Closed-loop powered-coast-powered predictive guidance for spacecraft rendezvous with non-singular terminal sliding mode steering

The present study aims to present a guidance algorithm based on the relative motion prediction for orbital rendezvous, in which a coast phase is allowed between two powered phases. In both powered phases, the solution of the Hill-Clohessy-Wiltshire equations is used to find the required state variables at each time instant. To track the required trajectory and compensate for any orbital perturbations and uncertainties, a non-singular terminal sliding mode method is utilized as the steering law. Then, the finite time convergence of the state variables is mathematically proved. In addition, the starting time of the second powered phase is adapted to perturbations and uncertainties by another closed-loop algorithm during the coast phase. The prediction of the relative state variables along with the inclusion of a coast phase decreases the fuel consumption, while the last powered phase is responsible for the exactness of the terminal rendezvous. Numerical simulations indicate that the proposed guidance and steering laws result in reduced fuel consumption, exactness of the final conditions, and robustness in the presence of disturbances and model uncertainties.