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REVIEW 3 major objections 5 minor 25 references

Construction of a Multiple-DOF Under-actuated Gripper with Force-Sensing via Deep Learning

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A two-finger gripper senses its own grasp force from motor current and joint geometry, with average deviation below 1.71 N.

desk verdict Real mechanical novelty and honest experiments, but the force-sensing headline rests on supervised calibration and known contact geometry—strong mechanism paper, unproven sensing generalization. read the letter →

arxiv 2506.11570 v1 pith:SOZBEI3D submitted 2025-06-13 cs.RO

Jihao Li , Keqi Zhu , Guodong Lu , I-Ming Chen , Huixu Dong This is my paper · ORCID
classification cs.RO MSC 70B1568T4093C85
keywords under-actuatedgripperforcesensingwithoutsensorLSTMparallelandenvelopinggraspsfive-linkagemechanismkinematicstransmissionmodelforce-feedbackcontrolroboticgraspingpayload
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 reports an under-actuated gripper, GL-Robot, whose two three-joint fingers are driven by one motor and whose finger motion comes from a five-linkage mechanism stacked from two four-bar linkages. The central claim is that the gripper can run force-feedback control without any force sensor: a filtered motor-current signal feeds an LSTM classifier that detects when the grasp switches from parallel to enveloping mode, and the resulting joint angle is plugged into the kinematic and transmission model to compute per-phalanx contact forces. On the tested range, the measured normal grasping force deviates by less than 1.71 N on average, with maximum deviation 6.5 N and an average deviation rate of 1.6%; multi-point enveloping grasps stay within 2.9 N. If true, this gives a low-cost single-actuator gripper both high payload and sensorless force feedback, two properties that are usually traded off in existing under-actuated designs.

What carries the argument

The load-bearing mechanism is a finger built as a five-linkage chain that stacks two parallelogram four-bar linkages sharing the middle phalanx; a torsional spring at one joint keeps the phalanges rigid during parallel grasps and lets them collapse sequentially during enveloping grasps. The argument then runs through three connected pieces: inverse kinematics by vector-loop equations, static equilibrium via virtual work, and a transmission matrix $\mathbf{T}$ obtained by Kennedy's theorem from the instantaneous center of velocity of the four-bar linkage. The final piece is the MS-LSTM estimator: a median-then-mean filtered current signal, a statistical model of current uncertainty, and an LSTM that outputs the grasping mode, from which the critical angle $\theta_1$ is predicted and then corrected by polynomial fitting. Equation (34) inverts the lower-triangular Jacobian $\mathbf{J}$ to convert actuator torque and spring torques into contact forces $f_1, f_2, f_3$.

What would settle it

Repeat the force-sensing experiment with an object and motor speed outside the calibration set (for instance, $\theta_1$ at 25 or 70 degrees, or speed at 40 or 90 rpm) while instrumenting each phalanx with a thin commercial force sensor, and compare the measured contact forces with those computed by Eq. (34). Exceeding the claimed average deviation of 1.71 N or the mode-switch angle error of 1.3 degrees would falsify the claimed generality.

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Extended reading notes

Core claim

The paper's discovery is that force feedback in a rigid under-actuated gripper can be reconstructed from quantities already available at the motor — current, position, and velocity — instead of from tactile or force sensors. During closing grasps the actuator current has a Gaussian spread that grows with load; median and mean filtering turn this into a stable signal, and the LSTM classifies each time step as parallel-grasp or enveloping-grasp mode, predicting the critical angle $\theta_1$ at the switching instant. That predicted angle, combined with three decoupling cases for the order of phalanx contact, supplies the missing configuration to the lower-triangular Jacobian and transmission-matrix model, so Eq. (34) yields the contact forces $f_1, f_2, f_3$. The paper reports average normal-force deviation below 1.71 N, maximum deviation 6.5 N, mode-switch $\theta_1$ prediction error mostly within 0.7–0.8 degrees, normal payload over 340 N in some poses, and radial/axial payloads of 150 N and 180 N in parallel grasps, and argues this exceeds Robotiq85 in both sensing error and payload.

Load-bearing premise

The accuracy rests on the assumption that the current-to-angle mapping learned on 16 training objects, with $\theta_1$ from 30 to 60 degrees and motor speeds of 50 to 80 rpm, continues to give the correct mode-switch angle for objects, speeds, sizes, and contact orders outside that envelope; the paper demonstrates the accuracy inside the envelope and itself notes that irregular shapes such as a gamepad make sensorless force sensing difficult.

