Pressure sensing composite material

Abstract

A pressure sensing conductive elastomeric composite material, the material comprising a polymer matrix, itself comprising an elastomeric material, and a conduction network within the polymer matrix. The conduction network comprises: a plurality of particle chains, with each particle chain comprising a plurality of metallic ferromagnetic particles, a plurality of liquid metal droplets, and a plurality of non-ferromagnetic conductive platelets, wherein the conductivity of the composite material varies as a function of the pressure applied to the material.

Description

[0001] PRESSURE SENSING COMPOSITE MATERIAL

[0002] Field of the Invention

[0003] The present invention relates to pressure sensing composite materials. The present invention also relates to tactile sensing devices utilising pressure sensing composite materials. The present invention further relates to methods of manufacturing such composite materials, and methods of manufacturing and operating such tactile sensing devices.

[0004] Background

[0005] Efforts spanning decades have aimed to develop manipulators or prostheses with the tactile sensations comparable to a human finger (Refs 1-5). The human finger, endowed with four types of mechanoreceptors (RA, PC, SA-I, and SA-II) (Refs 6, 7), exhibits a high sensitivity that enables the perception of multidimensional tactile forces, encompassing pressure, vibration, shear stress, and tensile strain. The combination of these sensations enables complex tactile information processing, such as force direction, sliding state, and texture. This is essential for interacting with the environment and executing daily tasks, from picking up objects to intricate activities requiring fine motor skills and dexterity (Refs 8, 9). Consequently, the development of high-performance multidimensional tactile sensors is imperative for advancing next-generation robots with dexterous manipulation capabilities (Refs 10-12).

[0006] In recent years, diverse tactile sensors have emerged to replicate the 3D tactile sensation of skin (Refs 13, 14). These sensors employ various mechanisms, such as changes in resistance (Refs 15, 16), capacitance (Refs 17, 18), output voltage (Ref 19), magnetic field (Refs 20, 21), air pressure (Ref 22), or optical signal (Ref 23), to achieve the decoupling of normal and shear forces. As well-established technologies, optoelectronically or mechanically decoupled six-axis force & torque sensors or three-axis force sensors have been developed (Refs 24, 25). Unfortunately, their complex and bulky structures preclude their applicability in flexible robotic arms or prosthetic limbs (Refs 25-27). Some flexible sensors based on multilayer piezoresistive materials or patterned electrodes are able to produce different resistance, capacitance or voltage signal changes under normal and shear forces, and therefore can distinguish between the two (Refs 28, 29). Nonetheless, most of them are unable to identify the direction of tangential force or can only measure shear.

[0007] To achieve precise force direction identification, 3D force sensors incorporating electrode arrays within each sensor unit have been developed (Refs 15, 17, 42, 43). Different deformation modes of the sensor under normal and shear loading generate distinct output signals on the electrode array, enabling the inverse calculation of normal and shear forces based on a mathematically decoupled model. However, these proof-of-concept demonstrations face challenges in their large size, poor linearity, low sensitivity, or narrow measurement range, rendering them unsuitable for industrial application scenarios, especially miniaturised devices such as micro-manipulators (Refs 15, 18, 23). Moreover, these approaches usually involve complex and high-cost processing technologies including photolithography, micro-nano processing, and layer-by-layer assembly, which greatly reduces manufacturing efficiency and limits their large-scale practical application (Refs 16, 17, 43).

[0008] In summary, replicating human finger sensing with artificial materials and structures remains a formidable challenge, particularly in combining high pressure sensitivity with wide detection range and accurately identifying spatial force directions.

[0009] The present invention has been devised in light of the above considerations.

[0010] Summary of the Invention

[0011] The present inventors have conceived a pressure sensing conductive elastomeric composite material, to be incorporated into a tactile sensing device that addresses challenges encountered by the prior art.

[0012] In a first aspect, the present invention provides a pressure sensing conductive elastomeric composite material, the material comprising a polymer matrix, itself comprising an elastomeric material, and a conduction network within the polymer matrix. The conduction network comprises: a plurality of particle chains, with each particle chain comprising a plurality of metallic ferromagnetic particles, a plurality of liquid metal droplets, and a plurality of non-ferromagnetic conductive platelets, wherein the conductivity of the composite material varies as a function of the pressure applied to the material.

[0013] In a second aspect, the present invention provides a pressure sensing conductive elastomeric composite material, the material comprising a polymer matrix, comprising an elastomeric material, and a conduction network within the polymer matrix. The conduction network comprises: a plurality of particle chains, each particle chain comprising a plurality of metallic ferromagnetic particles, a plurality of liquid metal droplets, optionally, a plurality of non-ferromagnetic conductive platelets, wherein the composite material is porous, and wherein the conductivity of the composite material varies as a function of the pressure applied to the material.

