AUTHOR=Sands Timothy 

TITLE=Treatise on Analytic Nonlinear Optimal Guidance and Control Amplification of Strictly Analytic (Non-Numerical) Methods

JOURNAL=Frontiers in Robotics and AI

VOLUME=Volume 9 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/robotics-and-ai/articles/10.3389/frobt.2022.884669

DOI=10.3389/frobt.2022.884669

ISSN=2296-9144

ABSTRACT=Optimal control, is seen by researchers from a different perspective than that from which the industry practitioners see it. Either type of user can easily become confounded when deciding which manner of optimal control should be used for guidance and control of mechanics. Such optimization methods are useful for autonomous navigation, guidance, and control, but their performance is hampered by noisy multi-sensor technologies and poorly modeled system equations, and real-time on-board utilization is generally computationally burdensome. Some methods proposed here use noisy sensor data to learn the optimal guidance and control solutions real-time (online), where non-iterative instantiations are preferred to reduce computational burdens. This study aims to highlight efficacy and limitations of several common methods for optimizing guidance and control while proposing a few more, where all methods are applied to the full, nonlinear, coupled equations of motion including cross-products of motion from the transport theorem. Five disparate types of optimum guidance and control algorithms are presented and compared to a classical benchmark. Comparative analysis is based on tracking errors (both states and rates), fuel usage, and computational burden. Real-time optimization with singular switching plus nonlinear transport theorem decoupling is newly introduced and proves superior by matching open-loop solutions to the constrained optimization problem (in terms of state and rate errors and fuel usage), while robustness is validated in the utilization of mixed, noisy state and rate sensors and uniformly varying mass and mass moments of inertia. State tracking errors are reduced one-hundred ten percent. Rate tracking errors are reduced one-hundred thirteen percent. Control utilization (e.g., fuel) is reduced eighty four percent, while computational burden in reduced ten percent simultaneously, where the proposed methods have no control gains and no linearization.