Constant-thrust glideslope guidance algorithm for time-fixed rendezvous in real halo orbit

This paper presents a fixed-time glideslope guidance algorithm that is capable of guiding the spacecraft approaching a target vehicle on a quasi-periodic halo orbit in real Earth–Moon system. To guarantee the flight time is fixed, a novel strategy for designing the parameters of the algorithm is given. Based on the numerical solution of the linearized relative dynamics of the Restricted Three-Body Problem (expressed in inertial coordinates with a time-variant nature), the proposed algorithm breaks down the whole rendezvous trajectory into several arcs. For each arc, a two-impulse transfer is employed to obtain the velocity increment (delta-v) at the joint between arcs. Here we respect the fact that instantaneous delta-v cannot be implemented by any real engine, since the thrust magnitude is always finite. To diminish its effect on the control, a thrust duration as well as a thrust direction are translated from the delta-v in the context of a constant thrust engine (the most robust type in real applications). Furthermore, the ignition and cutoff delays of the thruster are considered as well. With this high-fidelity thrust model, the relative state is then propagated to the next arc by numerical integration using a complete Solar System model. In the end, final corrective control is applied to insure the rendezvous velocity accuracy. To fully validate the proposed guidance algorithm, Monte Carlo simulation is done by incorporating the navigational error and the thrust direction error. Results show that our algorithm can effectively maintain control over the time-fixed rendezvous transfer, with satisfactory final position and velocity accuracies for the near-range guided phase.