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REVIEW 4 major objections 6 minor 59 references

Geometric Contact Flows: Contactomorphisms for Dynamics and Control

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Pith's one-line read Geometric Contact Flows claims that contactomorphisms, by preserving the contact form, let a latent contact Hamiltonian dynamics reconstruct dissipative second-order systems and steer generalization toward the data manifold.

desk verdict Genuinely new contact-geometric learning framework with real robot demos, but the headline gains are not yet controlled because the latent action coordinate s is underdetermined and withheld from baselines; send to review with a request to fix the s-lift and the Eq. (8) sign. read the letter →

arxiv 2506.17868 v1 pith:3F5FYRZ7 submitted 2025-06-22 cs.RO cs.LGmath.DG

Andrea Testa , S{o}ren Hauberg , Tamim Asfour , Leonel Rozo This is my paper · ORCID
classification cs.ROcs.LGmath.DG
keywords contactHamiltoniandynamicscontactomorphismsdissipativedynamicalsystemsRiemannianmetriclearninguncertainty-awaregeodesicsphysics-informedrobotmanipulationmotiongeneration
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

Geometric Contact Flows (GCF) claims that a learned, second-order dynamical system can be made accurate and physically interpretable by anchoring it to a simple contact Hamiltonian dynamics in a latent space and connecting that latent space to the observed state space through contactomorphisms, which are diffeomorphisms preserving the contact form up to a scaling factor. The paper's thesis is that this geometric prior fixes what black-box models and existing physics-inspired baselines miss: dissipative systems with energy exchange need an extra odd-dimensional variable, the Lagrangian action, that symplectic and Hamiltonian methods do not carry. Concretely, the paper reports that GCF reduces dynamic-time-warping reconstruction error by 57% on a spring-mesh benchmark and by 60% on stochastic quantum dynamics, and that trajectories initialized from off-manifold grid points reliably converge back to the data manifold on handwriting tasks. Why it would matter: dynamics models built this way inherit stability or energy behavior from the latent system, come with a principled uncertainty signal from an ensemble of maps, and can be steered away from unsafe or data-poor regions by reshaping the metric. The same machinery is demonstrated on real robot tasks, including an energy-aware safety stop when an unexpected load drives the action variable to zero.

What carries the argument

The load-bearing object is the contact Hamiltonian vector field on the canonically coordinated contact manifold $T^*\mathbb{R}^d\times\mathbb{R}$ with state $\{q,p,s\}$, whose local equations are $\dot q=\partial H/\partial p$, $\dot p=-\partial H/\partial q-p\,\partial H/\partial s$, and $\dot s=p^\top\partial H/\partial p-H$; here $s$ is the Lagrangian action and $H$'s dependence on $s$ controls energy dissipation through Eq. (8). A contactomorphism is a diffeomorphism preserving the contact form up to a positive factor, and the paper builds each one as the time-$T$ composition of flows of learned contact Hamiltonians $H_{r_{\theta_k}}=\tfrac12 p^\top M_{\theta_k}(p)p+V_{\theta_k}(q)+F_{\theta_k}(q)s$, integrated with an analytically invertible contact splitting integrator. This machinery does two jobs: it transfers the latent system's stability or safety properties to the observed dynamics, and it supplies an ensemble whose disagreement defines an uncertainty metric that reshapes the latent geodesic problem, steering trajectories away from high-uncertainty, data-poor regions.

What would settle it

Run GCF on a damped mechanical system with a known non-unit-mass Hamiltonian, compute the $s$ series from Eq. (43), and compare it to the true mechanical action; if the reconstructed $s$ diverges from the true action and reconstruction error nonetheless stays low, the method is fitting the invented coordinate rather than the physics. A cleaner test: give the baselines the same estimated $s$ as input and see whether the reported 57% and 60% dynamic-time-warping margins survive.

