Stable Tracking-in-the-Loop Control of Cable-Driven Surgical Manipulators under Erroneous Kinematic Chains

Fei Liu; Florian Richter; Michael C. Yip; Neelay Joglekar

REVIEW 3 major objections 4 minor 28 references

Stable Tracking-in-the-Loop Control of Cable-Driven Surgical Manipulators under Erroneous Kinematic Chains

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A resolved-rate controller for the out-of-view joints of cable-driven surgical manipulators is provably stable despite erroneous joint readings, as long as the roll-joint reading error remains below 75 degrees.

desk verdict First stability analysis for hidden-chain RCM control, with a genuinely useful error bound, but the Lyapunov proof skips the drift of the lumped-error transform it itself flags, so the headline guarantee isn't actually established. read the letter →

arxiv 2507.05663 v1 pith:4KARXFCM submitted 2025-07-08 cs.RO

Neelay Joglekar , Fei Liu , Florian Richter , Michael C. Yip This is my paper

classification cs.RO MSC 93D2093C85

keywords cable-drivensurgicalmanipulatorsremotecenterofmotionresolved-ratecontrolkinematicchainerrorvisualtrackingintheloopLyapunovstabilitydaVinciResearchKitautonomy

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tackles a reliability gap in robotic minimally invasive surgery: cable-driven remote-center-of-motion (RCM) manipulators read their joint angles with errors, and the joints outside the camera view can never be corrected by visual tracking alone. It proposes a resolved-rate controller for that out-of-view chain that uses the erroneous joint readings directly, and proves the closed loop is globally asymptotically stable as long as the roll-joint reading error stays below 75 degrees. The controller is embedded in a bilevel scheme that coordinates the out-of-view chain with the visible tool chain, giving the full manipulator a stable tracking-in-the-loop controller. The authors verify the stability bound in simulation and in suture-thread grasping on a da Vinci Research Kit, which matters because autonomous subtasks such as suturing currently lack reliability guarantees under kinematic error.

What carries the argument

The load-bearing object is a factorization of the out-of-view chain's body-frame Jacobian, $J_{n_b} = D Q W S$, where $Q$, $W$, and $S$ act in a four-dimensional "linear plus roll" subspace and $D$ lifts the result into six-dimensional twist space. The controller ignores $S$ by an assumption about the smallness of $\dot q_1 \sin q_2$ and uses the erroneous factors $\tilde Q$ and $\tilde W$ in the pseudoinverse control law. Stability is carried by the Lyapunov function $V = \tfrac{1}{2} v_{n_b}^\top v_{n_b}$: substituting the control law turns $\dot V$ into a quadratic form whose Hessian is positive definite precisely within the 75-degree roll-error bound, verified by Sylvester's criterion.

What would settle it

Run the out-of-view controller in simulation or on hardware with an error bias on the roll joint that stays below 75 degrees but drifts at a small nonzero rate (for example a slow sinusoidal signal), and check whether the end effector still converges; failure would show the static-error assumption is load-bearing.

Watch

Extended reading notes

Core claim

The central claim is that a tracking-in-the-loop resolved-rate controller for the unobservable portion of an RCM manipulator kinematic chain remains stable even when the joint angle readings feeding it are wrong. The control law $\dot q_{1:n_b} = -\alpha(\tilde Q \tilde W)^\dagger v_{n_b}$ applies a pseudoinverse built from erroneous matrices to the measured pose error; the proof shows the Lyapunov derivative $\dot V$ is negative definite whenever the error on the roll joint satisfies $|e_{n_b}| < \tau$, with $\tau = 75^\circ$ for the dVRK. This bound is derived from the positive definiteness of a Hessian via Sylvester's criterion, and the other three out-of-view joint errors are left unconstrained except by joint limits. Experiments show the controller converges up to the predicted threshold and degrades only after it is exceeded, and the same error bound empirically applies to an inverse-kinematics controller on the full chain.

Load-bearing premise

The proof assumes the out-of-view joint errors barely change while the robot moves, but the paper notes the lumped error correction itself drifts with the joint readings, so the guarantee may not cover slowly drifting cable errors.

