Customized Real-Time Interior-Point Methods for Onboard Powered-Descent Guidance

Abstract

This paper presents a new onboard-implementable, real-time convex optimization-based powered-descent guidance algorithm for planetary pinpoint landing. Earlier work provided the theoretical basis of convexification, the equivalent representation of the fuel-optimal pinpoint landing trajectory optimization problem with nonconvex control constraints as a convex optimization problem. Once the trajectory optimization problem is convexified, interior-point method algorithms can be used to solve the problem to global optimality. Though having this guarantee of convergence motivated earlier convexification results, there were no real-time interior point method algorithms available for the computation of optimal trajectories on flight computers. This paper presents the first such algorithm developed for onboard use and flight-tested on a terrestrial rocket with the NASA Jet Propulsion Laboratory and the NASA Flight Opportunities Program in 2013. First, earlier convexification results are summarized and the resulting second-order cone-programming problem for fuel-optimal trajectory optimization is presented. Then, the proposed, fairly generic, second-order cone-programming interior point method algorithm is presented in detail with an overview of the customization process for real-time computations. Customization exploits a specific problem structure to increase the computational speed, which is shown to decrease run times by two to three orders of magnitude in many applications. A new convexification result for maximal-divert trajectories with active velocity constraints is also presented herein.