Advances in Underactuated Spacecraft Control

Abstract

This dissertation addresses the control of a spacecraft which either becomes underactuated due to onboard failures or is made underactuated by design. Successfully controlling an underactuated spacecraft can extend spacecraft operational life in orbit and improve the robustness of space missions. The novel contributions of the dissertation include the following.

Firstly, switching feedback controllers are developed for the attitude control of an underactuated spacecraft equipped with two pairs of thrusters, or two reaction wheels (RWs), or two control moment gyros (CMGs). The problem is challenging; e.g., even in the zero total angular momentum case, no smooth or even continuous time-invariant feedback law for stabilizing a desired orientation exists. The method exploits the separation of the system into inner-loop base variables and outer-loop fiber variables. The base variables track periodic reference trajectories, the amplitude of which is governed by parameters that are adjusted to induce an appropriate change in the fiber variables towards the desired pointing configuration.

Secondly, nonlinear Model Predictive Control (MPC) is applied to the attitude dynamics of an underactuated spacecraft with two RWs and zero angular momentum. MPC has the remarkable ability to generate control laws that are discontinuous in the state. By utilizing nonlinear MPC, the obstruction to stabilizability is overcome and attitude maneuvers can be performed while enforcing constraints.

Thirdly, an unconventional pathway is discussed for recovering the linear controllability of an underactuated spacecraft with two RWs by accounting for the effects of solar radiation pressure (SRP) in the spacecraft attitude model. Necessary and sufficient conditions for recovering linear controllability are given, and with linear controllability restored, conventional controllers can be designed for underactuated spacecraft.

Lastly, two sets of coupled translational and rotational equations of motion for a spacecraft in a central gravity field are derived. The spacecraft is assumed to have only internal attitude actuators and the equations of motion are relative with respect to an equilibrium orbit. Under reasonable assumptions on the spacecraft configuration and equilibrium orbit, the coupled dynamics are small-time locally controllable (STLC), which opens a path to utilizing conventional control techniques to move translationally in space by employing attitude control only.