Real-Time Optimal Control of a 6-DOF State-Constrained Close-Proximity Rendezvous Mission

A rendezvous mission with a tumbling space object has been studied by developing a novel three-phase mission design architecture which includes model and state uncertainties by utilizing Ensemble Optimal Control and warm-start Bellman Pseudospectral Optimal Control. Ensemble optimal control problem is solved via in-house developed Stochastic-Collocation based Ensemble Pseudospectral Optimal Control Software (SC-EPOCS) by modeling the uncertainties via samples generated by Conjugate Unscented Transformation based on the initial statistical distributions. Then, a new concept called checkpoints has been introduced to decide a feasible and optimal transition trajectory from uncertainty-aware trajectories to a deterministic optimal trajectory. This is achieved by conducting a reachability analysis for all ensembles and uncertainties. As a result, two Deep Neural Networks (DNNs), one for translational and other for the rotational motion, have been trained by utilizing initial costate values that correspond to optimal trajectories, starting from the checkpoints. By deriving costate dynamics for optimal trajectories, a warm-start algorithm is developed by applying Covector Mapping Theorem. Finally, Bellman Pseudospectral Optimal Control is applied in a Caratheodory-Pi sense by recursively solving an optimal control problem, subjected to state estimation errors. Results prove the feasibility, robustness, and optimality of the approach.