Time-Optimal Low-Thrust Formation Maneuvering Using a Hybrid Linear/Nonlinear Controller
Bibliographic record
Abstract
M AINTAINING two spacecraft in a formation with a conventional fuel-based propulsion system could be challenging in its own right. But this problem becomes more difficult when the propulsion system has limited capabilities or control actuation is available in only one or two axes and timeoptimal and fuel-optimal control is desired. Fortunately, for the spacecraft relative motion problem, because the relative equations of motion are coupled, motion in more than one direction can be controlled by control actuation in only one direction. In this Note, we formulate a hybrid linear/nonlinear controller that can efficiently maneuver a spacecraft formation by applying control only in the along-track direction. We also assume that the available control is very small in magnitude. This type of problem could be anticipated when dealing with low-thrust systems such as plasma thrusters, control with differential drag or solar radiation pressure, or any other system with very-low-thrust capability. One of the very early papers on underactuated control of a spacecraft formation with low-thrust capability by Leonard [1] presented an elegant algorithm to control a formation with only differential drag (assumed to be a constant and acting only in the along-track direction). Although the derived control was proven to be time-optimal control, it was not fuel-optimal. This was because differential drag was assumed to be a free resource with no need to economize it. However, for a spacecraft relying on expendables for control (plasmic thrusters), fuel economy would be highly desired. Some of the recent papers on this topic [2,3] also address the problem of spacecraft formation control with limited resources. The idea is to use linear or nonlinear controllers with a saturation function. The resultant controllers are robust and globally stable but not time-optimal. In the applied control field, the problem to control less frequently andmore efficiently ismore often an issue and elegant solutions exist for the same problem [4,5]. In this Note, we borrow some ideas discussed from [1,5] and apply them to the spacecraft formation-control problem. The result is a time-optimal controller that is easy to implement for underactuated formation control with limited resources. Although the controller is not proven to be fueloptimal, it is shown to consume less fuel than a conventional timeoptimal or a linear robust controller.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".