Trajectory Design And Optimization Of Gravity-assist/low-thrust For Deep Space Exploration

As an important and popular research field in future astronautics, Deep space exploration missions like solar probe, re-entry Moon and small celestial body exploration missions have been implemented or listed in the timetable. A lot of efforts have been made on deep space trajectory design, which is one of the key technologies, considering how to accomplish the mission with lowest the energy consumption and still satisfying all the design constraints. This dissertation presents studies on the gravity-assist and low-thrust trajectory design and optimization, as well as the developments on a trajectory design and optimization software tool.Firstly, the traditional gravity-assist trajectory design problem is modeled. According to patched conic assumption, gravity-assist trajectory can be divided into two major segments: the heliocentric transfer segment and the planet centric flyby segment. The former segment is specified by solving the Lambert problem. For a certain launch and arrive date, the position and velocity of considering planets can be obtained by querying the ephemeris. Inside the sphere of influence, the spacecraft's orbit is hyperbolic. This dissertation derives a set of analytical equations that calculate the change in velocity, energy and angular momentum.Secondly, a study is performed on impulsive gravity assist, or powered gravity-assist. An impulse is performed in the SOI of gravity-assist planet to achieve a expecting effect of gravity-assist on the assumption of unrestricted C3 match. The changes in velocity, energy, and angular momentum caused by impulsive gravity assist are analyzed with design cases to find the efficient impulse. After that, a set of analytical equations to calculate impulse is derived. The optimization of impulse is formulated as a multi-variable, nonlinear problem and can be solved by genetic algorithm and nonlinear optimization methods like SQP. A lunar impulsive gravity-assist trajectory design case is modeled using the fore mentioned equations and solved by combined algorithm of SQP and genetic algorithm.Thirdly, the optimization method in gravity-assist trajectory design is performed. In this dissertation , a design strategy is presented of graphical analyze and optimal launch window search. Graphical analyze method using the P-Rp graph to provide an energetic feasible swing-by planets index. Energy counter plot is used to specify the possible design variable field and time range. All these work supplies a set of reference initials for the design variables, thus avoiding the arbitrary assumption in traditional gravity-assist trajectory design. For the optimization of these variables, a global-local optimization algorithm is presented in this dissertation , which is a combination of genetic algorithm in global optimization and gradient search in local optimization. Then, a flow chat of this algorithm is attached to illustrate it. In the design and optimization of low-thrust trajectory, the mathematical model is formulated by optimal control theory. Then the low-thrust trajectory design problem is mainly to solve a two-point boundary-value problem (TPBVP). The equations of optimal low-thrust control steering law is expressed in equinoctial elements. In this dissertation , studies on two methods in low-thrust optimization are presented. One is hybrid method; the other is nominal orbit method.The hybrid method don't solve the TPBVP directly, but rather exploit its structure and then use parameter optimization and NLP. Moreover, the costate equations and optimality condition derived from the TPBVP are employed so that the hybrid method is a mixture of calculus of variables and parameter optimization. A trajectory design case of Earth centered LEO-GEO low-thrust transfer is designed and optimized using hybrid method to testify the feasibility of this method.Nominal orbit design method introduces the concept of "nominal orbit", which is the Kepler orbit in ballistic transfer. Because the thrust of low-thrust engine is trivial, thus the trajectory of low-thrust probe can perform linearization and transfer the problem into linear system control. Then an analytical transfer matrix is derived and the optimal low-thrust control steering is solved by optimal control theory. A solar polar mission trajectory design is performed using this method in the low-thrust heliocentric transfer orbit design. After the gravity-assist by Jupiter, the probe jumped out of the ecliptic plane successfully.The last part of this dissertation is the development of a gravity-assist trajectory design and optimization software, which is coded using Matlab. The software is both convenient and user friendly. The basic idea of this software is the aforementioned strategy in gravity-assist trajectory design, with modules as computation, ephemeris, user interface and output. The function of this software includes solving Lambert problem, plotting energy counter in direct interplanetary transfer and P-Rp graph to specify the gravity-assist planet index, searching for direct transfer opportunity and the optimization of gravity-assist trajectory design. All these are essential methods in gravity-assist trajectory design. A design case of EMJ transfer is calculated and optimized in this dissertation to illustrate the function of the software, as well as testify the feasibility of the strategy.