自动微分技术及其在轨迹优化中的应用

研究了自动微分技术在直接配点法中的应用,将其与内点非线性规划算法相结合,用于求解配点法转化得到的非线性规划问题。采用前向自动微分模式,利用ADOL-C实现了基于算子重载的自动微分计算;为验证算法的性能,以经典的航天飞机再入轨迹优化问题为例,针对三种直接配点格式,比较了自动微分法和有限差分法用于微分计算的性能。研究结果表明,自动微分可以提高微分信息计算的精度和效率,进而提高非线性规划算法的稳定性和收敛速度。

Automatic differentiation and its application to trajectory optimization

The automatic differentiation(AD) technology combined with an interior point method was used to solve the nonlinear programming problem from a direct collocation method.The automatic differentiation forward mode was adapted to calculate the derivative by the ADOL-C which is a C/C++library based on an operator overloading method.The classical case on reentry trajectory optimization problems of a space shuttle was solved.The automatic differentiation method(ADM) was compared with the finite differentiation method(FDM) respect to derivative efficiency.The results demonstrate that the ADM improves precision and efficiency of derivative information calculation,which can boost both the convergence rate and robustness of NLP numerical algorithm.