Editorial extensions

If this is right

Out-of-view joint chains of cable-driven RCM manipulators can be servoed to a goal with a closed-form, non-iterative controller that is stable within a checkable error bound.
The same theoretical error bound appears to hold for the existing inverse-kinematics controller when the full chain is actuated, so the stability analysis covers a broader family of kinematics-based controllers.
The bilevel scheme makes the controller agnostic to tool type, extending the guarantee to underactuated tools such as blood-suction instruments.
For any serial RCM chain with the same joint order, the bound can be re-derived from joint limits, so the method transfers beyond the dVRK.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If an online estimate of the roll-joint error were available, the 75-degree threshold could serve as a safety monitor that warns before convergence degrades.
The static-error assumption means the guarantee does not yet cover smoothly drifting cable errors; a robust or adaptive version of the proof would be needed for long procedures.
The bilevel coordination idea could generalize to other partially observable manipulator chains where a low-dimensional hidden subspace is servoed with an erroneous pseudoinverse.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The paper is the first to analyze closed-loop stability of tracking-in-the-loop RCM control when the out-of-view part of the kinematic chain carries joint reading error. That is a real gap in the surgical robotics literature, and the paper goes about it the right way: decompose the out-of-view body Jacobian into D,Q,W,S, define a resolved-rate law in the 4D 'linear+roll' subspace, and derive a checkable bound on the roll-joint error (|e4|<75 degrees for the dVRK). The simulation study that ramps up errors and shows divergence near the threshold is well designed, and the hardware suture thread grasping is a legitimate, if small, demonstration. Credit where due: the problem framing is timely, the decomposition is elegant, and the empirical support is honest.

Now the soft spots. The proof in Appendix A conflates two different vnb's: the task-space error from (10) and the link-nb velocity in (16), and \dot V is printed as v^T vnb instead of v^T \dot vnb. Those are fixable typos. The deeper issue is that vnb is computed using the erroneous chain (3), so R_c_nb comes from the lumped-error transform T_b-^{b+}. Section III-A explicitly says that transform depends on the joint readings and therefore drifts as the robot moves, even when the underlying joint biases and base calibration error are constant. Appendix A's Eq. (16) assumes the closed-loop relation holds for the true link-nb frame, with T_b-^{b+} frozen. Assumption 2 only bounds \dot e1:nb; it says nothing about the drift of T_b-^{b+} or the frame mismatch. That unmodelled term can enter \dot V with a sign-indefinite contribution, so the claimed global asymptotic stability, and the 75-degree bound, are not proven for the actual time-varying system. The full-chain bilevel controller also gets no dedicated stability proof; its guarantee is inherited from the out-of-view proof, which is now in question. No code or data is shipped, so the simulation numbers are not independently checkable.

Proportionately, these are real but not fatal. The method behaves well in the experiments, and it is plausible that the drift term is small enough not to break the convergence—the hardware results support that. But the paper overclaims: 'provably stable' is not what the proof delivers.

My recommendation: send it to peer review with expectation of major revision. The reviewer should ask for either a modified Lyapunov analysis that includes the drift term and states a condition under which it is dominated, or a toned-down claim limited to the frozen-error model with empirical evidence that the time-varying case behaves similarly. The problem and the method deserve referee time; the theory just needs to match what is actually proven.

Referee Report

3 major / 4 minor

Summary. The paper studies control of cable-driven RCM surgical manipulators whose kinematic chain is partially out of view and subject to joint reading errors. It proposes a resolved-rate controller for the out-of-view chain that uses erroneous Jacobian matrices, claims a global asymptotic stability guarantee under three assumptions with a joint-error bound |e4| < 75 degrees, extends this controller to a bilevel full-chain scheme, and reports simulation and dVRK hardware experiments (suture thread grasping) comparing against an IK controller and a calibration-based baseline.

Significance. If the stability proof were correct, this would be a meaningful contribution: it would give the first theoretical characterization of tracking-in-the-loop stability under RCM kinematic-chain errors, with a simple non-iterative controller and an explicit, experimentally testable error threshold. The paper is honest about its assumptions, the threshold is falsifiable, and the simulation results show the expected degradation near the threshold. The hardware experiment is modest but appropriate as a first validation. However, the theoretical proof in Appendix A has a load-bearing gap that must be addressed before the claimed guarantee can be accepted.

major comments (3)

