An MPC Formulation on $SO(3)$ for a Quadrotor With Bidirectional Thrust and Nonlinear Thrust Constraints
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Bibliographic record
Abstract
We examine the problem of agile trajectory tracking for a quadrotor vehicle with bidirectional thrust capabilities. A time-dependent linearization of the dynamics is presented based on the Lie algebra of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$SO(3)$</tex-math></inline-formula> . The obtained linear dynamics are used as the basis for a nonlinear model predictive control algorithm that does not require operating around equilibrium state-input pairs. Our approach allows the problem to be transcribed as a quadratic program with an analytical Hessian. A method for ensuring the controller satisfies the nonlinear motor constraints involved with bidirectional thrust is then suggested, and the modelling of the thrust dynamics is discussed. Simulations for the performance of the controller are carried out on a basic half-flip maneuver as well as challenging aggressive turnaround and barrel roll maneuvers. The proposed controller performs well on all three maneuvers, significantly outperforming a reference Euler angle-based nonlinear MPC formulation and improving upon the simplified handling of the thrust constraints over the prediction horizon of the MPC.
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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 | 0.000 |
| 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 it