An analytical guidance law of planetary landing mission by minimizing the control effort expenditure

Abstract

An optimal trajectory design of a module for the planetary landing problem is achieved by minimizing the control effort expenditure. Using the calculus of variations theorem, the control variable is expressed as a function of costate variables, and the problem is converted into a two-point boundary-value problem. To solve this problem, the performance measure is approximated by employing a trigonometric series and subsequently, the optimal control and state trajectories are determined. To validate the accuracy of the proposed solution, a numerical method of the steepest descent is utilized. The main objective of this paper is to present a novel analytic guidance law of the planetary landing mission by optimizing the control effort expenditure. Finally, an example of a lunar landing mission is demonstrated to examine the results of this solution in practical situations.

Non-linear solution to the maximum height orbit transfer guidance problem

“…Also, m 0 and _ m are initial mass and mass variation rate of the spacecraft, respectively. To avoid several computational difficulties and present a more meaningful definition of the system, it is attempted to transfer the equations and boundary conditions to non-dimensional form by using a set of reference parameters of (u*, y*, t*, m*) as [11] "…”

“…A novel approach to synthesize the optimal feedback law for the satellite injection problem is introduced using fuzzy systems by Pourtakdoust et al [9] In this work, an attempt was made to develop the closed-loop fuzzy guidance law in the presence of environment noises and system uncertainties. Afshari et al [1,[10][11][12] and Roshanian et al [13] have tried to design optimal guidance solutions for different space missions by employing mathematical theories, such as perturbation theorem, backward sweep method, and calculus of variations in exact forms. Considering novel approaches of control theories such as fuzzy guidance law (FGL) and L 1 adaptive method has caused new guidance solutions to be achieved.…”

A perturbation approach in determination of closed-loop optimal-fuzzy control policy for planetary landing mission

“…Naghash et al [7] developed an explicit guidance law that maximized terminal velocity for a re-entry vehicle to a fixed target employing inverse problem approach and genetic algorithm. Afshari et al [8,9] worked on the development of optimal feedback control law for several space missions. To achieve their goals, they employed analytical procedures to solve nonlinear two-point boundary value problems.…”