Low Thrust Trajectory Optimization Based On Multiple-phase Refinement And Homotopy Methods

With the large specific impulse and high efficiency,the low thrust technique has become one of the key techniques in the space missions such as the on-orbit service,space detection.However,low-thrust trajectories are much more difficult to solve than chemical impulsive-maneuver trajectories.Based on the multi-phase refinement and homotopy strategies,this dissertation researches on the solving methods for the continuous,discontinuous and constrained solar electric propulsion(SEP)low thrust problems with the long-duration.The main research achievements are summarized as follows.The solving methods to the continuous low-thrust problems with the longduration are studied.(1)Through the analysis of the critical reasons that the problems are difficult to overcome,a multiple-phase strategy with several specific treatments of costates improving the numerical converigence is offered.(2)Combined with the multiplephase strategy,two typical methods are provided to refine phases to one whole trajectory,which are the pseudo-spectral refinement method and indirect refinement method.(3)With several numerical examples,the properties of the methods are analyzed,and the results show: for the long-duration continuous low-thrust problems,both two methods have good performance,and the pseudo-spectral refinement method is good at solving stability and the indirect refinement method with the great robosutness.The solving methods to the discontinuous low-thrust problems with the longduration are studied.(1)The homotopic method of the indirect method is firstly introduced and a novel homotopy based on the pseudo-spectral method is provided.(2)Combined with the indirect refinement method and the homotopy of the indirect method,an indirect homotopic optimization method is researched.(3)Combined with the pseudospectral smoothing method and the homotopy of the pseudo-spectral method,a pseudospectral homotopic optimization method is researched.(4)Finally,a hybrid homotopy method is offered to make full use of the high efficiency from the indirect homotopic method and the stability from the pseudo-spectral homotopic method.Design methods and characteristics of multi-revolution trajectory under the variable bounded thrust and thrust-direction limitation using solar electric propulsion are studied.(1)In consideration of the two factors that the maximal magnitude of low thrust is variable and the direction of low thrust are limited,a mathematical solving model is deduced.(2)According to the mathematical model,the hybrid homotopy method is modified to solve the problems.(3)Through the several numerical examples,the characteristics of fuel-optimal trajectories using solar electric propulsion are analyzed and demonstrated.The prototype system of general orbital-maneuver planning and analyzing is developed.(1)A multiple-phase optimal model that can use in multiple-impulse maneuver optimal problems and low thrust optimal problems is proposed.(2)Based on architecture techniques,the compenent-based software architecture of the prototype system is designed and developed by standard C++11 programming language in Visual Studio 2010.Focused on the low thrust problems,with the foundermental multiple-phase refinement and homotopy strategies,this dissertation has systematically proposed the solving methods for the low thrust problems.These methods overcome the continuous,discontinuous low thrust problems and the solar electric propulsion with thrust-direction limitation problems.In both the theory research and engineering application,theses work makes important contribution.