Development, Analysis, and Testing of Robust Nonlinear Guidance Algorithms for Space Applications

Abstract

This work focuses on the analysis and application of various nonlinear, autonomous guidance algorithms that utilize sliding mode control to guarantee system stability and robustness. While the basis for the algorithms has previously been proposed, past efforts barely scratched the surface of the theoretical details and implications of these algorithms. Of the three algorithms that are the subject of this research, two are directly derived from optimal control theory and augmented using sliding mode control. Analysis of the derivation of these algorithms has shown that they are two different representations of the same result, one of which uses a simple error state model (Δr/Δv) and the other uses definitions of the zero-effort miss and zero-effort velocity (ZEM/ZEV) values. By investigating the dynamics of the defined sliding surfaces and their impact on the overall system, many implications have been deduced regarding the behavior of these systems which are noted to feature time-varying sliding modes. A formal finite time stability analysis has also been performed to theoretically demonstrate that the algorithms globally stabilize the system in finite time in the presence of perturbations and unmodeled dynamics. The third algorithm that has been subject to analysis is derived from a direct application of higher-order sliding mode control and Lyapunov stability analysis without consideration of optimal control theory and has been named the Multiple Sliding Surface Guidance (MSSG). Via use of reinforcement learning methods an optimal set of gains has been found that make the guidance perform similarly to an open-loop optimal solution. Careful side-by-side inspection of the MSSG and Optimal Sliding Guidance (OSG) algorithms has shown some striking similarities. A detailed comparison of the algorithms has demonstrated that though they are nearly indistinguishable at first glance, there are some key differences between the two algorithms and they are indeed not identical. Finally, this work has a large focus on the application of these various algorithms to a large number of space based applications. These include applications to powered-terminal descent for landing on planetary bodies such as the moon and Mars and to proximity operations (landing, hovering, or maneuvering) about small bodies such as an asteroid or a comet. Further extensions of these algorithms have allowed for adaptation of a hybrid control strategy for planetary landing, and the combined modeling and simultaneous control of both the vehicle's position and orientation implemented within a full six degree-of-freedom spacecraft simulation.