Editorial extensions

If this is right

  • Force-feedback control can protect fragile or deformable objects without adding a force sensor; elastic-ring deformation tests match the set forces of 50 N, 75 N, and 100 N.
  • A single actuator with a non-back-drivable screw-nut transmission maintains grasp pose and supports high payloads: over 340 N normal in some poses, 250 N radial, and 150 N radial / 180 N axial in parallel grasps.
  • Automatic mode switching extends the graspable dimension range from a 1.85 mm coin to a 125 mm cube.
  • The sensing pipeline, being built from current statistics plus a mechanism model, is portable in principle to other linkage-based under-actuated grippers that lack force sensors.
  • The reported force-sensing error below 3% and the payload advantage position GL-Robot as a low-cost alternative to Robotiq85 in industrial settings.

Reading between the lines

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

  • Inference beyond the paper: the three contact-order categories (distal-first, middle-first, proximal-first) imply that objects whose contact sequence falls outside these categories are exactly where Eq. (34) lacks a valid decoupled input, which matches the paper's admitted difficulty with shapes such as a gamepad.
  • Inference beyond the paper: because the polynomial correction surface absorbs screw gaps, shaft-pin fit errors, and encoder resolution into one fitted surface, the same sensing pipeline could be calibrated per production unit rather than per design, making the claimed low-cost commercialization more robust.
  • Inference beyond the paper: training the mode classifier in simulation with randomized object geometry, contact order, and speed coverage could supply the wide data distribution the current 16-object, 50–80 rpm training set lacks; the testable prediction is whether the 1.6% error rate survives that domain shift.
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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

3 major / 5 minor

Summary. This paper reports the design and evaluation of GL-Robot, a two-finger, three-phalanx under-actuated gripper driven by a single motor. The finger mechanism uses stacked four-bar linkages to switch between parallel and enveloping grasp modes. The authors derive inverse kinematics and a static-equilibrium model that maps actuator current and joint angles to per-phalanx contact forces, with the angle needed for the mode transition supplied by a filtered-current statistical analysis and an LSTM classifier whose output is compensated by polynomial fitting. Experiments report force-sensing accuracy with average deviation below 1.71 N and an average deviation rate of 1.6%, payloads up to 340 N in some configurations, and radial/axial loads well above those of Robotiq85. The paper claims that this constitutes force-feedback control without any force sensor.

Significance. The mechanism-level results—high payload, form-closure with three phalanges, wide dimensional range, and the parallel/enveloping transition—are concrete and are supported by the reported experiments and the standard kinematic analysis. If the force-sensing pipeline worked for arbitrary objects, it would be a significant step toward low-cost sensorless force control. The work also offers a useful combination of model-based static equilibrium and learned mode classification. However, the headline accuracy claim is validated only under conditions where the contact locations are known in advance and where the learning pipeline operates inside its training envelope; the paper itself concedes that force sensing on irregular objects remains difficult. The central novelty therefore requires substantial additional evidence or a narrower statement of scope.

major comments (3)
  1. [II.C, Eq. (34); IV-A-1a] The contact force vector is computed via f = J^{-T} T^T t, and the Jacobian entries in Eq. (19) depend on k_i, the distances from the joints to the contact points. The manuscript provides no sensor or estimator for these k_i for a general object. In the normal-force validation the force sensor is deliberately mounted so its center is at the distal-phalanx midpoint, k_3 = L_3/2, and in the multi-point enveloping tests on a cylinder the contact locations are geometrically fixed. The reported average deviation of 1.71 N and 1.6% rate therefore holds only when the contact positions are supplied externally. Because a single distal contact gives f_3 = tau'_3 / k_3, a 20% error in k_3 causes roughly a 20% error in the estimated force, an order of magnitude above the claimed error rate. The gamepad caveat in Sec. IV-C is a direct consequence of this missing contact-position observability rather than an isolated irregular-object case.
  2. [III.C; IV-A] The LSTM is trained on 16 objects spanning theta_1 in [30 deg, 60 deg] at motor speeds 50-80 rpm, using the actual theta_1 value as the supervisory label, and the force-sensing experiments are conducted within the same envelope. This makes the reported angle and force accuracy an interpolation result. No held-out objects, speeds, angles, or cross-validation are reported, so the load-bearing assumption that the current-to-configuration mapping generalizes is unproven. Either add out-of-envelope validation or explicitly restrict the force-sensing claim to the calibrated envelope.
  3. [II.C, contact-order decoupling] The three decoupling cases are introduced heuristically, with the statement 'After conducting a large number of grasping experiments...' providing the justification, but no quantitative criterion is given for detecting which phalanx makes first contact. The LSTM output is binary, '0' for parallel and '1' for enveloping, so it cannot select among the three cases. Case (3) requires a mapping in which theta_2 and theta_3 move while theta_1 is unchanged, yet that mapping is not written down. Since Eq. (34) needs both the correct joint angles and the correct set of active contacts, an incorrect decoupling case produces forces from the wrong Jacobian. The taxonomy should be formalized and validated against directly measured joint angles.
minor comments (5)
  1. [II.B, Eq. (10)] The third line of Eq. (10) defines rho_2 again; based on the derivation it should define rho_3.
  2. [II.C, Eq. (14)] The indexing 'n(n=1)' is inconsistent because the vectors below have three entries; the range of n and the placement of the torsional springs should be restated without this typo.
  3. [Fig. 8 and III.C] The text says the data are fitted 'using quadratic polynomials and quartic polynomials, respectively,' but it is unclear which polynomial is applied to the speed axis and which to the object-size axis; label the fits in the figure and caption.
  4. [Table IX and IV.C] The comparison with Robotiq85 should cite the published specification source and report the test conditions or uncertainty for the Robotiq85 numbers, since the five-times and seven-times comparisons are central to the commercialization claim.
  5. [Abstract and II.A] Terminology for the finger linkage is inconsistent: the abstract calls it a 'five-linkage mechanism stacked by double four-linkages' while Section II.A calls it a 'six-bar mechanism'; use one name and show the bar count in the schematic.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the force-sensing claim is a calibrated estimator built from the mechanism model and supervised current-to-angle mapping, with force accuracy checked against an independent force sensor.

