the Time Shift Governor (TSG), which is an add-on scheme to the nominal closed-loop system used to enforce constraints by time-shifting the reference trajectory in spacecraft rendezvous applications. We incorporate Kolmogorov-Arnold Networks (KANs), an emerging architecture in the AI community, as a fundamental component of CINN and propose a Constrained-Informed Kolmogorov-Arnold Network (CIKAN)-based approximation for TSG. We demonstrate the effectiveness of the CIKAN-based TSG through simulations of constrained spacecraft rendezvous missions on highly elliptic orbits and present comparisons between CIKANs, MLP-based CINNs, and the conventional TSG.

Figures (4)

• Figure 1: Reference trajectory tracking using a CIKAN-based model: TSG employs the output of the CIKAN-based model to guide the system The nominal controller stabilizes to the virtual reference, $X_{v}$, which guides the system state, $X_d$,
• Figure 2: (a) The reference highly elliptic orbit, and (b) a sample RPO mission, expressed in the inertial frame.
• Figure 3: Simulations of extreme cases and Monte Carlo runs using various models: (a) Relative trajectories of Deputy spacecraft expressed in the VNB frame and Time histories of (b) time shift parameter $t_{\rm shift}$, (c) mean of time shift $\mathbb{E}[t_{\rm shift}]$, (d) relative distance, and (e) relative velocity of the Deputy spacecraft with respect to the Chief spacecraft.
• Figure 4: Time histories of (a) LoS cone constraints; (b) thrust magnitude limit; (c) approach velocity limit.