[Section IV-A / Appendix A, Eq. (16)] The proof states 'Let vnb be the velocity of link nb' and then writes vnb = -alpha QW(Qtilde Wtilde)^dagger vnb, but the vnb defined in Eq. (10) is a task-space error expressed using the estimated link-nb rotation R_c_nb from the erroneous chain (3). No derivation is given for the time derivative of this error. Section III-A explicitly notes that the lumped-error transform T_b-^{b+} depends on the joint readings qtilde and therefore changes as the robot moves, so the estimated frame used to compute vnb rotates relative to the true link-nb frame. The additional terms in the error derivative that arise from this frame drift are not bounded by Assumption 2, which only concerns dot e_{1:nb}. Because the Lyapunov computation in Eqs. (17)-(18) is based on (16), the claimed global asymptotic stability and the |e4| < 75 degree bound do not follow from the printed proof for the controller as implemented.
[Appendix B, Assumptions 1 and 2] Assumption 1 states ||dot q1 sin q2|| << ||dot q4||, but dot q is the output of the controller in Eq. (11), so this is a condition on the closed loop, not an independent geometric fact; the proof should either verify it from the control law and error bound or state explicit conditions under which it holds. Assumption 2 dismisses dot e_{1:nb}, but the authors' own discussion in Section III-A implies that even a constant joint bias produces a time-varying lumped-error transform T_b-^{b+} as qtilde changes. A quantitative bound on the resulting drift term in the Lyapunov derivative is needed; without it, the stability guarantee rests on an unverified smallness assumption.
[Appendix A, proof notation and derivation] The proof as printed is not internally consistent: Eq. (16) uses the symbol vnb for both the link-nb velocity and the task-space error, and the printed derivative dot V = v^T_n vnb should evidently be v_nb^T dot v_nb. If Eq. (16) is intended as an equation for dot v_nb, that equation requires a derivation from the definition of vnb in Eq. (10), including the effect of the estimated frame's rotation. Rewriting the proof with distinct symbols and an explicit derivation of dot v_nb is necessary to make the claims checkable.

minor comments (4)

[Introduction] There is a typo in 'jeapordizing the reliability'; it should be 'jeopardizing the reliability'.
[Section V-A] The word 'peforms' should be 'performs' in the sentence about the IK controller.
[References] Reference [24] lists the authors as 'I. Wampler, C. W. and L. J. Leifer'; this should be corrected to C. W. Wampler and L. J. Leifer.
[Section V-B / Table III] The hardware experiment demonstrates task success but does not vary e4 across the claimed stability region; the paper should state explicitly that the hardware results do not directly validate the 75-degree bound.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the stability bound is derived from Sylvester's criterion rather than fitted, and the controller is benchmarked against external baselines.

full rationale

The paper's central claim is a Lyapunov stability proof for a resolved-rate controller under erroneous out-of-view joints. The 75-degree threshold is produced by applying Sylvester's criterion to the Hessian in Eq. (18), not by fitting a parameter to data or by renaming an empirical pattern. The control law in Eq. (11) is new to this paper and is tested against a calibration-based baseline and a previously developed IK controller, which are external comparators rather than consequences of the paper's fitted values. The self-citations, chiefly [14] for the lumped-error transform, provide the problem setup and are published prior work with independent experimental support; the Lyapunov derivation itself does not reduce to that citation. The identified weaknesses, such as the drift of T_{b-}^{b+} and the neglect of S, are potential errors in modeling or assumptions, not circularity: they concern whether Eq. (16) describes the implemented closed loop, not whether the stated result is equivalent to its own inputs by definition. No step was found in which a prediction is statistically forced, a fitted parameter is renamed as a prediction, or a conclusion is identical to an assumption by construction.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The only new construction is the controller and its error bound; the imaginary base frame b+ is inherited from prior lumped-error work [14], not introduced here. No new physical entity or mediator is postulated.

free parameters (1)

Control gain alpha = 1/6
Set for all controllers in Section V-A; the stability theorem only requires alpha > 0, so this is a chosen tuning value, not a fitted constant for the claim.

assumptions (6)

domain assumption Modified DH kinematics for the dVRK, with parameters from [16], are correct.
Section IV uses the dVRK modified DH parameters to write the out-of-view Jacobian (4).
domain assumption The lumped-error transform Tb- b+ from [14] correctly summarizes base calibration and out-of-view joint errors.
Section III-A defines the imaginary chain (3) on this prior framework; the control loop feeds vnb computed through this chain.
ad hoc to paper Assumption 1: the S contribution to Jnb is negligible (||qdot1 sin q2|| << ||qdot4||).
Section IV-A and Appendix B drop S to obtain (16); the proof uses (16).
ad hoc to paper Assumption 2: time variation of joint biases is negligible (edot1:nb ~ 0).
Appendix B declares edot1:nb out of scope and relies on hardware verification.
ad hoc to paper Assumption 3: |e4| < 5pi/12 rad for the dVRK and q, qtilde stay within joint limits.
Section IV-A states this bound; Appendix A uses it to make H positive definite.
standard math Sylvester's criterion certifies positive definiteness of the Hessian H.
Appendix A invokes [28] to conclude global asymptotic stability from H > 0.