full rationale

Eq. (34) is obtained from the virtual-work relation t^T omega_a = F^T v = tau^T theta_dot, with the Jacobian (19) and transmission matrix (22)-(31) derived from geometry and Kennedy's theorem. No force data are used to fit these equations, so the force model is not an output of the experiments. The remaining inputs are tau_a = A I and the phalanx angles. Theta1 is obtained from a supervised LSTM classifier and polynomial compensator whose training labels are the actual theta1; this makes the reported theta1 accuracy an interpolation result within the 30-60 deg / 50-80 rpm envelope, but it is a calibration step that is explicitly disclosed, not a hidden assumption of the conclusion. Force-sensing validation uses an external force sensor at a deliberately known contact point k3=L3/2; this supplies a quantity the model requires but does not estimate. That limits the claim for arbitrary objects and is acknowledged in Sec. IV-C as a 'quite difficult challenge' for irregular-shaped objects, but it is a correctness/generalizability caveat, not circular reasoning. The self-citations [3], [14], and [15] are contextual and not load-bearing for the derivation. Therefore no step reduces to its own input by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central sensing pipeline rests on empirical fits and modeling assumptions. The LSTM and polynomial compensator are the main fitted components, and no CAD or data are released. No new physical entities such as particles, forces, or dimensions are postulated.

free parameters (3)
  • LSTM network weights and hyperparameters = Not disclosed; trained on 1,600 labeled current-angle samples
    The LSTM classifies the grasping mode and predicts the critical angle theta_1; its accuracy depends entirely on the fitted weights and chosen architecture.
  • Polynomial compensation coefficients for theta_1 deviation = Quadratic in motor speed, quartic in object size (Fig. 8)
    These coefficients are fitted to the difference between LSTM-predicted and actual theta_1 across 16 objects and 4 speeds, and they are what bring the reported angle error below one degree.
  • Current filter parameters and mode-switch threshold = Not specified; two-stage median and mean filters used
    The statistical detection of the parallel-to-enveloping transition relies on empirically chosen filter windows and current-surge thresholds, which are not given as numeric values.
assumptions (5)
  • domain assumption Static equilibrium: input virtual power equals output virtual power (Eq. 13), with frictionless contacts.
    Used to derive contact forces from motor torque and joint angles; ignores friction and dynamic effects, so computed forces are normal-only estimates.
  • ad hoc to paper The three-joint motion can be decoupled into three contact-order cases so accurate mapping relationships between the actuation angle and joint angles exist.
    The text states that exact coupling mapping is not possible, then classifies grasps by which phalanx contacts first and asserts that other cases rarely occur in real scenarios.
  • domain assumption Motor current is approximately Gaussian about its setpoint and its standard deviation increases with load, enabling mode-switch detection from current fluctuations.
    Empirical statistical model used to trigger parallel-to-enveloping detection; no formal derivation or quantitative fit of sigma is provided.
  • standard math Kennedy's theorem and four-bar instantaneous centers correctly determine the transmission matrix T.
    Standard linkage kinematics used in Eqs. (25) to (31) to map actuator angular velocity to phalanx velocities.
  • ad hoc to paper When the Jacobian is singular due to fewer than three contacts, deleting the row and column of the non-contacting phalanx preserves the correct force balance.
    Proposed to handle k1*k2*k3 = 0; assumes the remaining contacts determine the force distribution without interaction from the missing contact.

