| In the process of deep space exploration,humans have always been passionate about Mars,which has many similarities with the earth.In the Mars exploration mission,the design of the ground-fire transfer orbit is always a very important part.Meanwhile,because the low-thrust thruster has the characteristics of high fuel utilization,making the low-thrust transfer orbit one of the key technologies.This thesis focus on the Earth-Mars low-thrust transfer trajectory,to analyze the design and optimization methods.The specific content is as follows.In this thesis,the inverse quintic polynomial trajectory shape-based method is selected as the initial design method of the low-thrust transfer trajectory.The inverse quintic polynomial can be uniquely determined by the launch and arrival position and velocity information of spacecraft,as well as the number of laps.So the problem of initial orbit design can be transformed into an mathematical problem which searches the optimal launch-arrival time sequence within a given period of time.In order to solve this problem and satisfy the requirement of better convergence,based on the classic genetic algorithm,the thesis proposes a improved method added recognition and coverage operations.The recognition operation is used for after the population entering a stable period.The purpose is to retrieve the stable gene sequence earlier.The coverage operation is to keep the identified gene block,then covers them on the corresponding position of each individual.After this operation,the total fitness performance of the population become better,and the evolutionary direction tends to be consistent.In order to verify the effect of the improved genetic algorithm,two genetic algorithms are used to optimize the same multimodal function for 10 times,then the average of the results is compared.The simulation results show that the improved genetic algorithm has better convergence rate and maintains better stability in the later stage of the calculation.The method was applied to the initial design of the trajectory.A reasonable flight trajectory was also obtained.Since the essence of the shape-based method is to approximate the shape of the real trajectory through similar curves to complete the solution of the corresponding design parameters,it lacks consideration of actual factors.Because of this characteristic,this thesis proposes a stepwise optimization method combining pseudospectral method and homotopy method.On the one hand,in the first optimization,thrust is introduced as the control variable,and the energy optimal performance is selected to be solved.So that the generated trajectory is closer to the actual situation.On the other hand is to adopt the idea of homotopy method,by setting reasonable homotopy step length and forming corresponding performance.By iteratively solving the optimal control problem,the energy optimal performance iwill gradually transitions to the fuel optimal performance.Compared with the direct pseudo-spectrum method to solve the fuel-optimized low-thrust trajectory optimization problem,the thrust curve obtained by this stepwise optimization method has smaller oscillations,which improves the disadvantage of the pseudo-spectrum method in solving the fuel optimal control problem. |
