Deep Koopman Approach for Nonlinear Dynamics and Control of Tendon-Driven Continuum Robots
Bibliographic record
Abstract
Tendon-driven continuum robots (TDCRs) have received widespread attention, particularly in the medical domain, due to their slender shape and flexibility. Modeling the dynamics of TDCRs is inherently complex and involves continuum mechanics that result in nonlinear and computationally intensive models. Consequently, current modeling approaches pose challenges for real-time control, essential for practical implementations. In this work, we propose a novel method for efficient and control-oriented modeling of the nonlinear dynamics of TDCRs using an intrinsic bilinear model leveraging the Deep Koopman approach. This method transforms the states of the system into an intrinsic nonlinear manifold, identified via deep learning, where the autonomous dynamics can be approximated linearly and the actuation input enters the system with a bilinear term. The proposed model captures the nonlinearities including space-dependent variations in the system spectrum. Task-space position control is implemented using a linear quadratic controller, leveraging the linear nature of the Koopman operator. The accuracy of the proposed method is experimentally validated using a dual-tendon robotic steerable catheter with a bending section of 55 mm, achieving a position tracking error of 1.79±1.26 mm with a control loop frequency of 250 Hz. The results demonstrate the potential for applying the proposed approach for real-time control of a broad range of TDCRs.
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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 | 0.000 |
| 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".