Autonomous Guidance & Control of Earth-Orbiting Formation Flying Spacecraft: Closing the Loop
- Paper number
IAC-07-C1.6.02
- Author
Mr. Jean-Francois Hamel, Universite de Sherbrooke, Canada
- Coauthor
Dr. Jean de Lafontaine, NGC Aerospace Ltd., Canada
- Year
2007
- Abstract
This article follows an article presented last year at IAC 2006. In the previous article, the key technologies required to autonomously perform guidance and control of formation flying spacecraft were identified. This paper summarizes solutions recently developed that form the missing links required to obtain a formation flying guidance and control loop able to autonomously perform formation reconfiguration and maintenance.
The first challenge identified in previous work was the need for an analytical model of relative motion that takes into account J 2 perturbation and reference orbit eccentricity. An analytical model, in the form of a state transition matrix, was recently developed for this purpose. The model uses the linearized mean element drift rate difference between the spacecraft to accurately predict relative motion over several orbits without any numerical propagation. This model can therefore predict the relative motion of all the elements of the formation, including drift caused by the J 2 perturbation with the computation of only one matrix, for which the elements are given analytically.
The second identified key technology was the need for a tool to autonomously perform trade-offs between conflicting requirements. A recently developed tool, the fuel-equivalent space, is an answer to the problem. The mapping of the relative orbit elements in a “fuel-equivalent” space translates the problem of minimizing the propellant cost of a maneuver into a simple geometric problem. Based on the results of the impulsive feedback controller, this mapping translates relative orbit elements into a space where a similar displacement on all axes require a similar propellant cost. If the formation flying configurations can be described geometrically (which is the case of the most common configurations), the most fuel-efficient way to reach the formation can be obtained analytically with very simple geometrical relations by finding the minimal distance between a point and a geometric shape.
Finally, the third identified need was a feedback control law that can help to perform maneuvers with good accuracy and reasonable propellant cost. This has been achieved with a neighbouring optimal control law. With this feedback control law, only one gain matrix needs to be numerically solved for the complete formation. Once this matrix is solved, an analytical neighbouring optimal control is obtained for the complete formation that can easily be implemented on board. Weighting matrices in the solution leave room to easily perform the accuracy/fuel consumption trade-off when synthesizing the control law. This feedback control law ensures optimal or sub-optimal fuel consumption for all the elements of the formation.
The paper summarizes the results of each of these three recent developments and presents with simulation results how they can be connected together. The simulation results show that these three improvements can be linked together to yield a fully autonomous guidance and control system that can perform formation reconfiguration or maintenance without the need of ground support.
- Abstract document
- Manuscript document
IAC-07-C1.6.02.pdf (🔒 authorized access only).
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