Coordination and control of a multiple spacecraft using convex optimization techniques

Abstract

Formation flying of multiple spacecraft is an enabling technology for many future space science missions. These future missions will, for example, use the highly coordinated, distributed array of vehicles for earth mapping interferometers and synthetic aperture radar. This thesis presents coordination and control algorithms designed for a fleet of spacecraft. These algorithms are embedded in a hierarchical fleet architecture that includes a high-level coordinator for the fleet maneuvers used to form, re-size, or re-target the formation configuration and low-level controllers to generate and implement the individual control inputs for each vehicle. The trajectory and control problems are posed as linear programming (LP) optimizations to solve for the minimum fuel maneuvers. The combined result of the high-level coordination and low-level controllers is a very flexible optimization framework that can be used off-line to analyze aspects of a mission design and in real-time as part of an on-board autonomous formation flying control system. This thesis also investigates several critical issues associated with the implementation of this formation flying approach. In particular, modifications to the LP algorithms are presented to: include robustness to sensor noise, include actuator constraints, ensure that the optimization solutions are always feasible, and reduce the LP solution times. Furthermore, the dynamics for the control problem are analyzed in terms of two key issues: 1) what dynamics model should be used to specify the desired state to maintain a passive aperture; and 2) what dynamics model should be used in the LP to represent the motion about this state. Several linearized models of the relative dynamics are considered in this analysis, including Hill's equations for circular orbits, modified linear dynamics that partially account for the J2 effects, and Lawden's equations for eccentric orbits. The complete formation flying control approach is successfully demonstrated using a nonlinear simulation environment that includes realistic measurement noises, disturbances, and actuator nonlinearities.