Learning Hamiltonian Dynamics with Bayesian Data Assimilation

In this paper, we develop a neural network-based approach for time-series prediction in unknown Hamiltonian dynamical systems. Our approach leverages a surrogate model and learns the system dynamics using generalized coordinates (positions) and their conjugate momenta while preserving a constant Hamiltonian. To further enhance long-term prediction accuracy, we introduce an Autoregressive Hamiltonian Neural Network, which incorporates autoregressive prediction errors into the training objective. Additionally, we employ Bayesian data assimilation to refine predictions in real-time using online measurement data. Numerical experiments on a spring-mass system and highly elliptic orbits under gravitational perturbations demonstrate the effectiveness of the proposed method, highlighting its potential for accurate and robust long-term predictions.

Constrained Control for Autonomous Spacecraft Rendezvous: Learning-Based Time Shift Governor

This paper develops a Time Shift Governor (TSG)-based control scheme to enforce constraints during rendezvous and docking (RD) missions in the setting of the Two-Body problem. As an add-on scheme to the nominal closed-loop system, the TSG generates a time-shifted Chief spacecraft trajectory as a target reference for the Deputy spacecraft. This modification of the commanded reference trajectory ensures that constraints are enforced while the time shift is reduced to zero to effect the rendezvous. Our approach to TSG implementation integrates an LSTM neural network which approximates the time shift parameter as a function of a sequence of past Deputy and Chief spacecraft states. This LSTM neural network is trained offline from simulation data. We report simulation results for RD missions in the Low Earth Orbit (LEO) and on the Molniya orbit to demonstrate the effectiveness of the proposed control scheme. The proposed scheme reduces the time to compute the time shift parameter in most of the scenarios and successfully completes rendezvous missions.

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

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.

Time Shift Governor for Constrained Control of Spacecraft Orbit and Attitude Relative Motion in Bicircular Restricted Four-Body Problem

This paper considers constrained spacecraft rendezvous and docking (RVD) in the setting of the Bicircular Restricted Four-Body Problem (BCR4BP), while accounting for attitude dynamics. We consider Line of Sight (LoS) cone constraints, thrust limits, thrust direction limits, and approach velocity constraints during RVD missions in a near rectilinear halo orbit (NRHO) in the Sun-Earth-Moon system. To enforce the constraints, the Time Shift Governor (TSG), which uses a time-shifted Chief spacecraft trajectory as a target reference for the Deputy spacecraft, is employed. The time shift is gradually reduced to zero so that the virtual target gradually evolves towards the Chief spacecraft as time goes by, and the RVD mission objective can be achieved. Numerical simulation results are reported to validate the proposed control method.