Robust Control of Collaborative Manipulators - Flexible Object System
Bibliographic record
Abstract
Abstract In many manufacturing and automobile industries, flexible components need to be positioned with the help of coordinated operations of manipulators. This paper deals with the robust design of a control system for two planar rigid manipulators moving a flexible object in the prescribed trajectory while suppressing the vibration of the flexible object. Dynamic equations of the flexible object are derived using the Hamiltonian principle, which is expressed as a partial differential equation (PDE) with appropriate boundary conditions. Then, a combined dynamics is formulated by combining the manipulators and object dynamics without any approximation. The resulting dynamics are thus described by the PDEs, having rigid as well as flexible parameters coupled together. This paper attempts to develop a robust control scheme without approximating the PDE in order to avoid measurements of flexible coordinates and their time derivatives. For this purpose, the two subsystems, namely slow and fast subsystems, are identified by using the singular perturbation technique. Specific robust controllers for both the subsystems are developed. In general, usage of the singular perturbation technique necessitates exponential stability of both subsystems, which is evaluated by satisfying Tikhnov's theorem. Hence, the exponential stability analysis is performed for both subsystems. Focusing on two three-link manipulators holding a flexible beam, simulations are performed and simulation results demonstrate the versatility of the proposed robust composite control scheme.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".