PaperlayerView exact revision on arXiv

Source-linked AI summary

CADeT: Causal-Aware Deformation Transmission for Indirect Robotic Manipulation of Soft Tissue

Junlei Hu, Dominic Jones, Pietro Valdastri

arXiv:2609.38483v1cs.RO

TL;DR

Indirect manipulation of deep anatomy is difficult because intervening tissues filter deformation and passive observations can leave decoupling indistinguishable from blockage. CADeT combines causal mode inference, active probing, and learned coupling within belief-aware control. Simulation and dVRK evaluations support mode identification and indirect shape control under the tested conditions.

  • Problem

    Spatial filtering can make Decoupled and Blocked modes produce similar target-motion observations, although they reflect different interaction mechanisms.

    Source: §I · p. 1, B. Observational Ambiguity under… · p. 4

  • Method

    CADeT uses an SCM and active sensing to infer transmission mode, learns a state-dependent adhesion Jacobian, and incorporates both into belief-aware model predictive control.

    Source: §I · pp. 1–2

  • Results

    Simulation and dVRK evaluations support distinguishing competing transmission modes and controlling locally reachable target configurations under the evaluated conditions.

    Source: §X · p. 17, §IX · p. 17

  • Takeaways & Limitations

    Information-guided probing improved the consistency and efficiency of mode inference compared with random probing in the reported simulation ablations.

    Source: §IX · p. 17

    Extremely weak adhesion can make transmitted deformation indistinguishable from measurement noise, and the framework provides no formal tissue-safety guarantee.

    Source: §IX · p. 17

Abstract

from arXiv · show

Indirect manipulation of deep-seated deformable anatomy inaccessible to the robot is challenging in robot-assisted minimally invasive surgery (RAMIS) because intervening tissues spatially filter deformation transmission. Passive observations can be ambiguous because the Decoupled and Blocked modes may produce similar motion responses. We propose CADeT, a causal-aware deformation transmission framework that integrates structural causal model (SCM) with active sensing to infer a latent transmission mode and estimate a state-dependent adhesion Jacobian online. During normal manipulation, control actions update the mode belief; when ambiguity persists, an additional probing action is selected to improve mode distinguishability. The mode belief and learned Jacobian are incorporated into a belief-aware model predictive controller for indirect target-shape control. Validation in simulation and on the da Vinci research kit (dVRK), using phantom and ex vivo porcine tissues, shows higher mode-identification accuracy and faster shape-error convergence than the evaluated model-free and model-based baselines. These results show that active sensing improves mode identification and indirect deformation control under the evaluated conditions.

I. INTRODUCTION

Indirect manipulation uses accessible proxy tissues to deform deep targets, but viscoelastic filtering weakens and smooths transmitted motion. CADeT combines causal mode inference with active probing and belief-aware deformation control to address ambiguity between decoupling and external blockage.

I. INTRODUCTION

  • Spatial filtering attenuates localized deformation, weakening target responses and making fine-grained shape servoing more challenging.The intermediary tissue acts as a spatial low-pass filter.Source: §I · p. 1
  • Passive observations can leave Decoupled and Blocked modes indistinguishable, although they require different control actions.Continuing manipulation may retract a coupled target but increase compression when the target is blocked.Source: §I · p. 1

A. Modelling and Control of Deformable Objects

  • Existing physically based and model-free deformable-object methods typically assume a continuous, globally consistent actuator-to-deformation mapping, which indirect contact-state changes can violate.Such methods do not explicitly represent latent transmission modes.Source: §I · p. 1, A. Modelling and Control of Deformable… · p. 2

C. Active Sensing and Causal Inference

  • CADeT uses an SCM and Bayesian mode belief, updates that belief from ordinary control responses, and probes when those responses do not distinguish Decoupled from Blocked modes.The probing action is treated as an intervention, and the resulting belief and learned coupling model inform deformation transmission control.Source: §I · pp. 1–2, C. Active Sensing and Causal Inference · p. 3

B. Indirect Manipulation and Transmission Dynamics

  • In surgical indirect manipulation, soft heterogeneous tissues attenuate motion and force cues, while absent target motion can reflect either lost transmission or an external constraint.Both scenarios can be difficult to distinguish visually.Source: B. Indirect Manipulation and… · p. 3

III. PROBLEM FORMULATION

The formulation treats the robot as directly actuating a proxy while tracking a partially visible target whose deformation is transmitted through a changing, uncertain interaction. It distinguishes three local transmission modes and frames their inference as difficult when spatial filtering makes target responses ambiguous.

