A report presents the mathematical basis of a method of controlling multiple spacecraft flying in formation, subject to control constraints. The spacecraft are assumed to be equipped with relative-position-sensing, relative-velocity-sensing, and communication infrastructure, and with maneuvering actuators. The method involves a leader-following control scheme. A graph is used to represent the hierarchy of, and the data dependencies among, the leading and following spacecraft. Graph-theoretic concepts are shown to play a vital role in determining the basic properties of the leader-following control architecture; hence, changes in the hierarchy (represented by changes in the graph) translate directly to the required changes in control.
This work was done by Fred Hadaegh and Mehran Mesbahi of Caltech for NASA's Jet Propulsion Laboratory. To obtain a copy of the report, "Formation Flying Control of Multiple Spacecraft via Graphs, Matrix Inequalities, and Switching," access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Mechanics category.
NPO-20902
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Theory of Formation-Flying Control for Multiple Spacecraft
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Overview
The document titled "Theory of Formation-Flying Control for Multiple Spacecraft" presents a comprehensive approach to controlling multiple spacecraft operating in formation, focusing on the mathematical foundations and practical applications of a leader-following control scheme. Authored by Fred Hadaegh and Mehran Mesbahi from Caltech for NASA's Jet Propulsion Laboratory, the report outlines a method that integrates relative-position and relative-velocity sensing, communication infrastructure, and maneuvering actuators to achieve effective control of spacecraft.
At the core of the proposed method is a leader-following control architecture, where one spacecraft (the leader) guides the others (the followers) in maintaining desired formation patterns. The document emphasizes the importance of graph theory in representing the hierarchical relationships and data dependencies among the spacecraft. By utilizing graph-theoretic concepts, the authors demonstrate how changes in the control hierarchy can be effectively managed, allowing for dynamic adjustments in response to varying operational conditions.
The report also introduces guidelines for hierarchical control assignments that consider the existing sensing and communication capabilities of the spacecraft. This ensures that the control strategy is not only theoretically sound but also practically applicable in real-world scenarios. A significant aspect of the proposed control scheme is its ability to prevent actuator saturation, which can occur when control commands exceed the physical limits of the spacecraft's maneuvering capabilities.
To address this challenge, the authors propose a hybrid control scheme that combines linear matrix inequalities (LMIs) with a graph-theory-based switching control approach. This innovative framework allows for modifications in the control hierarchy while maintaining system stability, a critical requirement for successful formation flying.
Overall, the document provides a detailed exploration of the theoretical underpinnings and practical implications of formation-flying control for multiple spacecraft. It highlights the collaborative efforts of the authors and the support of NASA, underscoring the significance of this research in advancing space exploration technologies. The findings and methodologies presented in this report are expected to contribute to the development of more sophisticated and reliable control systems for future space missions involving multiple spacecraft operating in close proximity.
