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LUMO: Designing Luminous Contact Morphology for Repeatable Whole-Finger Contact Observation

Dong Ho Kang, Youngsu Ko, Luis Sentis

arXiv:2609.18165v1cs.RO

TL;DR

Joint torque alone cannot resolve contact location along a low-impedance finger. LUMO co-designs finger morphology and optical response, then evaluates location-dependent sensing and force estimation. Optimized morphologies improve separation relative to re-contact variation, and optical location cues support force estimation from joint torque.

  • Problem

    Joint torque can indicate contact load but cannot uniquely determine contact location, while whole-finger sensing and external-vision approaches have instrumentation or inference constraints.

    Source: §I · p. 1

  • Method

    LUMO optimizes contact morphology for progressive-constraint contact and spatial optical separation using contact simulation, ray tracing, and multi-objective Bayesian optimization.

    Source: §I · p. 2

  • Results

    Qrecontact over Baseline increases for every tested material–indenter combination: 15–44% for Solaris and 45–59% for Dragon Skin; force-estimation MAE is 1.44 N.

    Source: B. Spatial Distinguishability and… · p. 5, E. Location-Aware Proprioceptive Force… · p. 7

  • Takeaways & Limitations

    Morphology-shaped optical location cues provide the contact geometry needed to combine joint torque with normal-force estimation along the finger.

    Source: §I · p. 2, §V · p. 7

    Quantitative evaluation is limited to single contacts, controlled longitudinal locations, and the tested loading and imaging conditions; simulation ranks morphologies rather than predicting absolute measured responses.

    Source: §V · p. 7

Abstract

from arXiv · show

A low-impedance robot finger reports through joint torque how strongly it is loaded, but the same torque can arise from a small force near the fingertip or a large force near the joint. Resolving the force therefore requires knowing where along the finger contact occurred. LUMO makes that location externally observable. Embedded LEDs illuminate a compliant silicone pad, and contact deforms the pad so that light emerging from the finger's side changes in a pattern set by where the load acts. Because the same structure also carries the contact load, we optimize its cross-section, including the pad profile, rigid carrier, and lateral void, for two behaviors at once. Mechanically, the pad conforms under low preload while the carrier increasingly restricts further deformation as load rises. Optically, different contact locations produce separated responses on the finger's side. The search uses rigid--soft contact simulation, ray tracing, and multi-objective Bayesian optimization. Across two silicones, six contact locations, and 10- and 30-mm spherical indenters, the optimized morphologies improve neighboring-location separation relative to variation from re-establishing contact by \(15\)--\(59\%\). Estimating contact location from the optical response using the known LED spacing and combining it with joint torque gives \(1.44~\mathrm{N}\) normal-force MAE over 931 samples. In a two-finger hand, localized side responses appear on several links simultaneously during grasps.

I. Introduction

Joint torque indicates load strength but cannot uniquely identify where along a finger contact occurs. LUMO co-designs the load-bearing finger morphology to make contact location observable through spatial optical responses on its side.

I. Introduction

  • Low-impedance QDD joint torque reveals contact load, but the same torque can arise from contacts at different locations.Distributed sensing adds sensor elements, wiring, and mechanical integration, while external vision relies on cues affected by object geometry, viewpoint, and occlusion.Source: §I · p. 1
  • LUMO shapes contact-induced deformation so different longitudinal contact locations produce distinct optical responses on externally visible finger regions, even when the interface is hidden.The lateral surface can cover multiple potential contact locations without a dedicated sensing element at each site.Source: §I · p. 1
  • The compliant pad, rigid carrier, and internal void jointly shape force transmission, deformation, and light transport, coupling mechanical and optical design objectives.The mechanical target is low-preload conformation with increasing restriction of further deformation as load rises; optical responses should remain spatially distinguishable and consistent across re-established contacts.Source: §I · p. 1, Figure 1 · p. 1
  • LUMO targets progressive-constraint contact: the pad forms a finite contact patch at low preload while the carrier increasingly limits further deformation as load rises.The authors hypothesize that limiting continued deformation can reduce optical variation across independently re-established contacts.Source: §I · p. 2
  • The contributions include contact-morphology co-design, physical validation across two silicones and two indenter sizes, and LED-referenced location estimation combined with joint torque for force estimation.The location estimate supplies the contact geometry needed for force estimation along the finger.Source: §I · p. 2
  • The optimized morphologies improve spatial distinguishability relative to re-contact variation, while experiments assess repeatability, deformation limiting, and location-aware force estimation.The introduction frames repeatability as an evaluation rather than a directly optimized objective.Source: §I · p. 2