III. PROBLEM FORMULATION

  • The robot actuates a proxy organ while visually tracking features on a partially visible target; completely occluded targets are outside the formulation.The target state represents the observed region rather than complete organ geometry.Source: §III · p. 3
  • The setup assumes a stable proxy grasp before autonomous manipulation and leaves grasp planning outside the controller's scope.Control is local to the current grasp.Source: §III · p. 3
  • The target is under-actuated: robot commands move the proxy, and target motion is induced through deformation transmission rather than directly controlled.The command is an incremental Cartesian end-effector position command.Source: §III · p. 3

A. Hybrid Deformation Transmission Dynamics

  • The hybrid transmission model combines continuous coupling parameters with an unobserved, locally persistent mode that can change with interaction conditions.The mode is discrete, while the continuous parameters can include local stiffness or a deformation Jacobian.Source: A. Hybrid Deformation Transmission… · pp. 3–4
  • In Decoupled Mode, insufficient or broken adhesion severs effective transmission; in Coupled Mode, adhesion transfers deformation through a state-dependent Jacobian.Blocked Mode retains mechanical coupling but an external constraint locally restricts transmission along the current direction.Source: A. Hybrid Deformation Transmission… · p. 4

B. Observational Ambiguity under Spatial Filtering

  • Soft-tissue spatial filtering attenuates high-frequency interaction cues, so different transmission modes can produce nearly identical target observations.A stationary target may indicate either decoupling or external blockage, making passive observation insufficient to distinguish the causes.Source: B. Observational Ambiguity under… · p. 4
  • Observational ambiguity is defined as a non-injective mapping from interaction history to latent transmission mode, with uncertainty represented separately for the mode and continuous coupling.Mode-belief entropy is used to trigger and design probing actions.Source: B. Observational Ambiguity under… · p. 4

C. Control Objective

The control objective is to plan proxy motions that move the target toward a desired configuration despite uncertain transmission. The causal model separates actuation, potential coupling, and the latent mode that gates target deformation.

C. Control Objective

  • The controller minimizes finite-horizon expected cost to drive the target toward a desired configuration under the current grasp and transmission conditions.The objective penalizes target tracking error and control effort.Source: C. Control Objective · pp. 4–5
  • When mode belief is uncertain, the controller attenuates predicted deformation transmission; when belief favors Coupled Mode, it primarily uses the learned coupling model.The GP posterior represents continuous coupling uncertainty, with its mean used for real-time MPC prediction.Source: C. Control Objective · p. 5

IV. STRUCTURAL CAUSAL MODELLING

  • The SCM represents directed causal dependencies and latent variables, distinguishing adhesive coupling from motion blockage.Its graph describes three structural dependencies.Source: §IV · p. 5, A. The Causal Graph · p. 5

1) Actuation Mechanism:

2) Continuous Coupling Potential:

  • The continuous coupling function Ψ describes target displacement under ideal mechanical coupling and forms the continuous component of the transmission term.Its parameters represent the potential deformation transmission between proxy and target.Source: 2) Continuous Coupling Potential · p. 5

3) The Latent Transmission Mode:

  • The latent mode gates the proxy-to-target transmission pathway: Coupled activates it, Decoupled suppresses it, and Blocked locally suppresses motion along the constrained direction.Blocked Mode does not imply global loss of coupling; the local model distinguishes Decoupled and Blocked modes through their proxy responses.Source: 3) The Latent Transmission Mode · p. 5

B. Non-Parametric Modelling of Coupling Parameters

The framework estimates the state-dependent adhesion Jacobian from coupled observations and uses Gaussian-process predictions to represent coupling uncertainty. Mode-conditioned likelihoods combine target transmission and action-induced proxy response to support Bayesian inference across Coupled, Decoupled, and Blocked conditions.

B. Non-Parametric Modelling of Coupling Parameters

  • A data-driven Gaussian-process model estimates the nonlinear, patient-specific adhesion Jacobian without restrictive parametric assumptions.A sliding window of recent Coupled-mode observations supplies local Jacobian estimates, and independent GPs model its elements.Source: B. Non-Parametric Modelling of… · p. 5
  • The GP posterior mean supplies the current Jacobian estimate, while posterior variance contributes to predicted target-displacement uncertainty.Training estimates are admitted after the Coupled-mode belief exceeds the specified threshold for consecutive updates.Source: B. Non-Parametric Modelling of… · pp. 5–6

