Convex Programming Approach to Powered Descent Guidance for Mars Landing

Abstract

We present a convex programming algorithm for the numerical solution of the minimum fuel powered descent guidance problem associated with Mars pinpoint landing. Our main contribution is the formulation of the trajectory optimization problem, which has nonconvex control constraints, as a finite-dimensional convex optimization problem, specifically as a second-order cone programming problem. Second-order cone programming is a subclass of convex programming, and there are efficient second-order cone programming solvers with deterministic convergence properties. Consequently, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications.