Singularity control of robot manipulators using closed-form kinematic solutions
Bibliographic record
Abstract
In robotics, kinematic singularities of serial chain manipulators arise at places where the transformation from Cartesian coordinates to robot joint coordinates becomes ill-defined, with a loss of one or more degrees of freedom. Traveling close to a singularity while following a path in Cartesian coordinates typically results in unacceptably high joint velocities and accelerations. The problem of singularity control is to keep the joint velocities and accelerations bounded while still trying to stay close to the desired path. The paper explores an alternative method of singularity control which directly utilizes closed-form inverse kinematic solutions. While not all robots have closed-form solutions, most six degree-of-freedom robots in common use do. Closed form kinematic solutions offers the advantages of speed and computational stability. Perhaps most importantly, they also enable us to know exactly where the various singularities are. We specifically consider straight line Cartesian trajectories, and discuss a method for constructing a velocity profile that allows these trajectories to pass near or through singularities without any deviation in the spatial path, while keeping both the joint velocities and accelerations bounded.>
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| 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".