Authors: Qingzheng Cong, Alexis W. M. Devillard, Abu Bakar Dawood, Xinxin Zhang, Wen Fan, Neri Niccolò Dei, Cem Suulker, Kaspar Althoefer, +2 more
Organizations: Queen Mary University of London, E1 4NS, UK · The Imperial College of Science, Technology and Medicine, London SW7 2AZ, UK · King’s College London, SE1 7EU, UK
This paper presents a stacked two-layer force-sensing resistor (FSR) array designed for robotic fingertips that combines high-resolution pressure mapping with shear-force estimation. A compliant lattice elastomer spacer converts shear loading into a measurable inter-layer displacement, producing relative center-of-pressure (CoP) shifts between layers. A physics-based moment balance links inter-layer CoP displacement to shear force, while an end-to-end CNN--GRU model captures nonlinear effects from load-dependent compression and contact redistribution. This model, with both layers as input, achieves coefficients of determination R2=0.914 for Fx and R2=0.944 for Fy, consistently outperforming single-layer baselines for shear-force estimation. Robotic manipulation experiments show that, for contact-motion tracking, the deep layer tracks the translation and rotation imposed by the robot arm, whereas the superficial layer tracks the slip at the contact surface. Transient changes in the difference between the total pressure responses of the two layers provide the best slip-event detection performance among the tested cues. These results demonstrate that two-layer FSR arrays can provide three-axis force estimation, contact-motion tracking, and slip-event detection beyond conventional normal-force sensing.
Figures & tables
Figure 1
Fig. 1: Concept of two-layer FSR response under normal, shear, and torsional loading. Blue and red contours represent the pressure distributions on the superficial and deep sensing layers. (a) Under normal compression, the two pressure centers remain aligned; OS and OD are the vertically aligned layer origins and hspacer the undeformed spacer height. (b) Under lateral translation, shear deformation of the spacer offsets the pressure centers by △x ; h is the fitted effective height above the deep sensing plane at which the shear force acts. (c) Under torsion, the pressure distribution becomes directionally biased, and its principal axis (PCA) angle △θ describes the response.
Fig. 2: Fabrication of the two-layer FSR array. (a) Single-layer FSR structure formed by laminating a Velostat sheet between crossed FPCB electrodes. Each layer has vertical and horizontal electrodes on opposite faces, and the electrode array is a square with 24 mm side. (b) Final two-layer sensor assembled by stacking two FSR layers with the compliant spacer in between. (c) Cast Ecoflex 00-10 silicone spacer with a hexagonal lattice structure.
Operation
Configuration
Output shape
Input window
C∈{1,3}
T×C×16×16
Shared frame encoder
Conv 1
C→32 , stride 1
T×32×16×16
Conv 2
32→64 , stride 2
T×64×8×8
Conv 3
64→64 , stride 1
T×64×8×8
Flatten
–
T×4096
TABLE I: Architecture of the CNN–GRU network. Dimensions are for one sample. All convolutions use 3×3 kernels with padding 1. Dropout with probability 0.1 is applied after the fully connected projection.
Fig. 3: Experimental setup for translational and torsional loading. (a) Initial contact configuration between the two-layer FSR sensor and the fixed rod. The blue dashed box denotes the gripper frame, and the yellow dashed box denotes the contact region of the superficial FSR layer. ArUco markers attached to the superficial layer are used for visual tracking. (b) Translational loading, in which the robot arm translates by △xarm in X0 direction while the gripper maintains contact with the fixed rod. (c) Torsional loading, in which the robot arm rotates the gripper by an angle △θarm .
Metric
Lin.
T-s1
T-s5
S-s1
S-s5
D-s1
D-s5
Fx
R2
0.474
0.888
0.914
0.842
0.869
0.426
0.342
MAE (N)
0.275
0.098
0.094
0.126
0.118
0.217
0.231
Fy
R2
0.443
0.937
0.944
0.900
0.894
0.457
0.396
MAE (N)
0.229
0.068
0.065
0.085
0.087
0.175
0.178
Fz
R2
0.902
0.988
0.983
0.992
0.989
0.928
0.926
MAE (N)
0.318
0.105
0.113
0.094
0.104
0.252
0.256
TABLE II: Per-axis force-estimation performance. Lin.: linear regression using the six features in Eq. 4 ; T/S/D: CNN–GRU with two-layer/superficial/deep inputs; s1/s5: sequence lengths of 1/5 frames. MAE: mean absolute error; best values are in bold.
Fig. 4: Per-axis force estimation from (a) the linear regression and (b) the nonlinear two-layer s5 model. Dashed lines denote the ideal prediction; color indicates temporal progression within each contact trial.
Fig. 5: Representative layer-specific contact-motion tracking and slip-event detection for translation (a,c) and torsion (b,d) at a grip depth of 12 mm. (a,b) Grip-specific calibrated deep-layer and superficial-layer readouts compared with the arm motion and the vision-measured slip, respectively. (c,d) Slip-event detection using the inter-layer difference cue and the grip-specific threshold learned from the training trials. Vertical dashed lines indicate vision-derived ground-truth slip events. Green triangles, orange inverted triangles, and blue crosses denote true positives (TP), false positives (FP), and false negatives (FN), respectively.
Deep (arm)
Superficial (vision)
Motion
g
a
R2
MAE
a
R2
MAE
Translation
6 mm
1.35
0.996
0.13
0.94
0.991
0.19
9 mm
1.23
0.996
0.15
0.90
0.991
0.16
12 mm
1.22
0.989
0.26
0.91
0.973
0.25
15 mm
1.25
0.973
0.41
0.97
0.882
0.41
Torsion
6 mm
1.16
0.897
3.92
0.92
0.953
2.46
TABLE III: Grip-specific LOTO tracking performance. The slope a is averaged across the LOTO folds, whereas R2 and MAE are calculated from the pooled out-of-fold predictions. MAE is reported in millimeters for translation and degrees for torsion.
Translation
Torsion
Cue
Global
Grip
Oracle
Global
Grip
Oracle
Inter-layer diff.
0.672
0.840
0.859
0.731
0.787
0.809
Superficial-layer
0.642
0.795
0.836
0.621
0.681
0.730
Geometric cue
0.652
0.821
0.851
0.585
0.651
0.675
Fxyz
0.649
0.808
0.855
0.607
0.664
0.682
Fz
0.638
0.728
0.765
0.625
0.695
0.720
TABLE IV: Slip-event detection F1 scores (trial-macro, LOTO). Global: one threshold across all grips; Grip: within-grip threshold; Oracle: label-informed per-trial upper bound.