On the Merits of Joint Space and Orientation Representations in Learning the Forward Kinematics in SE(3)
Bibliographic record
Abstract
This paper investigates the influence of different joint space and orientation representations on the approximation of the forward kinematics. We consider all degrees of freedom in three dimensional space SE(3) and in the robot's joint space Q. In order to approximate the forward kinematics, different shallow artificial neural networks with ReLU (rectified linear unit) activation functions are designed. The amount of weights and bias' of each network are normalized. The results show that quaternion/vector-pairs outperform other SE(3) representations with respect to the approximation capabilities, which is demonstrated with two robot types; a Stanford Arm and a concentric tube continuum robot. For the latter, experimental measurements from a robot prototype are used as well. Regarding measured data, if quaternion/vector-pairs are used, the approximation error with respect to translation and to rotation is found to be seven times and three times more accurate, respectively. By utilizing a four-parameter orientation representation, the position tip error is less than 0.8% with respect to the robot length on measured data showing higher accuracy compared to the state-of-the-artmodeling (1.5%) for concentric tube continuum robots. Other three-parameter representations of SO(3) cannot achieve this, for instance any sets of Euler angles (in the best case 3.5% with respect to the robot length).
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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".