Watch

Extended reading notes

Core claim

The core claim is that composing a latent contact Hamiltonian flow with an ensemble of learned contactomorphisms yields a model of non-conservative, second-order dynamics that is both accurate on the data support and stable outside it. In the paper's construction, the latent dynamics $\dot{z}=Z_{H_g}$ is chosen to encode desired behavior, such as periodic, stable, or safe motion, and the learned maps $\phi_{r_n}$ carry that behavior to the observed coordinates through $x(t)=\phi_r^{-1}\circ \phi_g(t)\circ \phi_r(x_0)$, so a long-horizon prediction needs only one forward and one inverse mapping. The paper argues that preserving the contact form is what keeps the ambient dynamics physically interpretable: the damping coefficient $\partial H_m/\partial s$ and the action $s$ retain their mechanical meaning, and the ensemble's variance, injected into the latent metric as an extra traversal cost, makes off-manifold predictions bend toward the data. On the evidence offered, this yields the reported error reductions and convergence rates, and on the robot tasks it produces a stable energy-consumption profile and a safety stop when the Lagrangian action reaches zero under unexpected loading.

Load-bearing premise

The argument depends on the unmeasured 'Lagrangian action' coordinate $s$ being faithfully reconstructed from the observed positions and velocities; if that reconstructed coordinate does not represent real energy exchange, the comparisons against methods that never receive $s$ are not controlled.

Editorial extensions

If this is right

  • If the central claim is right, geometry alone, rather than hand-tuned losses, can bias a learned dynamics toward dissipative and even odd-dimensional phase spaces, since the action variable $s$ is part of the state.
  • A model trained once with stable latent dynamics can reproduce a demonstrated robot skill under loading never seen during training at roughly the same energy expenditure, because the contact structure keeps the energy bookkeeping physically consistent.
  • Ensemble uncertainty is not just a diagnostic but an active control signal, so predictions started outside the data support can be expected to converge back to the manifold rather than diverge.
  • The reported reductions of 57% and 60% in dynamic-time-warping distance imply that on spring-mesh and quantum-dynamics benchmarks, the structure-preserving map extracts more usable signal from the same trajectories than the best baselines compared in the paper.

Reading between the lines

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

  • Because the action variable $s$ is estimated from $(\mathbf{q},\dot{\mathbf{q}})$ rather than measured, a fair stress test would feed the same estimated $s$ to symplectic-style baselines or train GCF without it; the paper does not run this control, so part of the reported margin could reflect the extra input channel.
  • The same uncertainty-as-cost construction could be repurposed for costs other than ensemble variance, such as predicted collision risk, actuator limits, or time-to-contact, without changing the optimization scheme in Eq. (18).
  • If the contactomorphism ansatz behaves like a normal form, skills learned on one robot platform might transfer to another by re-estimating only the inertia-scaled momentum map, a conjecture the paper does not test.
  • The sensitivity of the learned dynamics to the unspecified initial value $s_0$ in Eq. (44) is a natural ablation: on datasets with non-unit mass, if reconstruction error depends strongly on this constant, the latent action should be treated as an additional learned variable rather than a fixed preprocessing outcome.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper introduces Geometric Contact Flows (GCF), a framework for learning dissipative second-order dynamical systems from data. GCF couples a latent contact Hamiltonian model, chosen to encode properties such as stability or energy depletion, to the observed dynamics through an ensemble of learned contactomorphisms. The ensemble provides predictive uncertainty, which is used to reshape a Riemannian metric and guide trajectories toward the data manifold. Experiments are reported on a 60-dimensional spring mesh, a single-mode bosonic quantum system, two handwriting datasets (LASA and DigiLeTs), and two robotic manipulation tasks, with comparisons against EF, NCDS, HNN, DHNN, and MLP baselines. The paper claims a 57% DTWD reduction on the spring mesh, a 60% reduction on the quantum system, superior convergence to the data manifold on handwriting generalization, and successful energy-aware robot task execution.

