Rapid Lunar soft-landing trajectory optimization by a Legendre pseudospectral method
- Paper number
IAC-06-C1.P.4.01
- Author
Dr. Jianjun Luo, Northwestern Polytechnical University, China
- Coauthor
Dr. Mingguang Wang, Northwestern Polytechnical University, China
- Coauthor
Prof. Jianping Yuan, Northwestern Polytechnical University, China
- Year
2006
- Abstract
Determining how to seek the optimal soft-landing trajectory of the lunar probe from the lunar satellite orbit so that it is able to safely and efficiently reach the lunar surface involves the solution of an optimal trajectory design and control problem. Traditionally, this trajectory optimization problem, which can be posed as an optimal control problem, is considered to be difficult and solved on the ground prior to flight, and the optimal works are found regardless of computing time by most of algorithms. However, it is crucial to find the optimal trajectory and controls quickly for some flight tasks and situations. As yet, traditional trajectory optimization algorithms are not competent for an onboard optimization task. In this paper, the problem of rapid Lunar soft-landing trajectory optimization by using a Legendre pseudospectral method was studied. This rapid trajectory optimization methodology could be used to design the reference trajectory for autonomous navigation system and emergency landing. Firstly, Some new hypotheses were introduced according to the distinguished features of the lunar and soft-landing trajectory. Based on these hypotheses, the set of dynamics and kinematics equations of the Lunar soft-landing was simplified in order to reduce the computation load, and the rationality of the simplification was analyzed. Next, the soft-landing trajectory optimization problem was transformed into a constrained parameter optimization problem by using a Legendre pseudospectral method, and a combination of nonlinear programming methods (Methods of Multipliers and BFGS algorithm) was used to solve the transformed problem, that is, the Methods of Multipliers was applied to deal with the constraints and transformed a constrained parameter optimization problem into a unconstrained one solved by the BFGS. At last, some simulation works were carried out and the minimum principle of Pontryagin was used to verify the optimal condition of the optimal trajectory. Simulation results show the methodology and algorithms were able to generate a feasible soft-landing trajectory quickly on a desktop computer.
- Abstract document
- Manuscript document
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