Three taxels read force at the jaw face
Robotic minimally invasive surgery separates the surgeon from the instrument tip, so the forces the tissue feels must be inferred visually rather than felt. The paper's answer is to put sensing directly where contact happens: on the grasping face of the jaw, rather than at the motors, the shaft, the trocar, or the wrist. The authors argue this is the most direct access to local contact mechanics, and it is the point where contact pressure, distributed shear, and tissue-dependent friction actually occur.
The device carries three sensing elements, called taxels, each 2.50×1.20×2.50 mm and arranged along the principal axis of the jaw. The assembled sensor measures 9.3×6.5×19.5 mm and weighs 2.06 g. Three taxels were the maximum that fit given tool-tip dimensions, PCB manufacturing constraints, Hall sensor size, low-cost materials, and the safe radius needed around the magnets. That count matters because tissue rarely spans the full jaw: multiple taxels let the sensor report local pressure and cascading pressure changes across the interface, which is how slip becomes observable.
Magnets moving over Hall sensors encode both axes
Each taxel works by magnetic displacement sensing. Small NdFeB magnets are embedded in a deformable elastomer layer, and beneath them sit Hall effect sensors that measure magnetic flux density. When the elastomer is pressed or sheared, the magnet shifts relative to its sensor pair, changing the field the sensor detects and producing a voltage change that is converted onboard into magnetic field values.
The geometry separates the two force directions. A pure increase in contact pressure displaces the magnet vertically and strengthens the field response in Bz. A combined pressure and shear load displaces the magnet diagonally, changing the response in both By and Bz. Each taxel uses a pair of Hall sensors to give a richer field measurement for reconstructing force, and a separate proximal pair is reserved for background stray-field compensation, leaving three taxels in the design. The magnet-to-sensor distance is 0.7 mm, and the elastomer is kept to a maximum 1 mm thickness so the magnet can displace adequately during contact while the field stays strong enough to read.
A neural network maps magnetic fields to force
Calibration used a 6-DoF parallel robot carrying a 5 mm diameter circular indenter on a 6-axis load cell, which recorded the forces and torques applied to the sensor. Indentations spanned a cone around the surface normal, with angles from 0 to 45 degrees and a maximum depth of 0.5 mm, distributed over 21 locations on four concentric rings. The sensor was indented at 0.01 mm/s and sampled at 490 Hz; after downsampling and synchronization the calibration set ran at 150 Hz, totaling roughly 400,000 datapoints per taxel.
A feed-forward neural network with one hidden layer of 25 ReLU neurons and Bayesian regularization was trained to map the magnetic measurements to applied force. The network was needed because the relationship between field and force is nonlinear, arising from elastomer deformation and magnetic field coupling. Forces were converted to pressure using the indenter area of 19.635 mm², so the reported errors are pressures rather than point forces. Per-taxel RMSE ranged from 0.67 to 1.46 kPa in fx, 0.72 to 0.78 kPa in fy, and 3.9 to 5.4 kPa in fz, giving the 2.133 kPa average. The authors note calibration accuracy is bounded by the load cell's own resolution of 1.4 mN, or 0.198 kPa.
Pressure RMSE and force resolution answer different questions
The headline 2.133 kPa figure is a pressure error, computed over the indenter area, and it should not be read as a force error in newtons. The paper's design targets were stated in force terms: detect normal and shear forces within 0–2 N and reach a resolution of 0.1 N. The authors report that calibration errors in each axis align with that 0.1 N resolution, but the RMSE values themselves are pressures. Mixing the two units would overstate or understate performance depending on the axis.
The axis breakdown also matters. The z-axis, normal to the sensor face, carries the largest errors, from 3.9 to 5.4 kPa, while the in-plane shear axes stay below 1.5 kPa. The sensor's stated operating range is 0–255 kPa, and the authors describe achieving at least 6% resolution of the maximum pressure. Separately, the design resolves a mean pressure of 74.49 kPa, the maximum retraction pressure reported in the validation. These are different quantities: one is a resolution floor relative to range, the other is an observed retraction load.
Hysteresis and creep bound how repeatable readings are
Two material behaviors qualify the calibration numbers. Hysteresis, the gap between loading and unloading readings, was 14.75% on taxel 1, 10.67% on taxel 2, and 13.55% on taxel 3, with standard deviations of 0.68, 0.39, and 1.17 respectively. Creep, the drift under sustained load, produced drops of 4.49%, 1.71%, and 3.81% across the three taxels, with correlations of 0.996, 0.997, and 0.995.
These figures sit alongside the RMSE values rather than replacing them. A low average error measured during dynamic indentation does not guarantee that a static grasp reads the same value on release, and the roughly 11–15% hysteresis indicates the elastomer does not return perfectly. For a reader comparing this sensor with other jaw-mounted designs, the relevant question is not only the error at calibration but how much the reading shifts between loading and unloading and over a held grasp.
Phantom and porcine tests show retraction and slip
The calibrated sensor was validated on silicone phantoms and ex vivo porcine tissue. The authors report tactile sensing during retraction as well as slip, and taxel-wise shear progression during incipient slip under clinically relevant loading. They also demonstrate live force profiles during human manipulation with da Vinci teleoperation. The slip detection rests on a coefficient-of-friction-based metric that displayed slip across the sensing surface.
The validation has a stated simplification: the retraction and slip experiments focused on the principal axis where slip would occur, which the authors describe as a departure from clinical use. Tissue traits such as variable thickness, hydration, and elasticity also change the achieved grasp, as do tissue type, contact area with the sensor, and pull angle or plane. These conditions bound how far the slip results transfer to real procedures.
The sensor face grips less firmly than the toothed jaw
Adding the sensor changes the instrument itself. The flat, smooth elastomer face permits more slip than the unmodified fenestrated toothed jaw, so grasps are not as strong and robust as before modification. The sensor also covers the existing teeth and fenestration, making the sensor face the contact area at 107 mm², and a 10-degree offset face accounts for sensor thickness while reducing the maximum open jaw angle from 90 degrees. The sensor adds to the instrument footprint.
The authors also flag a materials issue: the interface pairs hyperelastic tissue with hyperelastic elastomer, making behavior harder to characterize. Sterilization requirements and sealing against fluid ingress are left to future iterations. These are not incidental caveats; they determine whether a device that performs on phantom and ex vivo tissue can move toward repeated clinical use.
Local shear progression is the capability worth tracking
The paper's distinctive claim is not simply that force can be measured on a jaw, but that three taxels make slip observable as a spatial pattern. A single sensing element can report that force is changing; three elements arranged along the jaw can show shear progressing across the contact surface during incipient slip. That is the capability the authors position as previously undemonstrated at this scale for RAMIS graspers, and it is the one that most changes how a reader should evaluate the design against bulk kinesthetic feedback, which reports interaction force without telling anyone what contact pressure the tissue experiences.
The practical reading follows from the numbers. The sensor covers 0–255 kPa with z-axis RMSE between 3.9 and 5.4 kPa and shear-axis RMSE below 1.5 kPa, but carries 10.67–14.75% hysteresis and a flat face that grips less well than the original jaw. For anyone weighing this approach, the priority is the trade between local, multi-axis contact information and the grip quality and packaging work still outstanding, not the single average error figure on its own.
Sources used in this answer
Hall Effect-Based Tactile Force Detection Sensor for Robot-Assisted Minimally Invasive Surgery
A 2.06 g, three-taxel Hall effect sensor mounted on a robotic grasper jaw detected normal and shear forces with an average RMSE of 2.133 kPa, and was validated on phantoms and ex vivo porcine tissue for retraction and slip sensing.