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Cite this review

Pith. "Pith review of Stable Tracking-in-the-Loop Control of Cable-Driven Surgical Manipulators under Erroneous Kinematic Chains." pith.science (2026). https://pith.science/paper/4KARXFCM

@misc{pith2026250705663,
  author       = {Pith},
  title        = {Pith review of: Stable Tracking-in-the-Loop Control of Cable-Driven Surgical Manipulators under Erroneous Kinematic Chains},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4KARXFCM}},
  note         = {Machine review of arXiv:2507.05663}
}

read the original abstract

Remote Center of Motion (RCM) robotic manipulators have revolutionized Minimally Invasive Surgery, enabling precise, dexterous surgical manipulation within the patient's body cavity without disturbing the insertion point on the patient. Accurate RCM tool control is vital for incorporating autonomous subtasks like suturing, blood suction, and tumor resection into robotic surgical procedures, reducing surgeon fatigue and improving patient outcomes. However, these cable-driven systems are subject to significant joint reading errors, corrupting the kinematics computation necessary to perform control. Although visual tracking with endoscopic cameras can correct errors on in-view joints, errors in the kinematic chain prior to the insertion point are irreparable because they remain out of view. No prior work has characterized the stability of control under these conditions. We fill this gap by designing a provably stable tracking-in-the-loop controller for the out-of-view portion of the RCM manipulator kinematic chain. We additionally incorporate this controller into a bilevel control scheme for the full kinematic chain. We rigorously benchmark our method in simulated and real world settings to verify our theoretical findings. Our work provides key insights into the next steps required for the transition from teleoperated to autonomous surgery.

Figures

Figures reproduced from arXiv: 2507.05663 by the authors.

**Figure 2.** A 2D example: a) An ideal kinematic chain can be constructed [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Simulated experiment examples for out-of-view chain (top) and full chain (bottom) control. We gradually added errors to the out-of-view joints [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Simulated experiment results for out-of-view chain (left) and full chain (right) control. We gradually added errors to the out-of-view joints and [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: We implement our controller on hardware and verify its performance [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

State of the art in movement around a remote point: a review of remote center of motion in robotics,

W. Zhang, Z. Wang, K. Ma, F. Liu, P. Cheng, and X. Ding, “State of the art in movement around a remote point: a review of remote center of motion in robotics,” Frontiers of Mechanical Engineering , vol. 19, no. 2, p. 14, 2024

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B. T. Ostrander, D. Massillon, L. Meller, Z.-Y . Chiu, M. Yip, and R. K. Orosco, “The current state of autonomous suturing: a systematic review,” Surgical Endoscopy, vol. 38, no. 5, pp. 2383–2397, 2024

work page 2024

[3] [3]

Stitch: Augmented dexter- ity for suture throws including thread coordination and handoffs,

K. Hari, H. Kim, W. Panitch, K. Srinivas, V . Schorp, K. Dharmarajan, S. Ganti, T. Sadjadpour, and K. Goldberg, “Stitch: Augmented dexter- ity for suture throws including thread coordination and handoffs,” in 2024 International Symposium on Medical Robotics (ISMR) . IEEE, 2024, pp. 1–7

work page 2024

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J. Ge, M. Kam, J. D. Opfermann, H. Saeidi, S. Leonard, L. J. Mady, M. J. Schnermann, and A. Krieger, “Autonomous system for tumor resection (astr)-dual-arm robotic midline partial glossectomy,” IEEE robotics and automation letters , vol. 9, no. 2, pp. 1166–1173, 2023

work page 2023

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MEDiC: Autonomous Surgical Robotic Assistance to Maximizing Exposure for Dissection and Cautery

X. Liang, C.-P. Wang, N. U. Shinde, F. Liu, F. Richter, and M. Yip, “Medic: Autonomous surgical robotic assistance to maximizing ex- posure for dissection and cautery,” arXiv preprint arXiv:2409.14287 , 2024

work page Pith review arXiv 2024

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Real-to-sim registration of deformable soft tissue with position-based dynamics for surgical robot autonomy,

F. Liu, Z. Li, Y . Han, J. Lu, F. Richter, and M. C. Yip, “Real-to-sim registration of deformable soft tissue with position-based dynamics for surgical robot autonomy,” in 2021 IEEE International Conference on Robotics and Automation (ICRA) , 2021, pp. 12 328–12 334

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