Significance. The core idea is attractive and potentially significant for the learning-dynamics community: it brings the odd-dimensional contact Hamiltonian formalism, with its physically meaningful action variable, into a neural-network framework that supports uncertainty quantification and control via metric reshaping. The paper is also honest in its reporting: error bars, ablations (contactomorphism vs diffeomorphism, latent loss weight, ensemble vs single map), and architectural details are provided, and the flow-based contactomorphisms are analytically invertible. If the empirical claims survive scrutiny, the framework would be a meaningful advance over first-order diffeomorphism-based methods and over Hamiltonian networks lacking a dissipation coordinate. However, the current validation is undermined by the underdetermined construction of the canonical-coordinate lift, by an internal sign inconsistency in the theoretical energy law, and by at least one headline claim that is contradicted by the paper's own tables. These issues are fixable within the scope of the manuscript, but they must be addressed before the central claims can be accepted.

major comments (4)
  1. [App. D.3, Eqs. (43)–(44)] The canonical-coordinate lift used in every experiment is underdetermined and internally inconsistent. Equation (43) is a second-order ODE for s, so a well-posed initial value problem requires both s0 and sdot0. The paper lists sdot0 = qdot0^T qdot0 and imposes sddot0 = 0, but does not specify s0; conversely, if s0 is chosen freely, then sddot0 is determined by Eq. (43) and cannot be imposed independently. Moreover, with the stated sdot0 the first term in Eq. (43) vanishes identically, so the condition sddot0 = 0 reduces to 2 qdot0^T qddot0 = 0, which is not satisfied by generic trajectories. In addition, the parametrization beta(q) = T - t introduces explicit time dependence into the 'Hamiltonian' (38) and makes s a time-to-go proxy, which conflicts with the autonomy assumption stated in App. D.1. Because the baselines EF, NCDS, and DHNN never receive s, the headline 57% and 60% DTWD reductions may reflect the presence of this extra input rather than contact geometry. The contactomorphism-versus-diffeomorphism ablation does not resolve this, since both variants receive s. This issue is load-bearing for the central empirical claim of the paper.
  2. [Sec. 3, Eq. (8)] Equation (8) has a sign error. For the contact Hamiltonian vector field written in Eq. (31), a direct computation gives dH/dt = -H * dH/ds, so the correct energy law is H(t) = H(0) * exp(-∫ dH/ds dτ). Equation (8) displays the opposite sign, and it is also contradicted by the paper's own Eq. (40) in App. D.3, which uses the negative sign. The text immediately after Eq. (8) uses the displayed expression to argue that the '+s' term in Eq. (7b) depletes the system energy; with the sign as written, the opposite behavior would follow. This internal inconsistency affects the theoretical motivation for the latent Hamiltonians HgB and HgC and should be corrected.
  3. [Sec. 6, Table 4 and Fig. 6] The claim that GCF achieves 'the highest average convergence ratio and lowest variance' on the handwriting generalization tests is not supported by the reported numbers. In Table 4, on LEAF 2, NCDS achieves 0.94 ± 0.19 while GCF achieves 0.69 ± 0.19; on ELLE, GCF achieves 0.66 ± 0.12, which is within one standard deviation of EF's 0.61 ± 0.30. The conclusion in the text that 'GCF shows greater reliability, ensuring all the dynamics predictions for the two characters converge to the data manifold' is too strong given these overlapping values. The authors should either restrict the claim to the cases where the advantage is statistically meaningful or add the appropriate significance tests.
  4. [Sec. 5, Eq. (18)] The uncertainty-aware control mechanism is not operationalized. The text states that trajectories are steered by a control input u obtained from the optimal control problem (18), but no solver, discretization scheme, cost weight for sigma_z, or stopping criteria are provided, and no algorithm is given in the appendix. The generalization experiments in App. E.3 and the ensemble ablation in Table 16 depend on this mechanism, since the ensemble's uncertainty is claimed to reshape the latent metric. Without a precise specification, the convergence-to-data-manifold results are not reproducible, and the contribution of the uncertainty-aware geodesics cannot be separated from the behavior of the latent dynamics alone.
minor comments (6)
  1. [Throughout] The acronym is inconsistent: the abstract uses 'GFC' while the main text uses 'GCF'; please choose one spelling and use it consistently.
  2. [Sec. 6, Table 3] The two rows in Table 3 are not labeled with the character names; the corresponding rows in Table 14 of App. E.3 should be reproduced or referenced so the reader knows which characters are being compared.
  3. [App. D.3] The notation beta(q) = T - t is misleading because T - t is a function of time, not of q; this should be clarified and reconciled with the statement in App. D.1 that the model treats the dynamical system as autonomous.
  4. [App. D.3, Eqs. (39)–(41)] The derivation of Eq. (41) by substituting Eq. (39) into Eq. (40) is hard to follow and appears circular as written; please spell out the substitution and the role of H0, or add a reference for this step.
  5. [Sec. 6] The baselines enumeration lists EF, NCDS, HNN, and DHNN but Tables 1 and 2 also report MLP; MLP should be included in the enumeration for completeness.
  6. [Fig. 5] The caption says 'From top to bottom rows, EF, NCDS, DHNN and GCF methods' but the figure is arranged as a 4-row-by-2-column grid; please clarify what the two columns represent.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: GCF's reconstructions are supervised fits benchmarked externally; the s-lift and uncertainty-guided convergence are design choices, not circular reductions.

