A Unified Arbitrarily Predefined -Time Convergent Recurrent Neural Network for Motion Control of Redundant Robot Manipulators: A Unified Paradigm
Bibliographic record
Abstract
In general, the motion control problem of redundant robot manipulators (RRMs) can be transformed into a constrained time-varying quadratic programming (TVQP) problem. Recently, various recurrent neural networks (RNNs) with predefined time convergence (PTC) abilities have been proposed to solve this constrained TVQP problem in real-time. However, there is still a lack of a unified paradigm to guide researchers and engineers design such RNNs more effectively based on specific requirements. To bridge this gap, we propose a unified paradigm derived from a novel segmentation evolution formula incorporating a special <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathfrak{B}$</tex-math></inline-formula>–<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Class</i> function. This paradigm enables the construction of various RNNs, collectively referred to as unified arbitrarily predefined-time convergent RNNs (U-APTC-RNNs). Compared with most existing RNNs, the constructed U-APTC-RNN has two significant advantages: 1) it has the arbitrarily PTC (APTC) ability, meaning its actual convergence time can be arbitrarily and precisely predefined without setting other model parameters and 2) using a novel piecewise computation strategy, redundant nonlinear calculations are effectively minimized, leading to a notable reduction in computational costs. The stability and APTC ability of the constructed U-APTC-RNN are demonstrated through detailed theoretical analysis. Numerical simulation experiments confirm the APTC capabilities of various U-APTC-RNNs constructed using the proposed unified paradigm. Comparative experiments show that U-APTC-RNN has more competitive convergence performance and lower computational cost than other state-of-the-art RNNs with PTC abilities. Finally, simulation and physical motion control experiments on the Jaco and UR5 robotic arms demonstrate the superiority and practicality of the proposed U-APTC-RNN.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".