C. Mode-Conditioned Likelihoods

  • Mode-conditioned likelihoods factor observations into target transmission given proxy deformation and the action-induced proxy response.This decomposition helps distinguish Decoupled and Blocked modes because both can yield little target motion, while blockage also changes proxy response.Source: C. Mode-Conditioned Likelihoods · p. 6
  • The nominal proxy-response model is initialized from buffered probing responses for the current tissue sample and grasp region, then held fixed during the trial.Its action-response mean is estimated by least squares, and its covariance is the empirical residual covariance.Source: C. Mode-Conditioned Likelihoods · p. 6
  • Decoupled-mode likelihood treats target displacement as measurement noise independent of proxy motion, whereas Coupled-mode likelihood uses the GP predictive distribution.The Coupled likelihood marginalizes over adhesion-Jacobian uncertainty and includes effective target-response noise.Source: C. Mode-Conditioned Likelihoods · p. 6
  • Blocked Mode is modeled by an attenuated nominal proxy response, while its target response can resemble Decoupled Mode.The attenuation factor scales the nominal response mean, and the likelihoods support recursive Bayesian mode updates.Source: C. Mode-Conditioned Likelihoods · pp. 6–7

D. Passive Observational Indistinguishability

As task actions vanish near a stationary target, passive observations cannot distinguish the Decoupled and Blocked modes. CADeT updates mode beliefs from task responses and adds probing when ambiguity persists.

D. Passive Observational Indistinguishability

  • As task actions approach zero in the stationary-target regime, the Decoupled and Blocked observation likelihoods become asymptotically indistinguishable in KL divergence.This motivates additional probing to elicit distinguishable responses.Source: D. Passive Observational… · p. 7

V. TRANSMISSION-MODE INFERENCE WITH ACTIVE SENSING

  • Task-directed responses may leave Decoupled and Blocked modes ambiguous when target motion is negligible, so CADeT applies an additional intervention when that ambiguity persists.The probing action is selected to improve mode distinguishability and its response updates the mode belief.Source: §V · p. 7

A. Bayesian Belief Update

  • After each control input and observation, Bayes’ rule recursively updates the transmission-mode belief using mode-conditioned likelihoods.The recursion uses a local-persistence approximation without an explicit mode-transition model.Source: A. Bayesian Belief Update · p. 7

B. Causal Interpretation of Probing Actions

  • Although Decoupled and Blocked modes both predict negligible target motion, their proxy responses differ, allowing mode-conditioned likelihoods to reduce ambiguity.The probing action is small and approximately orthogonal to the task direction, increasing response separation while limiting its effect on task progress.Source: B. Causal Interpretation of Probing… · p. 8

C. Information-Guided Probing

CADeT selects bounded probing actions to gain information about the latent transmission mode. It approximates this objective through predictive entropy and evaluates sampled candidate directions.

C. Information-Guided Probing

  • CADeT formulates probing as optimal experimental design, selecting the action that maximizes expected information gain about the latent transmission mode.Expected information gain is the mutual information between the mode and observation under the candidate intervention.Source: C. Information-Guided Probing · p. 8
  • Because current belief entropy is independent of the probing action, maximizing information gain is equivalent to minimizing expected posterior entropy.For real-time optimization, the objective is rewritten using predictive-distribution differential entropy.Source: C. Information-Guided Probing · p. 8
  • The method approximates the predictive mixture with a moment-matched Gaussian and selects the highest-entropy option from 12 sampled candidate directions.The bounded, non-convex search avoids gradient-based optimization.Source: C. Information-Guided Probing · p. 8

VI. DEFORMATION TRANSMISSION CONTROL

CADeT combines inferred mode belief and a learned coupling model in a belief-aware MPC for indirect target-shape control. Its prediction and optimization account for uncertain transmission, while the controller does not impose explicit force, strain, or collision constraints.

A. Belief-Based State Prediction

  • The belief-aware MPC combines transmission-mode belief with the learned GP coupling model, attenuating predicted target transmission as belief in the Coupled Mode falls.The local GP mean approximates coupling uncertainty, while GP predictive covariance is not propagated through the MPC horizon and instead affects later mode-belief updates.Source: §VI · p. 8, A. Belief-Based State Prediction · p. 9

B. Quadratic Programming Formulation and Solving

  • Substituting the belief-weighted local prediction into the finite-horizon cost yields a quadratic program, with the control Jacobian weighted by Coupled-mode belief and the local GP mean.The proxy deformation Jacobian is estimated using the shape-servoing method in. The QP has no explicit force, tissue-strain, or collision-avoidance constraints.Source: B. Quadratic Programming Formulation… · p. 9