II. Related Work

Related work addresses whole-finger contact inference, computational optomechanical design, and contact-morphology design. LUMO differs by shaping the finger itself for spatially observable contact alongside mechanical contact behavior.

A. Whole-Finger Contact Observation

  • Proprioceptive inference, learning-based methods, and external RGB-D vision recover contact from robot or scene measurements; LUMO instead shapes morphology to produce spatially structured cues on an observable surface.Joint-torque inference can be non-identifiable for distinct contacts with similar measurements, with added ambiguity under multiple contacts.Source: A. Whole-Finger Contact Observation · p. 2

B. Computational Optomechanical Design

  • Prior computational optomechanical design evaluates optical geometry, elastic bodies, and compliant geometries, while LUMO couples contact progression with spatial optical separation as morphology objectives.The cited approaches include multi-objective exploration of sensing–actuation trade-offs in soft fingers.Source: B. Computational Optomechanical Design · p. 2

C. Contact Morphology Design

  • Earlier contact-morphology work shapes mechanical interface response; LUMO extends this approach to jointly design progressive-constraint contact and spatially distinguishable optical responses.Prior examples include synthesized finger profiles, optimized fingertip surfaces, rigid reinforcement, layer jamming, and self-contact.Source: C. Contact Morphology Design · p. 2

III. Methodology

LUMO searches a parameterized finger cross-section using coupled mechanical and optical simulations, then guides design selection with multi-objective Bayesian optimization.

III. Methodology

  • Each candidate morphology is evaluated by contact simulation and ray tracing to produce mechanical and optical objectives that guide multi-objective Bayesian optimization.The pipeline also compares matched rigid-carrier and lateral-void designs and reports empirical Pareto sets for four material–loading campaigns.Source: §III · p. 2, Figure 2 · p. 3

A. Morphology Parameterization

  • The cross-section parameterization uses five design variables for flat and elliptical pad regions, the internal stem, and lateral void width.The geometry defines the compliant pad, rigid carrier, and embedded light-source geometry; designs violating constraints or producing invalid cross-sections are discarded.Source: A. Morphology Parameterization · p. 2

B. Coupled Mechanical and Optical Evaluation

  • Contact scenarios specify indenter diameter, approach angle, and longitudinal location; simulation returns deformed states and ray tracing maps them to spatial optical responses.The reported settings include a 1 mm mesh, 5 mm/s loading, and prescribed loads of 1, 2, 5, 10, and 15 N.Source: B. Coupled Mechanical and Optical… · pp. 2–3

1) Contact Mechanics:

The methodology simulates rigid–soft contact under prescribed indenter approaches and loads, then traces light transport from the resulting deformed states to spatial optical responses.

1) Contact Mechanics:

  • The compliant pad uses a damped Neo-Hookean model, while the fixed rigid carrier interacts with the pad through penalty contact and signed-distance-field collision detection.Silicone self-contact is disabled.Source: 1) Contact Mechanics · p. 3
  • A spherical indenter advances along a prescribed approach direction, and its reaction force is projected onto that direction at each load state.The indenter is held for 1 s at each prescribed load before the mechanical and optical state is recorded.Source: 1) Contact Mechanics · p. 3

2) Optical Response:

  • OptiX evaluates light transport from each simulated mechanical state, including reflection, refraction, total internal reflection, attenuation, and diffuse carrier reflection.The externally visible finger surface is divided into fixed longitudinal regions, and contributions from all LEDs use the same deterministic ray-sampling pattern across morphologies and states.Source: 2) Optical Response · pp. 3–4

C. Mechanical and Optical Objectives

The objectives jointly score progressive-constraint contact and spatial optical separation. The mechanical score rewards forming a low-load contact patch, retaining the contacted surface as load rises, and increasing stiffness.

