Shielded soft force sensors

Force and strain sensors made of soft materials enable robots to interact intelligently with their surroundings. Capacitive sensing is widely adopted thanks to its low power consumption, fast response, and facile fabrication. Capacitive sensors are, however, susceptible to electromagnetic interference and proximity effects and thus require electrical shielding. Shielding has not been previously implemented in soft capacitive sensors due to the parasitic capacitance between the shield and sensing electrodes, which changes when the sensor is deformed. We address this crucial challenge by patterning the central sensing elastomer layer to control its compressibility. One design uses an ultrasoft silicone foam, and the other includes microchannels filled with liquid metal and air. The force resolution is sub-mN both in normal and shear directions, yet the sensor withstands large forces (>20 N), demonstrating a wide dynamic range. Performance is unaffected by nearby high DC and AC electric fields and even electric sparks.


Supplementary note 1: Deformation of empty vs liquid-metal filled channels
Liquid-metals can undergo large deformations while maintaining their electrical conductivity. They require however encapsulation for most of the applications. Due to their incompressibility, the encapsulation stiffens the structure if it is not designed properly. In our design, some of the channels are filled with the liquid-metal eutectic gallium-indium (EGaIn) to serve as the electrodes. The remaining channels are intentionally left empty in order to provide available space for the displacement of the liquid-metal when the sensor is pressed. These empty channels compensate for the incompressibility of the liquid-metal and of the elastomer.
Supplementary Fig. 2 compares the deformation profiles of two designs: 1) one with all channels are empty and 2) one with some channels are filled with liquid-metal while the remaining channels are empty. The results are obtained using COMSOL Multiphysics. In both simulations, the bottom of the structures is fixed and a uniform pressure is applied to the top surface. The structures deform as shown in Supplementary Fig. 2. Since the channels that are filled with liquid-metal are incompressible, these channels have slightly different deformation profiles; the liquid-metal pushes the lower resistance silicone wall (towards empty channels) when the sensor is pressed.

Supplementary note 2: Candidate sensor designs for shear and normal force measurements
We use COMSOL Multiphysics to optimize the layout of electrodes and of air pockets for sensitivity to normal and shear forces. The candidate designs are shown in Supplementary Fig. 3. In all simulations, the silicone layer is made of Sylgard 186 and has a Young's modulus of 750 kPa. The stretchable electrodes and shielding are assumed to be made of the same material as silicone layers. The liquid-metal channels are defined as incompressible, i.e., their volume is conserved.
Three parameters are considered when choosing between the designs; initial capacitance in the undeformed state, the total change in capacitance per unit change in normal force and the total change in capacitance per unit change in shear force (see Supplementary Table 1). Initial capacitance needs to be in a suitable range (< 17 pF) for it to be measured by the hardware used. Designs with higher changes in capacitance when a force is applied have higher sensitivity and are therefore considered to be better than the rest.
The layout with the best performance across the three parameters is one (design #5) in which the top row of electrodes is horizontally shifted with respect to the bottom row by half the channel width. This misalignment of the vertical walls reduces the effective mechanical stiffness of the and therefore amplifies the deformation under an external load (easier to compress the channels) which eventually enhances the sensing performance.

Supplementary note 3: The effect of shielding and the stiffness of the layers on the sensing capacitances
The effect of shielding is analyzed using COMSOL Multiphysics (see Supplementary Fig. 4b). This makes sensing capacitance 11 times more sensitive than parasitic capacitance for a given load. When the passive region is more deformable, parasitic capacitance changes rapidly (see Supplementary Fig. 4b). This is simulated using softer material. In this scenario, the ratio between the sensing and parasitic capacitances decreases to 1.8. Due to the very symmetric design and perfect loading condition in the simulations, we don't see any disturbance in the sensing electrodes due to this increased parasitic capacitance. In the real devices, however, we observe a decrease in the sensing capacitances when the passive region had comparable stiffness as the sensing region.
Therefore, the sensors are designed to have very high capacitance changes for the sensing capacitances and negligible change for the parasitic ones.

Supplementary note 4: Capacitive coupling between normal and shear deformation
Supplementary Fig. 9 shows the cross-section of the simple capacitive force sensor concept based on the parallel plate scheme. The sensor is made of a deformable block of dielectric material of dielectric permittivity ε. Three planar electrodes of negligible thickness are placed inside the block at a distance t, one symmetrically overlapping the other two over a w length. The system develops in the out-of-plane direction by a length b.
From theory [1] , the capacitances between the central (bottom) electrode and each top electrode in the undeformed configuration, namely CL,0 and CR,0, are given by: Let's suppose that a uniform load is applied to the top surface of the sensor as shown in Supplementary Fig. 9, which is resting on a flat surface. We can hypothesize that the sensor deforms homogeneously, causing the top electrodes to slide over the bottom one by an amount Δu and to decrease the gap width by Δt. The capacitance variations caused by the applied biaxial load ΔCL,0 and ΔCR,0 can be written as: Effects of applied normal and shear force can be estimated by evaluating sum and difference of the two capacitances: Whereas the sensor compression can be obtained directly from measuring the sum of the capacitance, the response to shear deformation will also depend on the applied compression, thus representing a coupling between normal and shear force effects.