full rationale

The paper's derivation chain does not reduce to its inputs by construction. The central reconstruction claims are produced by a supervised loss (Eq. 12) that compares predicted ambient and latent trajectories against the training data, and the paper explicitly decouples the latent dynamics choice from reconstruction quality: 'The choice of the latent dynamics does not affect the reconstruction of the target dynamics on the data support, but instead serves as an inductive bias to guide the generalization' (Sec. 4). The contactomorphism implementation is validated against external contact-transformation conditions from Bravetti et al. (2017) (App. B.3), and no load-bearing uniqueness theorem or fitted parameter is renamed as a prediction. The flagged weaknesses are real but are not circularity: App. D.3 defines the Lagrangian action by integrating Eq. (43) with initial conditions (Eq. 44) that list 's0' without specifying its value, making the s-lift underdetermined, and the handwriting potential β(q)=T−t makes s a time-to-go proxy that baselines never receive; this is an identifiability and experimental-control risk, not a derived quantity that equals an input. Similarly, the uncertainty-aware geodesic objective (Eq. 18) explicitly minimizes ensemble variance, and Table 4's convergence-to-data-manifold metric is aligned with that objective; this is a self-consistent controller evaluation, not a circular derivation. A sign inconsistency between Eq. (8) (positive exponent) and Eq. (40) (negative exponent) is a correctness issue, not circularity. Overall, the main experimental claims are self-contained supervised fits against external benchmarks, so no circular step meets the quote-and-reduction standard.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The model has no closed-form fitted constants; the fitted quantities are learned network parameters. The entries above are the hand-chosen hyperparameters and assumed constructions that the central claims depend on. Most important is the reconstructed action s, whose initial value is not specified. No new physical entities are postulated; the Lagrangian action s is a standard contact-geometric coordinate, not an invented particle or field.

free parameters (6)
  • Latent loss weight wz = 0.01
    Weight in Eq. (12); chosen by ablation in App. C.2 (wx = 1 fixed); affects regularization and reconstruction.
  • Contactomorphism flow duration tau and number of flows K = tau = 0.2, K = 12
    Architecture hyperparameters from App. D.1 controlling expressivity and invertibility.
  • RFF network hidden units nf = 200 (bandwidth 1, tanh bound [-2, 2])
    App. D.1; chosen for expressivity and smoothness balance (Table 11).
  • Ensemble size N = 5 for handwriting and robot, 1 for spring mesh and quantum
    App. D.1; chosen per task; ablations in App. E.3 show the ensemble helps generalization.
  • Initial Lagrangian action s0 = Not specified (Eq. 44)
    Initial condition for the ODE (43) used to construct s from data; its choice affects every experiment.
  • Potential parametrization beta(q) = T - t = beta decreases linearly to zero over demonstration time
    App. D.3; an assumed potential that is not derived from the data; injects the contact-structure assumption into the s coordinate.
assumptions (5)
  • standard math Contact Hamiltonian vector field (Eq. 31) with energy law \dot H = -H \partial H/\partial s, so H(t) = H(0) e^{-\int \partial H/\partial s dt}
    Invoked in Sec. 3-4 and App. A.3 as the model class; standard in contact mechanics (Bravetti et al., 2017), though the paper prints the sign wrong in Eq. (8).
  • domain assumption Existence of a learned contactomorphism phi_r in the class of flows of Hamiltonians (11) mapping latent to target dynamics
    Sec. 4 assumes the target dynamics can be written phi_r^{-1} ∘ phi_g ∘ phi_r with phi_r a composition of flows of Hamiltonians (11); no expressiveness theorem is given.
  • ad hoc to paper Data lift to canonical coordinates with unit mass, beta(q) = T - t, and s from Eq. (43) with initial conditions (44)
    App. D.3 constructs s from (q, qdot) under these assumptions; all experiments inherit this premise.
  • domain assumption Ensemble disagreement across N networks is a calibrated uncertainty signal sigma_z
    Sec. 5 assumes variance across N randomly initialized contactomorphisms measures model uncertainty; standard but not validated against calibration.
  • domain assumption Optimal control (18)-(19) with implicit unit cost weights yields geodesics that avoid uncertainty and obstacles
    Sec. 5 asserts the mechanism; no existence or uniqueness results and no solver details are given.

