Direct–Indirect Hybrid Strategy for Optimal Powered Descent and Landing

Abstract

A hybrid algorithm to solve optimal control problems is discussed in the present paper and applied to the powered descent guidance (PDG) problem. A reference solution is first obtained via a convex direct solver and is then used as guess for the primal–dual boundary-value problem associated with the initial problem. In this context, a covector mapping theorem is used to map the multipliers of the direct solution to the corresponding discrete costates of the indirect method. Collocation based on hp pseudospectral scheme is employed for the convex direct step, while single shooting is used for the indirect step. A switching-detection technique further equips the shooting. As opposed to the hybrid convex-indirect algorithm, a state-of-the-art purely indirect algorithm is outlined; such approach merges the same single shooting approach with a homotopic continuation. The proposed methods are applied to the pinpoint landing formulation of the PDG, framed in a three-dimensional environment. The results are finally outlined, comparing the proposed hybrid strategy to the purely indirect approach. The outcome highlights the gain in computational times for the hybrid optimization technique over the fully homotopic scheme, demonstrating the validity of the former for landing trajectory optimization purposes.