Funnel Synthesis for the 6-DOF Powered Descent Guidance Problem

Abstract

View Video Presentation: https://doi.org/10.2514/6.2021-0504.vid This paper presents a new implicit trajectory generation technique called quadratic funnel synthesis. In contrast to more standard explicit trajectory generation methods that compute a single trajectory that connects two single-vector boundary conditions, implicit trajectory generation uses a group of functions to define a set of trajectories that connect two sets of boundary conditions. Explicit trajectory generation for nonconvex optimal control problems has inherent limitations that do not permit theoretical guarantees that a feasible trajectory can be computed in real-time. These limitations motivate the study of new methods that are able to provide such guarantees. This paper introduces quadratic funnel synthesis and establishes a provably-convergent offline algorithm that is able to provide a group of functions that permit the computation of feasible trajectories using only numerical integration. A case study using the nonconvex 6-DOF powered descent guidance problem shows that a single quadratic funnel can provide feasible trajectories for any initial condition in a relatively large set in the state-space.