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Pith. "Pith review of Geometric Contact Flows: Contactomorphisms for Dynamics and Control." pith.science (2026). https://pith.science/paper/3F5FYRZ7

@misc{pith2026250617868,
  author       = {Pith},
  title        = {Pith review of: Geometric Contact Flows: Contactomorphisms for Dynamics and Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3F5FYRZ7}},
  note         = {Machine review of arXiv:2506.17868}
}
read the original abstract

Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the intricate interplay of geometric constraints and energy transfer. This paper introduces Geometric Contact Flows (GFC), a novel framework leveraging Riemannian and Contact geometry as inductive biases to learn such systems. GCF constructs a latent contact Hamiltonian model encoding desirable properties like stability or energy conservation. An ensemble of contactomorphisms then adapts this model to the target dynamics while preserving these properties. This ensemble allows for uncertainty-aware geodesics that attract the system's behavior toward the data support, enabling robust generalization and adaptation to unseen scenarios. Experiments on learning dynamics for physical systems and for controlling robots on interaction tasks demonstrate the effectiveness of our approach.

Figures

Figures reproduced from arXiv: 2506.17868 by the authors.

Figure 1
Figure 1. , a naive MLP network fails to capture the true dynam￾ics, leading to inaccurate predictions even within the data 1Bosch Center for Artificial Intelligence, Renningen, Germany 2 Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany 3 Section of Cognitive Sys￾tems, Technical University of Denmark (DTU), Lyngby, Denmark. Correspondence to: Andrea Testa <andrea.testa@de.… view at source ↗
Figure 2
Figure 2. Geometric Contact Flows: A state x(tk) in the ambient space (M, η) is mapped to a corresponding state z(tk) in the latent space (N , η′ ) via the ensemble of contactomorphisms{φrn (T)}n∈[1,N] . The uncertainty σz esti￾mated by the ensemble is depicted as a colored patch (dark and light colors denote low and high uncertainty). The latent dynamics is integrated by following a contact Hamiltonian model resulting into t… view at source ↗
Figure 3
Figure 3. The same scalar function f, via its 1-form df, yields two distinct vector fields (shown as streamlines) under different geo￾metric structures. In Riemannian geometry (left), the streamlines correspond to the gradient flow, following the direction of steepest ascent or descent of f, acting as a potential. In contrast, in contact geometry (right), the function f describes an energy, and the angle between the streamlin… view at source ↗
Figures from the paper (18 more)
Figure 4
Figure 4. Figure 4: Optimal control problem (18) in both latent (left) and ambient spaces (right). The learned dynamics z˙ = ZHg is ex￾tended by the control input u (represented by the golden arrow) to minimize uncertainty and quickly converge to the data support. The average prediction i…
Figure 5
Figure 5. Figure 5: Results on the handwriting datasets: Reconstruction and generalization of the LEAF 2 character from the LASA dataset and the ELLE character from the DigiLeTs dataset. From top to bottom rows, EF, NCDS, DHNN and GCF methods. Demonstrations and model predictions are show…
Figure 6
Figure 6. Figure 6: Generalization results for the LEAF 2 (left) and ELLE (right) characters. The violin plots depict the distribution of conver￾gence rates for predictions initialized from a grid of points in the state space. While NCDS performs well on LEAF 2, it struggles with ELLE. In…
Figure 7
Figure 7. Figure 7: Obstacle avoidance by LEAF 2 (red dot as obstacle) [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Snapshots of the unloaded (top) and loaded (bottom) WRAP-AND-PULL robotic task, showing rope pickup, wrapping around a drum, and pulling as the robot moves forward. WRAP-AND-PULL Robotic Task. In robotics, learning interaction tasks from demonstrations is more challeng…
