Progress of Indirect Method for Continuous Low-thrust Trajectory Optimization
The indirect method for low-thrust trajectory optimization is focused on,and the related research progress in the optimal control theory,initial guesses,and homotopy continuation method is summarized.Firstly,the continuous low-thrust trajectory optimization problem is established as the optimal control problem,where several types of state equations,constraints,and performance indices are introduced.The solution algorithms,advantages,and disadvantages of the two main optimization methods,direct method and indirect method,are compared.The indirect method can obtain the optimal control law by theoretical analysis,possess the high-accuracy orbit propagation,and guarantee the first-order optimality of solutions.However,the solution algorithm needs to be reconstructed and may be very complex for different kinds of constraints.The algorithm is generally very sensitive to the initial guesses,where the costate variables are difficult to guess due to a lack of physical interpretation.Then,the research progress in the preliminary design of low-thrust trajectories,initial guesses,and homotopy continuation is summarized,and the improvements led by the intelligent optimization and deep learning are presented.The indirect method has been improved in terms of the solution efficiency,optimality,and convergence.Furthermore,the applications of the indirect method are discussed in combination with the requirements of the global optimization for the mission design and the real-time optimal control in spacecraft guidance control.Finally,the possible development of the indirect method is prospected.
Space explorationContinuous thrustIndirect methodShooting methodInitial guessesHomotopy method
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