Geometric MPC Techniques for Reduced Attitude Control on Quadrotors with Bidirectional Thrust
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Bibliographic record
Abstract
We present two novel nonlinear MPC formulations for reduced attitude tracking on quadrotors with bidirectional thrust capabilities. Reduced attitude tracking is relevant to recovery from partial thrust loss, which can occur due to the failure of one or more motors. The first formulation builds on a linearization of the quadrotor attitude dynamics on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$S(2)$</tex> to achieve simultaneous tracking of reduced attitude and total thrust targets. The second formulation, meanwhile, accomplishes the same goal using a linearization of the dynamics on the Lie algebra of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$SO(3)$</tex> and a proposed method for projecting Lie algebra errors onto reduced attitude errors. Both methods achieve global tracking on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$S(2)$</tex> without requiring the use of computationally expensive sequential quadratic program solvers. Through simulations, we show that the second approach generally tracks aggressive attitude references better, while the first controller offers more reliable regulation.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 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)
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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