Hierarchical differential correction based transfer trajectory design for halo orbit with multiple constraints

To cope with the orbit transfer problem with multiple constraints and sensitive initial values around the libration point L1 of the Sun-Earth system (SEL1 point), a transfer trajectory design method based on hierarchical differential corrections and initial value polynomial is proposed. At first, constraints are analyzed in the process of designing the transfer trajectory around the libration point. According to different terminal constraints, the hierarchical differential correction method is proposed by considering orbit altitude, orbit inclination, right ascension of ascending node and track angle simultaneously. Then, by analyzing relation between constraint variables and control variables, the initial value expression is got to solve the initial value problem of differential corrections. Finally, transfer trajectory from the earth parking orbit whose altitude is 200 km to Halo orbit around SEL1 point is designed under the condition of multi-constraints. The simulation results indicate the hierarchical differential correction method can deal with the problem with multiple constraints and initial value polynomial can provide appropriate initial conditions for differential corrections so as to guarantee convergence of the algorithm. In conclusion, this method has good practicality.