Trajectory correction for lunar flyby transfers to libration point orbits using continuous thrust

Trajectory corrections for lunar flyby transfers to Sun–Earth/Moon libration point orbits(LPOs)with continuous thrusts are investigated using an ephemeris model.The lunar flyby transfer has special geometrical and dynamical structures;therefore,its trajectory correction strategy is considerably different from that of previous studies and should be specifically designed.In this paper,we first propose a control strategy based on the backstepping technique with a dead-band scheme using an ephemeris model.The initial error caused by the launch time error is considered.Since the perturbed transfers significantly diverge from the reference transfers after the spacecraft passes by the Moon,we adopt two sets of control parameters in two portions before and after the lunar flyby,respectively.Subsequently,practical constraints owing to the navigation and propellant systems are introduced in the dynamical model of the trajectory correction.Using a prograde type 2 orbit as an example,numerical simulations show that our control strategy can efficiently address trajectory corrections for lunar flyby transfers with different practical constraints.In addition,we analyze the effects of the navigation intervals and dead-band scheme on trajectory corrections.Finally,trajectory corrections for different lunar flyby transfers are depicted and compared.

Near-optimal cumulative longitude low-thrust orbit transfer

The indirect method for the continuous low-thrust near minimum cumulative longitude orbit transfer problem is addressed.The movement of the satellite is described by the Gauss equation using the modified equinoctial elements and replacing time as the system independent variable by the cumulative longitude.The maximum principle is adapted to design the optimal control in order to minimize the final cumulative longitude, and the twopoint-boundary-value problem is derived from the orbit transfer problem.The single shooting method is applied in a numerical experiment, and the simulations demonstrate that the orbit transfer mission is fulfilled and the product of the maximal thrust and the minimum cumulative longitude is near constant.

Nash-equilibrium strategies of orbital TargetAttacker-Defender game with a non-maneuvering target

This study investigates the orbital Target-Attacker-Defender(TAD)game problem in the context of space missions.In this game,the Attacker and the Defender compete for a Target that is unable to maneuver due to its original mission constraints.This paper establishes three TAD game models based on the thrust output capabilities:unconstrained thrust output,thrust constrained by an upper bound,and fixed thrust magnitude.These models are then solved using differential game theory to obtain Nash equilibrium solutions for the game problems,and the correctness and effectiveness of the solution methods are verified through simulations.Furthermore,an analysis of the winning mechanisms of the game is conducted,identifying key factors that influence the game’s outcomes,including weight coefficients in payoffs,the maximum thrust acceleration limit,and the initial game state.Considering the unique characteristics of space missions,a specific focus is given to the analysis of the Defender’s initial states in the hovering formation and in-plane circling formation,revealing overall success patterns for defense strategies from these two formations.In summary,this study provides valuable insights into the control strategies and winning mechanisms of orbital TAD games,deepening our understanding of these games and offering practical guidance to improve success rates in real-world scenarios.

Research on hovering control scheme to non-circular orbit

An open-loop control system for hovering at any selected position on spacecraft orbit is first presented given that the satellite＇s engine provides continuous finite thrust. Actually, the hovering states are unstable considering perturbations and thrust errors, so a feedback sliding mode variable structure control, which is adaptive and chattering-free, is designed. Under this feedback control scheme, the high-frequency chattering phenomenon is avoided, while the system stays highly robust at the same time. Simulation results show that the feedback control thrusts are continuous and the steady-states error can be confmed to 10-4 m at the presence of uncertain perturbations. Finally, the feasibility of realizing hovering orbits is analyzed taking the ＂Moliya＂ and geosynchronous Earth orbit （GEO） satellites as examples.