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Cite this review

Pith. "Pith review of Construction of a Multiple-DOF Under-actuated Gripper with Force-Sensing via Deep Learning." pith.science (2026). https://pith.science/paper/SOZBEI3D

@misc{pith2026250611570,
  author       = {Pith},
  title        = {Pith review of: Construction of a Multiple-DOF Under-actuated Gripper with Force-Sensing via Deep Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SOZBEI3D}},
  note         = {Machine review of arXiv:2506.11570}
}
read the original abstract

We present a novel under-actuated gripper with two 3-joint fingers, which realizes force feedback control by the deep learning technique- Long Short-Term Memory (LSTM) model, without any force sensor. First, a five-linkage mechanism stacked by double four-linkages is designed as a finger to automatically achieve the transformation between parallel and enveloping grasping modes. This enables the creation of a low-cost under-actuated gripper comprising a single actuator and two 3-phalange fingers. Second, we devise theoretical models of kinematics and power transmission based on the proposed gripper, accurately obtaining fingertip positions and contact forces. Through coupling and decoupling of five-linkage mechanisms, the proposed gripper offers the expected capabilities of grasping payload/force/stability and objects with large dimension ranges. Third, to realize the force control, an LSTM model is proposed to determine the grasping mode for synthesizing force-feedback control policies that exploit contact sensing after outlining the uncertainty of currents using a statistical method. Finally, a series of experiments are implemented to measure quantitative indicators, such as the payload, grasping force, force sensing, grasping stability and the dimension ranges of objects to be grasped. Additionally, the grasping performance of the proposed gripper is verified experimentally to guarantee the high versatility and robustness of the proposed gripper.

Figures

Figures reproduced from arXiv: 2506.11570 by the authors.

Figure 1
Figure 1. The prototype of GL-Robot, which allows robust grasps in real scenarios [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. A novel mechanism stacked by a double four-linkage mechanisms. The parallel grasp (A) and the enveloping grasp (B). The gray schematic diagram illustrates the state of the finger during the period of the finger performing grasps at previously sampled time. 𝑂௜(𝑖ൌ𝑎, 𝑏, 𝑐, 1, 2, 3) represents the number of rotation joints; 𝐿௜, ሺ𝑖 ൌ 1,2,3ሻ denote the rotation angle of the length of the the 𝑖-th phalange, respectively; 𝐿… view at source ↗
Figure 3
Figure 3. The prototype of GL-Robot (A), the schematic diagrams of the gripper’s parameters, kinematics and force transmission(B) as well as phalange’s velocities (C). 𝜃௔ is the actuation angle; 𝜃௜, 𝑘௜, 𝑓௜, 𝜏௜, 𝜏௜ ᇱ , 𝜏௜ ᇱᇱሺ𝑖 ൌ 1,2,3ሻ denote the rotation angle of the 𝑖-th joint, the segment between the the 𝑖-th joint and contact point, the contact force, the input torque, the output torque and the contact torque of the the 𝑖-… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: The schematic diagrams of two classifications of the instantaneous center [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: The current changes of opening-closing actions for GL-Robot [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: The current changes for the gripper grasping objects with different dimensions [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: The construction of the LSTM network model [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: The x-axis represents the speed of the motor, the y-axis represents the size of the grasping object, and the z-axis represents the deviation between 𝜃ଵ predicted by LSTM and the actual 𝜃ଵ, and the data are fitted in the x-z plane and y-z plane sequentially, both of whi…
Figure 9
Figure 9. Figure 9: The deviation results of 𝜃ଵ predicted by the LSTM method for different objects at the different actuator’s speeds [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: Schematic diagrams of measuring the normal grasping force [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: Deviation distributions of testing the normal fo [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: Deviation distributions of testing the radial forces [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]
Figure 13
Figure 13. Figure 13: Grasping dumbbells with 25kg (A) and 30kg (B) to test the radial force. [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]
Figure 14
Figure 14. Figure 14: Sampling the data of the force applied by dynameter to [PITH_FULL_IMAGE:figures/full_fig_p010_14.png]
Figure 15
Figure 15. Figure 15: Schematic diagram of the maximum grasping forces (payload) applied by the gripper with different angles of the first joint in the three directions [PITH_FULL_IMAGE:figures/full_fig_p010_15.png]
Figure 16
Figure 16. Figure 16: Sampling the data of the relationship between the force applied to the ring and the deformation of the ring (A) and the relationship of the grasping force and the corresponding deformation being in agreement with the fitted function (B) [PITH_FULL_IMAGE:figures/full_…
Figure 17
Figure 17. Figure 17: Several demonstrations to verify the performances [PITH_FULL_IMAGE:figures/full_fig_p011_17.png]

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Reference graph

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