End-Effector Trajectory Tracking of a Class of Flexible Link Manipulators
Bibliographic record
Abstract
A new controller for the end-effector trajectory tracking (EETT) of a class of flexible link manipulators which composed of a chain of rigid links with an end-link flexible (CREF) is introduced. The dynamic model of the CREF is expressed into the standard singularly perturbed form; that is, the dynamic model is decomposed into slow and fast subsystems. The states of the slow subsystem are the joints’ rotations and their time derivatives, while the states of the fast subsystem are flexible variables, which model the lateral deflection of the end-link, and their time derivatives. For the slow subsystem, corrective torque is added to the computed torque control commands of the rigid link counterpart of the CREF to reduce the EETT error. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. It was shown that this corrective term is of order ε2 where ε = 1/(2πf) and f is the smallest non-zero natural frequency of the CREF. To stabilize the fast subsystem, an observer-based controller is designed by the gain-scheduling technique. Due to the application of the observer-based controller there is no need for the measurement of the time derivative of the flexible variables, which their measurements are hardly practical. To facilitate the derivation and implementation of introduced controller here, several properties of the mass matrix of the CREF are introduced and used. The effectiveness and feasibility of the new controller are shown through the simulation and experimental studies.
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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".