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

Abstract

Development of time-optimal strategy for non-linear problem of planetary landing mission by using perturbation technique is investigated on two scenarios in this study. The first scenario includes finding an optimal control policy for descent in the variable gravitational field of the target planet analytically. In the second scenario, the optimal policy is derived by considering the effect of spacecraft mass variations in an analytic solution. To validate the accuracy of each generated policy, a numeric method such as steepest descent is employed. Afterwards, the fuzzy algorithm is followed to achieve the closed-loop guidance strategy for this non-linear system. The training process of the fuzzy system is based on the achieved perturbation solution of variable mass landing problem by utilizing a set of states-related non-dimensional variables for faster convergence rate. Finally, the lunar landing mission is demonstrated as a viable example of the non-linear planetary landing mission. Simulation results show that the presented optimal guidance laws are so effective which can be utilized in the real world spacecraft applications.

Adaptive backstepping control for optimal descent with embedded autonomy

“…Among those approaches, the tangent optimal guidance law [4,5,[7][8][9] has been investigated widely. The advantage of this steering law is that it is derived from optimal control theory, therefore it can achieve fuel optimal (suboptimal).…”

“…Therefore, the guidance acceleration can be solved from boundary conditions. Another method is developing a closed form solution for the simplified model of the full model initially, and then designing a control law to track the developed closed form solution [8,9].…”

Analytical Landing Trajectories for Embedded Autonomy

“…To design the guidance and control law, two factors should be taken into consideration to ensure missions success: a low touch down velocity and a vertical attitude on the planetary surface. Many studies on guidance for soft landing have been reported [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. These guidance laws can be divided into two catalogues: 1.)…”

“…This guidance law is derived from optimal control. Based on some assumptions (i.e., mass of lander or gravitational acceleration is assumed to be constant), an analytic optimal solution for 2-D planetary landing problem required for fuzzy training was previously determined using regular perturbation theorem, and then a fuzzy algorithm was followed to achieve the closed-loop guidance strategy [11]. However, in general, a closed form solution for this guidance law cannot be found for the full model [12].…”

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

“…To create a closed-loop guidance policy of the satellite injection problem, Pourtakdoust and Novinzadeh presented a fuzzy algorithm that was augmented to the solution of the timeoptimal guidance strategy [4]. Afshari et al presented some analytic approaches in spacecraft guidance [5][6][7]. An optimal guidance law that minimized the commanded acceleration in three dimensions was obtained by Souza [8].…”