Computationally inexpensive guidance algorithm for fuel-efficient terminal descent

This communication reports on the design of a computationally inexpensive algorithm for the synthesis of control functions for fuel-efficient powered terminal descent of a vehicle. Instead of solving a minimum fuel optimal control problem, the proposed algorithm is based on solving a related optimal control problem for which the solution can be expressed in analytic closed form. This property leads to an algorithm, which, for any initial condition (i.e., in any instance of the problem), will always require a low number of operations to compute the control functions, and no iterations are involved. The fuel performance achieved by the control inputs synthesized by the algorithm is evaluated by numerical simulations of the powered descent phase of a Mars landing and shown to be close to the minimum fuel performance.