Constant thrust glideslope guidance algorithm for rendezvous in multi-body realm

A guidance algorithm for spacecraft approaching a target vehicle in a quasi-halo orbit in the real earth-moon system is presented. The algorithm is based on the numerical solution of the time-variant linearized relative dynamics of RTBP in inertial coordinates. The whole trajectory is divided into several segments. The multi-impulse glideslope idea, traditionally used in the near-earth rendezvous, is employed to obtain estimated velocity increment (delta-v) at the joint of two legs. The instantaneous delta-v, as a matter of fact, can not be implemented by any real engine because the thrust magnitude is always finite. Here, the obtained delta-v is translated into thrust duration in the context of a constant thrust magnitude, which is the most simple and robust type in real applications. Ignition and cutoff delays of the thruster are modeled. Current relative state is used to calculate the next delta-v and then flows to the following segment after thrusting in the delta-v direction for the transcribed time period. A thrusting arc is usually followed by a coast arc. The last segment is retuned by being further subdivided into another group of legs using updated control parameters, in order to counteract the strong nonlinearity in multi-body realm. The whole process ends after the last delta-v is dealt with. Simulation environment is established by using DE405 ephemeris, taking into account gravities of the earth, moon, sun, and all other planets. Monte Carlo analysis is conducted by considering the navigation error and the thrust direction error. Results show that the proposed guidance algorithm can effectively maintain control over the flight time with rather satisfactory final position and velocity accuracy.