A Predictor-Corrector Algorithm for the Fast Determination of the Wrench-Feasible Workspace of Cable-Driven Parallel Robots
Bibliographic record
Abstract
In this paper, we present a method of determining the Constant-Orientation Wrench-Feasible Workspace (COWFW) of Cable-Driven Parallel Robots (CDPRs). This workspace is a critical property of CDPRs, as their reach is often limited by their ability to sustain required forces and moments while keeping their cable tensions within acceptable limits. Several manners of determining the COWFW are reported in the literature, among which the brute force method is probably the most popular, the easiest to implement and the slowest, as it consists in determining wrench-feasibility at a grid of points covering the workspace. On the other hand, the ray-tracing method implemented in WireX software is probably the fastest method available; It consists in sampling the COWFW boundary by performing line-searches from a common starting point along predetermined, evenly-spaced directions. The method proposed in this paper is the application to CDPRs of a predictor-corrector algorithm used in computer graphics to quickly sample implicit surfaces In this work, the implicit surface is defined by equating to zero the “capacity margin” an index developed by one of the authors. The predictor-corrector algorithm then “marches” over the implicit surface, triangulating it as it advances. Simulation results show that the determination of the COWFW surface by this technique can be faster than the ray-tracing method in at least some examples, and often yields a triangulation that is more regular. We should note, however, that the implementation of this method is more demanding, it requiring more lines of code than the ray-tracing method.
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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".