Indirect sequential convex programming for mars entry terminal altitude maximization

Abstract

The uniform trigonometrization method (UTM) faces two difficulties in solving the Mars entry problem with maximum terminal altitude. One is that two possible solutions need to be evaluated by Pontryagin's minimum principle (PMP). The other one is that using numerical continuation logic to solve the Hamiltonian two-point boundary value problem (TPBVP) involves a significant amount of computation. To overcome these two challenges, indirect sequential convex programming (ISCP), which combines the UTM and sequential convex programming (SCP), is developed in this article. The proposed method first modifies the two control options into a single solution, which eliminates the requirement for PMP evaluation. The nonlinear TPBVP resulted from the improved UTM is then relaxed into a convex programming problem that is established by introducing the virtual control and buffer. Subsequently, the SCP process generates a numerical solution to the Mars entry problem within a short time. Compared to the general pseudospectral method and UTM, simulations demonstrate the effectiveness and efficiency of the ISCP method for longitudinal Mars entry missions with or without path constraints.