Geometric approach to feedback stabilization of a hopping robot in the flight phase
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Bibliographic record
Abstract
Using a model of a hopping robot it is shown that a previously introduced novel approach for the synthesis of time-varying stabilizing feedback control for drift free systems, which is based on the trajectory intersection idea and primarily applies to systems whose controllability Lie algebra is finite dimensional, is also applicable to systems whose controllability algebra is infinite dimensional. The original model of the hopping robot is first approximated to yield a simplified model whose controllability Lie algebra is finite dimensional. A time varying stabilizing feedback law is then constructed for the simplified model. The latter can be viewed as a composition of a standard stabilizing feedback control for a Lie algebraic extension of the system and a periodic continuation of a parametrized solution to a certain open-loop, finite horizon trajectory interception problem which is stated and solved in logarithmic coordinates of flows. An adequately large stability robustness margin for the extended controlled system can always be insured and is shown to guarantee that the constructed feedback control is also stabilizing for the original model.
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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 | 0.001 |
| 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 it