C. Mechanical and Optical Objectives

1) Progressive-Constraint Contact:

  • The mechanical objective scores finite patch formation at 2 N, retention of the contacted surface from 2 to 10 N, and increasing stiffness with load.Its stiffness term compares secants spanning 1–2 N and 5–10 N.Source: 1) Progressive-Constraint Contact · p. 4
  • A geometric mean penalizes weak mechanical properties, while the minimum selects the worst tested scenario; repeatability is evaluated experimentally, not optimized directly.The 15 N state contributes to the optical objective but not J_contact.Source: 1) Progressive-Constraint Contact · p. 4

2) Spatial Optical Separation:

J_obs measures the worst-case optical separation among tested contact locations under matched interaction conditions.

2) Spatial Optical Separation:

D. Bayesian Optimization and Design Selection

The design search runs separate optimization campaigns for material and loading ensemble, then selects designs by balancing normalized objectives. Flat-Opt and Curved-Opt are the selected designs for their respective loading ensembles.

D. Bayesian Optimization and Design Selection

  • Four campaigns optimize each loading ensemble separately for Dragon Skin and Solaris; their nondominated evaluated designs define empirical Pareto sets.Campaigns use qLogNEHVI, with five heuristic reference designs and eight Sobol samples for initialization.Source: D. Bayesian Optimization and Design… · p. 4
  • The selected design maximizes the weaker of the two objectives after each is normalized by its maximum over evaluated designs.Source: D. Bayesian Optimization and Design… · p. 5
  • The selected designs are named Flat-Opt and Curved-Opt according to their loading ensemble.The evaluation figure covers baseline and optimized morphologies across two materials, six locations, and two indenter sizes.Source: D. Bayesian Optimization and Design… · p. 5, Figure 4 · p. 5

IV. Evaluation

Both optimized morphologies improve neighboring-location separation relative to re-contact variability, and the study also evaluates structural design changes and physical performance across materials and indenter sizes.

A. Morphology Design Study

  • Adding the rigid carrier increased J_contact in all 40 matched designs, with median ΔJ_contact = 0.121; a finite lateral void had morphology-dependent effects.Source: A. Morphology Design Study · p. 5
  • Flat-Opt and Curved-Opt were selected from four empirical Pareto sets and fabricated alongside the nominal Baseline for physical evaluation.Source: A. Morphology Design Study · p. 5

B. Spatial Distinguishability and Re-Contact Variability

  • Testing used five independent re-contacts at six locations with 10- and 30-mm indenters; Q_recontact compares neighboring-location response separation with re-contact variation.The nearest-template decoder tests discrete separability only among the six tested locations.Source: B. Spatial Distinguishability and… · p. 5
  • 15–44% for Solaris and 45–59% for Dragon Skin: both optimized morphologies increase Q_recontact over Baseline across every tested material–indenter combination.Location-aware force estimation achieves 1.44 N MAE over 931 contact samples.Source: B. Spatial Distinguishability and… · pp. 5–6, Figure 5 · p. 6

C. Contact Cycling and Approach-Angle Response

The cycling experiments distinguish repeatability during maintained contact from variability after re-contact. Optimized morphologies reduce re-contact variability, while high-load deformation results support the targeted deformation-limiting behavior.

