V-bar and R-bar Glideslope Guidance Algorithms for Fixed-Time Rendezvous: A Linear Programming Approach

This paper presents minimum-fuel glideslope autonomous guidance algorithms for approaching a target evolving on a circular orbit. In the context of a chemical propulsion, the classical multipulse glideslope algorithm of Hablani is revisited and it is shown that when considering specific common directions for the glideslope such as V-bar and R-bar directions, a linear formulation of the circular minimum-fuel linearized rendezvous problem may be deduced. Unlike the classical glideslope algorithm for which there is no direct control on the fuel consumption, additional degrees of freedom and relevant decision variables may be identified by combining an analytical expression for the maximal guidance error and Hill-Clohessy-Wiltshire relative equations of motion. For a fixed-time rendezvous with a pre-assigned number of maneuvers, a fuel-optimal solution with a bounded guidance error is obtained by solving a linear programming problem. Numerical examples demonstrate the usefulness of the approach with respect to the classical ones when the approach corridor has to fulfill stringent geometrical restrictions such as line-of-sight constraints.