Optimal Planar Powered Descent with Independent Thrust and Torque

Abstract

A powered descent problem with a body-fixed thrust vector and independent torque input is considered. By assuming that the entire descent maneuver takes place in an inertially-fixed plane, we show by using the maximum principle that the optimal thrust magnitude must lie on its boundary and may exhibit up to four switches with a min–max–min–max–min profile. The optimal torque input may be singular, and an expression for it is derived. Non-singular torque arcs are shown to be intimately related to the boundary conditions that are imposed on the vehicle’s attitude and the presence of minimum thrust arcs at the beginning and end of the descent. Our results can be thought of as a generalization of previous work on three-degree-of-freedom translational powered descent; with new theoretical insights obtained for powered descent problems that consider attitude in the problem formulation.