Study On Low-thrust Trajectory Optimization Of Multi-object Deep-space Exploration Missions

Solar electric propulsion has been widely used in deep-space exploration missions because of its high specific impulse.Its application can help reduce the fuel consumption and thus increase the payload.It increases the possibility of multi-target missions and is an important direction of future deep-space missions.Compared with traditional chemical propulsion which yields patch-conic trajectories,its trajectory is difficult to obtain analytically except for a few special cases.The optimization of low-thrust trajectories is essentially optimal control problem,so it is usually harder to solve compared with parameter optimization problem yielded by chemical propulsion.The high cost of deep-space mission contributes to the meanings of fuel-optimal trajectories.However,the intrinstic bang-bang control increases the difficulty.The increase in the scale of the problem due to multiple interior-point constraints makes the problem even harder to solve.This thesis investigates the key problems in the low-thrust trajectory optimization problem based on both domestic and international research.The main topic includes the solving of bang-bang control,the guessing of adjoint variables,and the method for dealing with multiple interior-point constraints.Numerical examples are presented to verify the correctness and validity of these methods.Firstly,the dynamics of the spacecraft with multiple description methods are modeled in both the two-body model and the circular restricted three-body model.Based on these equations of motion,we build the fuel-optimal trajectory optimization problem by applying optimal control theory.The first-order necessary conditions for optimality are derived through the Pontryagin maximum throry.We solve the single-leg transfer problem by exploting the homotopic approach,the adjoint normalization,and the switching detection method.An example of capturing near-Earth asteroids with low-thrust propulsion and invariant manifolds is used as an illustration.The efficiency of different descriptioin methods are compared,too.Secondly,we propose several methods for guessing the adjoint variables.First of all,we investigate the low-thrust transfer problems between two close near-circular near-coplanar orbits.The equations of motion are simplified so some adjoint variables can be solved.Then we try to solve more general cases.A nominal trajectory is built near which the equations of motion are linearized which consequentially transform the nonlinear system into a linear time-variant system.We use indirect method to solve an energy-optimal transfer problem in order to guess some adjoint variables.We also discretize the problem based on pseudospectral methods and solve the fuel-optimal problem by solving a serie of convex optimization problem.Finally the adjoint variables are obtained by the information of the multipliers of the convex optimization problem.Thirdly,we propose an innovative method for the low-thrust fuel-optimal transfer problem containing multiple interior-point constraints by the method of splitting and combining.We propose the adjoint scaling technique for fuel-optimal transfer problem.Then the transversality conditions arising from different types of interior point constraints are derived.They are combined and applied to missions where the spacecraft have to rendezvous with multiple targets and perform multiple gravity assists,respectively.Finally,we investigate the advantages and limitations of the methods proposed in this thesis.The possible problems that need further investigation are prospected.