Collocation points distributions for optimal spacecraft trajectories

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• 作者：Federico Fumenti ; Christian Circi ; Daniele Romagnoli
• 关键词：Collocation ; Optimal control problem ; Jacobi polynomials ; Spacecraft trajectory optimization
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2013
• 出版时间：March, 2013
• 年：2013
• 卷：18
• 期：3
• 页码：710-727
• 全文大小：1526 K

文摘

The method of direct collocation with nonlinear programming (DCNLP) is a powerful tool to solve optimal control problems (OCP). In this method the solution time history is approximated with piecewise polynomials, which are constructed using interpolation points deriving from the Jacobi polynomials. Among the Jacobi polynomials family, Legendre and Chebyshev polynomials are the most used, but there is no evidence that they offer the best performance with respect to other family members. By solving different OCPs with interpolation points not only taken within the Jacoby family, the behavior of the Jacobi polynomials in the optimization problems is discussed. This paper focuses on spacecraft trajectories optimization problems. In particular orbit transfers, interplanetary transfers and station keepings are considered.