Fourier series and Search Space Reduction based Control profiles for Reentry Trajectory Optimization

Abstract

In this paper, the reentry trajectory of a space shuttle is obtained using search space reduction (SSR) optimization technique along with the finite Fourier series-based parametrization of control variables. The reentry trajectory design for the space shuttle is most important and challenging because of non-linear entry dynamics, the vehicle being unpowered, the presence of boundary conditions and path constraints that are to be satisfied accurately. To solve this problem, it is essential to find optimal control profiles such as bank angle and angle of attack using which optimal reentry trajectory is generated. In this paper, finite Fourier series-based parametrization of the angle of attack and bank angle is proposed. To show that this novel parametrization approach results in a reentry trajectory, three reentry mission objectives are considered such as maximizing the crossrange, minimizing the total heat experienced by the vehicle and minimizing the total heat with mínimum oscillations in reentry trajectory. Further, the optimal Fourier coefficients are obtained using the search space reduction optimization technique to achieve mentioned reentry mission objectives. The simulation results show that this parametrization method has resulted in optimal reentry trajectories which satisfy the terminal constraints accurately.