C. Contact Cycling and Approach-Angle Response

  • Five force cycles from 2 to 15 N were collected without breaking contact, alongside three independently re-established runs per location–angle condition.The protocol used the 10-mm indenter at locations 1, 3, and 5 and angles −30°, 0°, and +30°.Source: C. Contact Cycling and Approach-Angle… · p. 6
  • 16.7–41.9% lower re-contact variability and mixed −10.4 to +5.9% changes in neighboring-location separation were observed across optimized morphologies.Because Q_recontact is defined relative to re-contact variability, it can improve even when neighboring-location separation does not increase.Source: C. Contact Cycling and Approach-Angle… · p. 6
  • Mixed W_cycle results indicate that repeatability within maintained contact and repeatability after re-contact are distinct properties.W_cycle measures matched-force variation across cycles; W_recontact and D_neighbor measure across re-established runs and neighboring-location separation.Source: C. Contact Cycling and Approach-Angle… · p. 6
  • Curved-Opt had positive Progressive-Constraint Gain at every tested angle in both materials, while Flat-Opt was angle-dependent.Gain is the baseline-relative reduction in projected indenter displacement from contact onset to 15 N.Source: C. Contact Cycling and Approach-Angle… · p. 6

D. Imaging Variation

The optical cue remained ordered under the tested imaging variations, and a causal optical location estimate combined with joint torque supported normal-force estimation. The integrated hand also showed localized optical responses across multiple links during grasps.

D. Imaging Variation

  • The force-dependent optical response remained ordered across tested camera viewpoints and ambient illumination despite changes in absolute magnitude, while the LED-off response was substantially weaker.This tests persistence of the cue under the tested imaging variations, not viewpoint- or illumination-invariant localization.Source: D. Imaging Variation · p. 6

E. Location-Aware Proprioceptive Force Estimation

  • The strongest thresholded peak in a causal green-channel profile was mapped to finger position using five detected LEDs spaced 11 mm apart, then combined with joint torque to estimate normal force.The decoder used only current and past frames and no labeled contact locations; processing took 0.86 ms median and 0.94 ms at the 95th percentile, excluding image decoding.Source: E. Location-Aware Proprioceptive Force… · pp. 6–7
  • Localized optical-change regions were identified simultaneously across distal and proximal links under different grasp configurations.The figure depicts detected regions relative to the nearest unloaded reference in joint-configuration space, with crosses marking residual-weighted centroids.Source: Figure 6 · p. 7
  • 1.44 N MAE was achieved across 931 contact samples using the causal optical location estimate; a fixed moment arm gave 2.72 N MAE and known jig locations gave 1.29 N.The remaining error includes torque estimation, moment-arm modeling, force direction, and temporal alignment.Source: E. Location-Aware Proprioceptive Force… · p. 7

F. Multi-Contact Grasp Responses in the Integrated Hand

The integrated-hand procedure detects localized optical responses across multiple links during grasps without labeled contact locations or an object model. The conclusion frames contact observation as a coupled morphology-design problem and limits the quantitative evidence to controlled single-contact conditions.

F. Multi-Contact Grasp Responses in the Integrated Hand

  • The grasp analysis compensates for global and slowly varying green-channel intensity differences, then segments prominent longitudinal residual regions and represents each by a residual-weighted centroid.The absolute residual is computed between grasp and unloaded images.Source: F. Multi-Contact Grasp Responses in… · p. 7
  • Multiple response regions can be identified simultaneously across the four finger links without labeled contact locations or an object model.Grasp images are compared with a nearest unloaded reference in joint-configuration space after registering the distal and proximal links independently.Source: F. Multi-Contact Grasp Responses in… · p. 7

V. Conclusion

  • The physical results show improved consistency across independently re-established contacts while retaining spatially distinguishable optical responses, with location cues supplying geometry for interpreting joint torque as contact load.Integrated-hand demonstrations show localized responses across multiple finger links during multi-contact grasps.Source: §V · p. 7
  • Reliable spatial observation requires location-dependent structure and consistency across repeated contact, not merely a strong optical response.The paper identifies coupling mechanical contact behavior with optical response as LUMO’s main design principle.Source: §V · p. 7
  • Quantitative evaluation is limited to single contacts, controlled longitudinal locations, and tested loading and imaging conditions; the camera readout can lose visibility with off-normal views or occlusion.The coupled simulation ranks candidate morphologies rather than predicting absolute measured responses.Source: §V · pp. 7–8
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