Figure 9
Figure 9. Figure 9: Position and Lagrangian action trajectories (left and right plots) of the WRAP-AND-PULL task, for both the unloaded and loaded scenarios, using safe GCF. 7. Conclusion Geometric Contact Flows (GCF) model dynamical systems leveraging geometric inductive biases. It start…
Figure 10
Figure 10. Figure 10: The same scalar function f, associated with the 1-form α = df, gives rise to three distinct vector fields under different geometric structures: Riemannian (top left), symplectic (top right), and contact (bottom). The streamlines of these vector fields are illustrated …
Figure 11
Figure 11. Figure 11: This figure illustrates the reconstruction and generaliza￾tion results for the character LEAF 2 when the contactomorphism connecting the ambient and latent spaces is replaced by a diffeo￾morphism. As a result, the Hamiltonian structure of the ambient dynamics is lost,…
Figure 12
Figure 12. Figure 12: The top plots show trajectory predictions from grid points for the character LEAF 2, comparing a model using a sin￾gle contactomorphism (left) to one using a naive diffeomorphism without physical structure (right). The bottom chart summarizes these trajectories by rep…
Figure 13
Figure 13. Figure 13: Demonstration reconstruction in the ambient space (left) and latent space (right) for different values of the latent weighting factor wz: wz = 0.0 (top), wz = 0.01 (middle), and wz = 1.0 (bottom) [PITH_FULL_IMAGE:figures/full_fig_p019_13.png]
Figure 14
Figure 14. Figure 14: Dynamics reconstruction of the first three nodes in the spring mesh experiment. The reference dynamics (dashed gray line) is compared against the predictions from GCF and other baseline models. E.2. Quantum Mechanical System Contact Hamiltonian formulation of quantum …
Figure 15
Figure 15. Figure 15: Trajectories of position q, momentum p, and La￾grangian action s for the evolution of a single-phase bosonic sys￾tem. The trajectory obtained from integrating the Schrodinger ¨ equation (gray dashed line) is compared against the predicted evo￾lution from the GCF model…
Figure 16
Figure 16. Figure 16: Generalization of the EF, NCDS, DHNN, and GCF methods. Predicted trajectories starting from grid points for the character LEAF 2 (16a, 16c, 16d) and for the character ELLE (16e, 16g, 16h). The gray dots (16i, 16j) represent these trajectories as points based on the ra…
Figure 17
Figure 17. Figure 17: The ablation study highlights the performance improve￾ment in generalization capability achieved through the use of an ensemble of contactomorphisms. Plots 17a and 17b depict trajec￾tory predictions from grid points for the character LEAF 2, while plots 17c and 17d pr…
Figure 18
Figure 18. Figure 18: Obstacle avoidance behavior demonstrated by the LEAF 2 (top) and the ELLE (bottom) characters. Obstacles are represented as red dots. Programmed Path (1, 2, 3, 4) Operator Intervention Demonstrations 0 500 1000 1500 Time Steps 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.2 Lagrangia…
Figure 19
Figure 19. Figure 19: Position and Lagrangian action trajectories (left and right plots) for the unloaded WRAP-AND-PULL task when dis￾turbed by the operator’s physical intervention. WRAP-AND-PULL Task under Physical Perturbations [PITH_FULL_IMAGE:figures/full_fig_p025_19.png]
Figure 20
Figure 20. Figure 20: Snapshots from the collaborative DISHWASHER LOAD￾ING task, illustrating key phases: reaching the basket, pulling (opening) the basket, operator placing a dish, pushing (closing) the basket, and the robot returning to home position. E.5. Scalability Evaluation with Syn…
Figure 21
Figure 21. Figure 21: Reconstruction results achieved by the GCF method, evaluated across varying numbers of parameters used to model a contactomorphism, for systems of different dimensionalities. different high-dimensional GCF models, as a function of the total number of parameters. Recon…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.