Minimum-Fuel Fixed-Time Impulsive Elliptic Glide-Slope Guidance Algorithms Using Semidefinite Programming

Abstract

A new minimum-fuel glide-slope guidance algorithm for approaching autonomously a target evolving on an elliptic orbit is proposed in this paper. Assuming chemical propulsion, the present work aimed at enhancing seminal methods. Although this reference method is efficient and easy to implement, there is no direct control on the fuel consumption and the guidance error. By identifying some relevant degrees of freedom, a new formulation of the glide-slope guidance algorithm is proposed to address these issues. For a fixed-time rendezvous and a given number of maneuvers, the fuel-optimal multipulse glide slope is expressed as a semidefinite programming problem. A solution to this optimization problem provides an impulsive control sequence that guarantees a minimal consumption and makes sure the chaser trajectory remains inside a user-defined corridor. Besides, if trajectory constraints are removed, or if a specific direction is considered (V-bar or R-bar), then the formulation is reduced to a simple linear programming problem. Three realistic scenarios of rendezvous are simulated to illustrate the benefit of the proposed methodology.