C. Algorithm Summary and Implementation

  • The architecture runs mode inference and probing above the cycle-level MPC, then executes its first optimized action as an incremental Cartesian position command.Task monitoring measures mean target-feature distance to the desired shape; settlement also requires Cartesian-command motion to remain under threshold for consecutive cycles.Source: C. Algorithm Summary and Implementation · p. 9

VII. SIMULATION EXPERIMENTS

Simulation trials model proxy-to-target tissue deformation with adhesion and external collision constraints, and compare ambiguity-triggered probing against a no-additional-probing variant. Representative trials show distinct proxy responses in Decoupled and Blocked modes despite similarly negligible target motion.

VII. SIMULATION EXPERIMENTS

  • The SOFA simulation uses deformable stomach, pancreas, liver, and surrounding tissues, with synthetic adhesion and rigid obstacles; ground-truth states and interactions are observable.Trials buffer 10 initial probing responses to initialize proxy-response distributions and the mode belief, without a separate calibration trajectory.Source: §VII · p. 10

A. Setup and Latent Mode Synthesis

  • The simulator models Decoupled Mode by disabling adhesion, Coupled Mode by retaining adhesion, and Blocked Mode by adding a rigid obstacle along the deformation path.Blocked Mode occurs when the target engages the external constraint, despite preserved adhesive coupling.Source: A. Setup and Latent Mode Synthesis · p. 10
  • Representative trials show similarly negligible target displacement in Decoupled and Blocked scenarios, while active sensing elicits distinct proxy-deformation signatures.When Coupled Mode is detected, proxy deformation is transmitted to the target and the controller drives it toward the desired shape.Source: A. Setup and Latent Mode Synthesis · p. 10

B. Ablation of Probing Actions

  • The probing ablation compares CADeT with a variant relying only on task-directed responses across 150 randomized trials, with ground-truth mode withheld from inference.The comparison keeps the initialization and Bayesian filter unchanged; Blocked trials count as correctly identified if Blocked evidence appears during constraint engagement.Source: B. Ablation of Probing Actions · p. 10

1) Classification Accuracy:

CADeT’s probing improves mode identification and belief convergence when passive observations leave Decoupled and Blocked modes ambiguous. The ablations also examine probing choice, blocked-response attenuation, and protection of manipulation against early inference errors.

1) Classification Accuracy:

  • 99.3% (149/150 trials) overall identification accuracy with full CADeT contrasts with 92% of no-probing Blocked trials misclassified as Decoupled.Rows in the confusion matrices are normalized over 50 trials per interaction condition.Source: 1) Classification Accuracy · p. 10, Figure 6 · p. 12

2) Belief Convergence:

  • Below 0.25 nat, CADeT’s mode-belief entropy fell across all three modes, while no-probing entropy stayed near 0.65 nat in Decoupled and Blocked modes.Task-directed observations alone did not reliably distinguish those two modes.Source: 2) Belief Convergence · p. 10, Figure 7 · p. 12

1) Quantitative Comparison:

2) Random-Probing Variability:

  • Random probing sometimes converged rapidly but took longer under temporarily ambiguous responses; information-guided selection favored more distinguishable predicted responses.The representative trajectories were from 50 trials in the Coupled Mode.Source: 2) Random-Probing Variability · pp. 11–12

1) Blocked-Response Attenuation:

2) Robustness to Early Mode Misclassification:

  • Confidence-gated GP updating stayed close to the clean reference after early misclassifications, whereas direct updating slowed target-shape-error convergence.The test introduced four non-Coupled observations that were temporarily misclassified as Coupled.Source: 2) Robustness to Early Mode… · p. 12

E. Component Ablation for Manipulation

Component ablations compare mode conditioning, belief weighting, and GP-based coupling estimation; the complete CADeT framework led the tested variants and evaluated methods on manipulation outcomes. Physical validation used dVRK phantom and ex vivo settings, including indirect pancreatic manipulation through the stomach.

