Multi-target Orbital Rendezvous Perturbed Trajectory Analytical Solution And Visiting Sequences Global Optimization

The global optimization of multi-spacecraft and multi-target perturbed orbit rendezvous is the key technology for the design of in-orbit service mission of constellation and active debris removal mission in the future.In this dissertation,a three-step framework is proposed to solve this problem efficiently,in which three basic problems are resolved in turn:fast estimation of velocity increment of orbit rendezvous with impulsive propulsion or electric propulsion,fast planning of order and rendezvous time for multi-target rendezvous sequences,and global optimization of target selection and multi-spacecraft target assignment with a large-scale candidate.The main results of this dissertation are as follows:1 Fast methods for analytical estimation and accurate trajectory optimization of perturbed impulsive orbit rendezvous are proposed.Based on the J₂ perturbation analytical dynamic equation and several reasonable approximations,the multi-impulse trajectory optimization problem is transformed into an equality constrained optimization problem（ECOP）with the changes in orbital elements as the variable.The relationship between the radial,tangential and normal components of the optimal four pulses and the orbital constraints are revealed.Then,a ten-parameter model is designed to express the optimal four-impulse trajectory.The accurate rendezvous trajectory can be solved using an iterative cycle including difference prediction and analytical parameters correction.The simulation results prove that the estimation method can quickly evaluate the velocity increment required for orbital rendezvous,and the results are accurate enough to be applied in the parametric optimization method as initial values.The methods adapt well to elliptical orbits of small eccentricity,and have good adaptability to both analytical dynamics and high-precision dynamic models.The efficiency is also better than previous methods.2 Fast methods for analytical estimation and accurate trajectory optimization of perturbed low-thrust orbit rendezvous are proposed.A fast estimation method for low thrust orbital rendezvous based on the approximate equivalent relationship between impulse and low-thrust propulsions using iteration method is proposed;The estimated results are then applied as a priori constraints of thrust to the indirect trajectory optimization considering J₂ perturbation,which can improve the efficiency of shooting process.Besides,a simplified thrust-switch model and an equality constrained optimization model are designed for circular orbit rendezvous to quickly obtain the optimal trajectory and control;To obtain the accurate trajectory efficiently,an analytical differences correction algorithm and corresponding iterative process are proposed.3 Efficient analytical gradient-guided non-linear programming method andmixed-encoding programming method for multi-target rendezvous sequence are proposed.Firstly,a non-linear programming algorithm guided by the analytical approximate gradient is designed for the multi-target sequential rendezvous problem with fixed rendezvous targets of a fixed order.Via the analysis of dynamic law,an analytical function of velocity increment for impulsive rendezvous depending on the rendezvous time and transfer duration is designed to derive the expression of gradient.The gradient information is then applied to the sequential quadratic programming algorithm and greatly improves the efficiency.Besides,for the optimization of multi-target rendezvous sequence with undetermined order,the proposed estimation methods for impulsive and low-thrust rendezvous are applied to the mixed-encoding differential evolution algorithm.The computational efficiency is proved by different simulation cases,and the results are better than other latest methods.4 A global optimization framework of rendezvous sequences in a large-scale target set is proposed.The global optimization of multi-spacecraft and multi-target rendezvous mission in a large target set is studied.The difficulty that gives consideration to both efficiency and accuracy is overcome by a multi-step approximation.Firstly,based on the effect of perturbation in low earth orbit,the optimization goal of rendezvous sequences is simplified to minimize the difference of RAAN instead of to minimize the propellant consumption.An integer optimization model is then decomposed from the original problem to reduce the complexity.On this basis,according to the characteristics of two typical global optimization problems,target-selection and target assignment to multi-spacecraft relationship,the evolutionary operators of genetic algorithm are customized based on orbit dynamic to accelerate the convergence.Finally,two widely studied numerical cases(problems of the 8^th Chinese Trajectory Optimization Competition and the 9^th Global Trajectory Optimization Competition)are tested and better solutions are obtained with higher efficiency.This dissertation creatively proposes fast methods of velocity increment estimation and trajectory optimization for perturbed orbit rendezvous based on equal constrained optimization,and designs a decomposed multi-step solving framework based on dynamic-guided evolutionary algorithm for optimization of large-scale rendezvous sequences.Consequently,the studies have certain theoretical significance.The systematic optimization method system for multi-target rendezvous sequences established in this dissertation can be well applied for the orbit design of missions such as space debris removal,in-orbit service of constellation and so on to reduce the fuel and time cost,which has important values of engineering application.