Stable Inversion Using the Assumed-Modes Rayleigh-Ritz Approximation for Tip Tracking of an Elastic Beam
Bibliographic record
Abstract
Inversion control has been very successful in the control of nonlinear dynamical systems. However, when applied to flexible manipulators, inverse dynamics through direct integration in temporal space causes unbounded controller command. For nearly three decades, researchers have exhausted all possible solutions. Still, a perfect solution does not exist that would yield a perfect tip tracking. It has been suggested that seeking an inverse dynamics solution for a given tip trajectory is an ill-posed problem. It has also been suggested that increasing model accuracy by including more terms in a truncated beam model worsens the controller’s ability of stability. In this paper, we seek to understand the nature of the inverse dynamics instability. We use one assumed mode to approximate the beam deflection in a single link manipulator. The mode shape is chosen to ensure a boundedness of the inverse dynamics solution. Such solution is then applied in an inversion controller. Numerical simulations and experiments have both been conducted to show its performance.
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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".