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利用Radau伪谱法求解临近空间飞行器的助推-滑翔段轨迹优化问题。该方法在一组Legendre-GaussRadau点上构造全局Lagrange插值多项式对状态变量和控制变量进行逼近,在动力学方程中状态变量对时间的导数可由插值多项式的导数来近似,故可将动力学方程约束转化为在Legendre-Gauss-Radau点上的代数微分方程约束。因此,可将连续时间的最优控制问题转化为有限维的非线性规划(NLP)问题,之后通过稀疏NLP求解器SNOPT即可对其进行求解。最后利用GPOPS软件对一种多级火箭助推-无动力滑翔的临近空间飞行器进行了上升-滑翔段的轨迹优化仿真研究和规律性总结。
Radar Pseudo - spectral Method for Solving Pace - Gliding Trajectory Optimization Problems of Near Spacecraft. The method constructs a global Lagrange interpolation polynomial on a set of Legendre-GaussRadau points to approximate the state variable and the control variable. In the dynamic equation, the derivative of the state variable to time can be approximated by the derivative of the interpolation polynomial. Therefore, the dynamic equation can be constrained Converted into algebraic differential equation constraints on Legendre-Gauss-Radau points. Therefore, the optimal control problem of continuous time can be transformed into a Finite Dimensional Nonlinear Programming (NLP) problem, which can then be solved by the sparse NLP solver SNOPT. At last, the GPOPS software is used to simulate and regularly summarize the trajectory optimization simulation of gliding segment with a multi-stage rocket-propelled approach glider-free spacecraft.