Convergence Analysis of an Inverse Flexible Manipulator Model Algorithm
Bibliographic record
Abstract
In this paper we present a convergence analysis of an iterative method to obtain the inverse model in the virtual joint space of a class of flexible manipulators. Virtual joints are defined so as to be related kinematically to the workspace. Thus, when the desired trajectory can be transformed from the workspace to the virtual joint space, the inverse model in the virtual joint space can be used to obtain a trajectory tip-tracking controller. Because the robot model in the virtual joint space is a non-minimum phase system, its inverse is unstable. The inverse method is then based on a causal-anticausal integration approach used in an iterative manner. The convergence analysis of this inverse algorithm is based on the contraction-mapping theorem and provides a very simple way to expand the desired trajectory to ensure its convergence. Finally, the inverse algorithm and its convergence analysis are validated by simulating a controller, based on the inverse model, that drives a two-link manipulator made up of one rigid and one flexible link. The simulation results demonstrate the good performance of the inverse algorithm and its convergence analysis presented here.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".