Predictive, Adaptive, and Time-Varying Control of Spacecraft Orbits and Attitude.

Abstract

This dissertation contributes several control strategies that provide advanced capabilities in spacecraft applications. Specifically, we consider predictive, adaptive, and time-varying control methods, and apply them to orbital and attitude control.

First, we develop a Model Predictive Control approach with dynamically reconfigurable constraints for orbital rendezvous and docking. The controller is designed to transition between MPC-based guidance during spacecraft rendezvous and docking, with each phase having distinct requirements, constraints, and sampling rates. The MPC controller is demonstrated in simulation studies using a nonlinear model of spacecraft orbital motion. An Extended Kalman Filter is used to estimate spacecraft states based on relative angles and relative range measurements.

Second, we consider spacecraft relative motion control based on the use of safe positively invariant sets. A connectivity graph is constructed between a set of forced equilibria, forming a virtual net around a nominal orbital position. The connectivity between two equilibria is determined based on safe positively invariant sets in order to guarantee that transitions can be effected while spacecraft actuator limits are adhered to and debris collisions are avoided. A graph search algorithm is implemented to find the shortest path around the debris.

Third, for attitude control, we extend the continuous inertia-free control law for spacecraft attitude tracking derived in prior work to handle magnetic actuation, reaction wheels, and control moment gyroscopes (CMGs). The actuators are mounted in a known configuration with an unknown orientation relative to the unknown spacecraft principal axes. We demonstrate effective attitude control capability without relying on inertia matrix characterization.

Lastly, we develop a forward-propagating Riccati-based linear time-varying feedback controller. We show that if the closed-loop dynamics matrix is symmetric, then the Forward-Propagating Riccati (FPR) controller is asymptotically stabilizing. We also show that in the case of periodic systems there exists a period below which the dynamics of the closed-loop system are asymptotically stable. Additionally, we show that there is a separation of estimator and FPR regulator dynamics and thus FPR control may be used in an output feedback configuration. We apply the FPR controller to both a magnetically actuated spacecraft and to a maneuvering spacecraft in an elliptic orbit.