Provably Robust Learning-Based Approach for High-Accuracy Tracking\n Control of Lagrangian Systems
Bibliographic record
Abstract
Lagrangian systems represent a wide range of robotic systems, including\nmanipulators, wheeled and legged robots, and quadrotors. Inverse dynamics\ncontrol and feedforward linearization techniques are typically used to convert\nthe complex nonlinear dynamics of Lagrangian systems to a set of decoupled\ndouble integrators, and then a standard, outer-loop controller can be used to\ncalculate the commanded acceleration for the linearized system. However, these\nmethods typically depend on having a very accurate system model, which is often\nnot available in practice. While this challenge has been addressed in the\nliterature using different learning approaches, most of these approaches do not\nprovide safety guarantees in terms of stability of the learning-based control\nsystem. In this paper, we provide a novel, learning-based control approach\nbased on Gaussian processes (GPs) that ensures both stability of the\nclosed-loop system and high-accuracy tracking. We use GPs to approximate the\nerror between the commanded acceleration and the actual acceleration of the\nsystem, and then use the predicted mean and variance of the GP to calculate an\nupper bound on the uncertainty of the linearized model. This uncertainty bound\nis then used in a robust, outer-loop controller to ensure stability of the\noverall system. Moreover, we show that the tracking error converges to a ball\nwith a radius that can be made arbitrarily small. Furthermore, we verify the\neffectiveness of our approach via simulations on a 2 degree-of-freedom (DOF)\nplanar manipulator and experimentally on a 6 DOF industrial manipulator.\n
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".