Optimization Of Earth-mars Transfer Trajectory With Low-thrust And Invariant Manifolds

On the background of the exploration of Mars, The optimization of Earth-Marstransfer trajectory with low-thrust and invariant manifolds is studied in this thesis. Thetransfer trajectory is divided into earth to Sun-Earth halo orbit transfer trajectory andSun-Earth halo orbit to Sun-Mars halo orbit transfer trajectory. The study is Primaryfocus on the choice of the entrance and the exit of the invariant manifolds, the fastoptimization of low-thrust transfer trajectory and the further accurate optimization oflow-thrust transfer trajectory. The details are as follow:To the strongly nonlinear of the optimization of low-thrust transfer trajectory, thetraditional optimization method has difficult in convergence. The method of fastoptimization of low-thrust transfer trajectory is proposed by combine the inversepolynomial shape-based algorithm with the genetic algorithm. Frist, the choice of theentrance and the exit in transfer trajectory based on the theory of invariant manifolds isgiven. Then, the optimization model of low-thrust transfer trajectory is simplified byusing inverse polynomial shape-based method. Last, this method is successfully appliedto the mission of this thesis, and the optimal trajectory is searched in large range.To the model of shape-based algorithm is not so accurate, a NonlinearProgramming (NLP) method based on Direct Collocation Method is proposed. Frist, theoptimal control problem of low-thrust transfer trajectory is discrete into a NLP problemby using Direct Collocation Method. Then, the method of calculation the initial value ofthe NLP problem by using the result of inverse polynomial shape-based algorithm isgiven. Last, the further accurate optimization of the mission in this thesis is made andthe result is compared with the fast optimization based on the inverse polynomialshape-based algorithm. Simulation concluded that the performance index is lower thanshape-based algorithm, and the error of the initial value of accurate optimizationobtained from the inverse polynomial shape-based algorithm is small and has fastconvergence characteristics.To the slow convergence of the Direct Collocation Method in solving sensitiveoptimal problem, a Gauss Pseudospectral Method is proposed. The optimal controlproblem of low-thrust transfer trajectory is discrete into a NLP problem in series ofGauss points. By comparing the result with Direct Collocation Method, conclude thatfor optimal control problem which is sensitive to initial state, the Gauss PseudospectralMethod has faster convergence characteristics than Direct Collocation Methodotherwise it is not. And the thrust obtained by the Gauss pseudospectral Method issmoother.