Minimum Time Rendezvous of Multiple Spacecraft Using Differential Drag

Abstract

This paper presents a method to solve the minimum time rendezvous problem of multiple spacecraft using differential drag. The problem is to rendezvous any number of vehicles using only the relative aerodynamic drag between the vehicles. Each vehicle is equipped with drag plates that can be opened or closed, thus modulating the drag force acting on the vehicle. By actuating the drag plates, the aerodynamic drag becomes the control used to accomplish the rendezvous. The optimal control problem is relaxed to a convex problem, and it is proved that a solution of the relaxed problem exists that is also a solution of the original problem. This process is called lossless convexification, and it leads to a solution method based on solving a finite number of linear programming problems. This method offers guaranteed convergence to the global minimum in polynomial time and does not require an initial guess. Two examples are solved with two and five vehicles and the results are compared with existing technologies. Because the method is fast and globally convergent, it is well suited for real-time use onboard a vehicle.