Re-entry trajectory optimization using an hp-adaptive Radau pseudospectral method

Aiming at increasing the convergence rate and the accuracy simultaneously, an hp-adaptive Radau pseudospectral method is presented to generate a re-entry launch vehicle's optimal re-entry trajectory. The method determines the number of mesh intervals, the width of the each mesh interval, and the degree of the polynomial in each mesh interval iteratively until a user-specified error tolerance is satisfied. In regions of relatively high curvature, convergence is achieved by dividing a segment into more mesh intervals, while in regions of relatively low curvature, convergence is achieved by increasing the degree of the approximating polynomial within a mesh interval. Simulation results show that the optimized trajectory obtained by the method satisfies the path constraints and the boundary constraints successfully. Moreover, the hp-adaptive Radau pseudospectral method is shown to be more efficient than either a global Radau pseudospectral method or a fixed-low-order Radau pseudospectral method. The results indicate that the hp-adaptive Radau pseudospectral method can be applied for real-time trajectory generation due to its high efficiency and high precision.