E. Component Ablation for Manipulation

  • The ablations varied whether inferred mode conditioned the coupling model and target prediction, whether MPC used a hard mode estimate, or whether GP coupling was replaced by recursive Jacobian estimation.The manipulation ablations were evaluated under the same coupling conditions, initial and desired configurations, and controller limits.Source: E. Component Ablation for Manipulation · p. 12
  • 98.0% success, 11.26% average DTR, and 30.1 ± 2.7 s task time made full CADeT the strongest component-ablation result.The No mode conditioning, Hard-mode MPC, and Jacobian coupling variants had success rates of 84.0%, 90.0%, and 86.0%, respectively.Source: E. Component Ablation for Manipulation · pp. 12–13, Table III · p. 13

F. Comparison with Existing Methods

A. Experiment Setup

  • Physical validation used two 7-degree-of-freedom PSMs, a 4-degree-of-freedom ECM, endoscopic RGB video, soft-tissue phantoms, and ex vivo porcine tissue.Initial responses initialized proxy-response distributions, which were reinitialized when the tissue sample or grasp region changed.Source: A. Experiment Setup · p. 14

B. Pancreatic Exposure via Stomach Manipulation

  • In pancreatic exposure trials, the stomach was the proxy and the pancreas the target; probing identified Coupled Mode before the estimated adhesion Jacobian guided retraction toward the desired configuration.Validation progressed from phantom stomach–pancreas models coupled by pressure-sensitive adhesive to fresh porcine tissue.Source: B. Pancreatic Exposure via Stomach… · p. 14

C. Mesentery Manipulation

The mesentery experiment demonstrates indirect shape control through the colon proxy, while physical trials distinguish reachable targets from mode-inference success. The discussion frames active probing and mode-conditioned control as useful under tested conditions, with reachability and modeling limits remaining.

C. Mesentery Manipulation

  • The colon proxy enabled mesentery manipulation, with mode belief converging to Coupled; high colon compliance required larger proxy motions because transmission was lower.The task was to flatten or retract the mesentery; final-cycle command displacement averaged 0.48±0.07 mm, with residual motion below the settlement threshold.Source: C. Mesentery Manipulation · pp. 14–15

D. Reachability and Failure Case

  • In the 12 physical cases, expected transmission conditions were identified in all; reachable Coupled cases fell from 36.8–45.3 mm to 2.1–2.7 mm mean shape error, while Decoupled cases showed little or no reduction.Blocked cases counted as correct when Blocked-Mode evidence appeared during local constraint engagement; the results are summarized in Table V.Source: D. Reachability and Failure Case · p. 16, Table V · p. 17
  • Three Coupled cases retained 16.5–32.5 mm residual error because requested shapes exceeded the local deformation range under the current grasp; the Blocked case retained 34.1 mm under external constraint.These cases distinguish limited target reachability from failure of mode inference.Source: D. Reachability and Failure Case · pp. 16–17

IX. DISCUSSION

  • Information-guided probing improved the consistency and efficiency of mode inference over random probing, which showed greater direction-dependent variability.Probing helped resolve ambiguity between Decoupled and Blocked modes, which can produce similar target-motion responses.Source: §IX · p. 17
  • Belief-weighted prediction reduces transmission gain as Coupled-Mode belief falls, discouraging corrective actions with limited predicted target effect.The behavior is consistent with higher task-success rates and faster convergence in component ablations and baseline comparisons.Source: §IX · p. 17
  • The framework assumes a predefined grasp, uses a first-order local transmission model, and lacks formal tissue-safety guarantees because force and strain are not measured or constrained.Reachability is limited by the current grasp and local transmission; dynamic constraints and unpredictable disturbances remain untested.Source: §IX · p. 17

X. CONCLUSION

  • Simulation and dVRK validation with phantom and ex vivo porcine tissues supported mode distinction and shape control for locally reachable targets under evaluated conditions.Future work is directed toward multi-organ transmission chains and real-time force feedback.Source: §X · p. 17

APPENDIX PROOF OF PROPOSITION 1

The proof shows why passive observations cannot reliably distinguish Decoupled from Blocked modes in the stationary regime. With vanishing target response and diminishing control effort, their proxy responses become asymptotically nondiscriminative under the stated model assumption.

  • In stationary regime S0, target response is approximately zero under both Decoupled and Blocked modes, so it provides no discriminative information.Source: APPENDIX PROOF OF PROPOSITION 1 · p. 18
  • The modes therefore differ only in their proxy-response distributions, whose shared covariance makes their KL divergence the relevant comparison.Source: APPENDIX PROOF OF PROPOSITION 1 · p. 19
  • The passive policy drives control effort toward zero when predicted target response is negligible; assuming a continuous nominal proxy-response model with μn(0)=0, DKL tends to zero, establishing asymptotic observational indistinguishability.Source: APPENDIX PROOF OF PROPOSITION 1 · p. 19

Related papers

Loading 2609.38483v1…