Cascaded Lyapunov Vector Fields for Acceleration-Constrained Spacecraft Path Planning
Bibliographic record
Abstract
A variant of Lyapunov vector fields is presented for tracking trajectories within tumbling and accelerating reference frames. This extension is computationally light, and is acceleration constrained rather than velocity constrained, making it suitable for real-time use in spacecraft. A general stability analysis proves globally asymptotic stability given a set of conditions that are analogous to those of standard Lyapunov vector fields. A special case of this novel path-planning law (referred to as a cascaded Lyapunov vector field) is closely studied, and a simple set of conditions guaranteeing bounded acceleration commands for perfect tracking are derived. A design procedure is presented. Finally, a full design example for a spacecraft proximity inspection mission is presented. The simulations demonstrate stable behavior while respecting acceleration and path constraints. Furthermore, all constraints are met by judicious design of the path-planning field, without the need for computationally expensive algorithms running in real-time.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".