Optimization of model predictive and inversive guidance control with waypoint constraints

To meet the requirements of mission scenarios such as space rendezvous and docking, formation configuration, on-orbit services, and maneuvering avoidance, it is necessary to optimize the guidance trajectory and control process during continuous low-thrust relative guidance in space, where the initial and final states are specified, and several intermediate waypoints must be traversed. The goal is to obtain optimal fuel consumption for the spacecraft by determining a reasonable passing sequence, passing time, and passing speed. In discrete-time systems, based on the system dynamics state transition model, variable substitution and progressive iteration methods are used to represent the unknown relative velocity of the waypoint using known states and the guidance control sequence to be solved. Combined with the generalized inverse least squares solution, the optimal control sequence under the global two norm condition is obtained. Then, a model prediction and inversion guidance control method for spatial relative guidance under time and waypoint position constraints is designed. To further optimize fuel consumption during the guidance process, a genetic algorithm is used to search for the optiaml sequence and timing of passing through each waypoint. The simulation results of near circular orbit rendezvous guidance control show that the proposed method can achieve fuel consumption optimization in high-precision, smooth relative guidance control processes under conditions of constrained/unconstrained waypoint sequence and passage time in three scenarios related to passage time and sequence.