Pseudospectral Convex Optimization for Powered Descent and Landing

Over the last years, two new technologies to solve optimal-control problems were successfully developed: that is, pseudospectral optimal control and convex optimization, with the former for solving the general nonlinear programming problem and the latter aimed at solving convex problems (for example, second-order conic problems) in real time. In this paper, a framework for combining them, with a motivational example, is described. The benefits of the new proposed method are demonstrated for the descent phase of the NASA Mars Science Laboratory. Numerical simulations show that the proposed algorithms lead to more accurate results with respect to standard transcription methods.