引用本文:韩鹏,单家元.基于Radau伪谱法的重复使用运载器再入轨迹优化[J].控制理论与应用,2013,30(8):1027~1032.[点击复制]
HAN Peng,SHAN Jia-yuan.Re-entry trajectory optimization using Radau pseudospectral method[J].Control Theory and Technology,2013,30(8):1027~1032.[点击复制]
基于Radau伪谱法的重复使用运载器再入轨迹优化
Re-entry trajectory optimization using Radau pseudospectral method
摘要点击 2537  全文点击 2366  投稿时间：2012-03-03  修订日期：2012-10-25
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DOI编号  10.7641/CTA.2013.12041
  2013,30(8):1027-1032
中文关键词  重复使用运载器  轨迹优化  直接法  Radau伪谱法
英文关键词  reusable launch vehicle  trajectory optimization  direct method  Radau pseudospectral method
基金项目  
作者单位E-mail
韩鹏* 北京理工大学 飞行动力学与控制教育部重点实验室 hanpeng@bit.edu.cn 
单家元 北京理工大学 飞行动力学与控制教育部重点实验室  
中文摘要
      为了提高数值解法的收敛速度, 本文利用Radau伪谱法求解重复使用运载器的再入轨迹优化问题. 该方法在一组Legendre-Gauss-Radau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. 最后的仿真结果显示, 通过该方法优化后的再入轨迹成功满足过程约束与边界约束. 由于该方法的高效率和高精度特性, 可将其应用于轨迹快速优化工程实际问题中.
英文摘要
      To increase the convergence rate of the numerical method, we employ the Radau pseudospectral method (RPM) in solving the optimal re-entry trajectory for the reusable launch vehicle. In this method, a finite base of global Lagrange interpolating polynomials is used to approximate the states and control at a set of Legendre-Gauss-Radau points. The time derivative of the state in the dynamic equations is approximated by the derivative of the interpolating polynomial, therefore they can be converted to the differential-algebraic equations at the Legendre-Gauss-Radau points. Consequently, the continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming (NLP) problem. Then, the resulting NLP problem is solved by a sparse nonlinear programming solver named SNOPT. Finally, simulation results show that the optimized re-entry trajectory satisfies the path constraints and the boundary constraints successfully. The results indicate that the RPM can be applied to fast trajectory-generation problems in practical engineering due to its high efficiency and high precision.