[0014] Advantageously, the composite material provided by the first aspect or the second aspect provides a highly sensitive composite material, suitable for pressure sensing, with a wide dynamic range.

[0015] In a third aspect, the present invention provides a method of manufacturing the composite material according to the first aspect or the second aspect, the conductivity of the material being configured to vary as a function of pressure applied to the composite material, wherein the method comprises performing the steps of:

[0016] (a) providing a mixture of a plurality of metallic ferromagnetic particles, a liquid metal, optionally a plurality of non-ferromagnetic conductive platelets, and an elastomeric material precursor, and

[0017] (b) curing the mixture in an applied magnetic field to form the composite material.

[0018] In a fourth aspect, the present invention provides a tactile sensing device, comprising a sensor element formed of the composite material of the first aspect or the second aspect. The device advantageously utilises the highly sensitive composite material in a pressure sensing application. In a fifth aspect, the present invention provides a method of operating the tactile sensing device of the fourth aspect, wherein the method comprises: contacting the device with an object, the device sensing the object, through the pressure of the object on the device causing a change in the conductivity of the composite material, and the device measuring the change in conductivity of the composite material.

[0019] Optional features of the present invention will now be set out. These can be applied singly or in any combination to any aspect of the invention, unless the context demands otherwise.

[0020] The composite material may be porous. Moreover, the composite material may comprise an interconnected porous structure. The pores may concentrate the conduction network within the composite material to improve its pressure sensitivity.

[0021] Each particle chain of the composite material may be arranged substantially along an alignment axis. The alignment axes of the plurality of particle chains may be arranged so that the conductivity response of the composite material is anisotropic, dependent on the direction of the pressure applied to the composite material. The anisotropic conduction network may enhance the pressure sensitivity of the composite material along the alignment axes, whilst also reducing its sensitivity to lateral deformation, making the composite material particularly suitable for pressure sensing applications. In particular, the anisotropic conduction network may enable a stable conductivity-pressure response even on curved surfaces.

[0022] The Young’s modulus of the composite material may be at least 1 MPa in one direction (more preferably at least 2 MPa or at least 4 MPa in one direction). The Young’s modulus of the composite material may be at most 20 MPa in one direction (typically the same direction). The Young’s modulus of the composite material may be at most 16 MPa, or at most 12 MPa or at most 8 MPa, in one direction. For example, the Young’s modulus of the composite material along the alignment axis may be between 4 MPa and 8 MPa.

[0023] The mass ratio of the plurality of metallic ferromagnetic particles in relation to the elastomeric material may be in the range of at least 1 : 1 (more preferably at least 1 .2 : 1 or at least 1.3 : 1). The mass ratio of the plurality of metallic ferromagnetic particles in relation to the elastomeric material may be in the range of at most 2 : 1. The mass ratio of the plurality of metallic ferrimagnetic particles in relation to the elastomeric material may be at most 1.9 : 1 : or at most 1 .7 : 1 , or at most 1.5 : 1. For example, the mass ratio may be about 1 .4 : 1 . A mass ratio greater than 2 : 1 may result in the composite material having an unacceptably high Young’s modulus and electrical conductivity (under zero applied stress), hindering its deformation and resistance reduction under pressure, resulting in lower pressure sensitivity. This may be due to an unacceptably dense conduction network which saturates upon compression. A mass ratio less than 1 : 1 may result in a sparse conductive network which has an insignificant conductivity change under deformation.

[0024] The mass ratio of the plurality of liquid metal droplets in relation to the elastomeric material may be in the range of at least 0.2 : 1 . The mass ratio of the plurality of liquid metal droplets in relation to the elastomeric material may be preferably in the range of at least 0.3 : 1 , or at least 0.4 : 1 , or at least 0.5 : 1. The mass ratio of the plurality of liquid metal droplets in relation to the elastomeric material may be in the range of at most 2 : 1. The mass ratio of the plurality of liquid metal droplets in relation to the elastomeric material may be preferably in the range of at most 1 .8 : 1 , or at most 1 .5 : 1 , or at most 1 : 1 , or at most 0.7 : 1. For example, the mass ratio may be about 0.6 : 1. The liquid metal droplets act to bridge metallic particle chains in the conduction network, and improve the conductivity of the composite material and its pressure sensitivity whilst also reducing the elastic modulus. A mass ratio less than 0.2 : 1 may result in an unacceptably low pressure sensitivity and conductivity / an unacceptably high elastic modulus. Conversely, a mass ratio greater than 2 : 1 may result in an unacceptably high conductivity, leading to the saturation of the conduction network in the composite material, and consequently a reduced pressure sensitivity.

[0025] The mass ratio of the plurality of non-ferromagnetic conductive platelets in relation to the elastomeric material may be in the range of at least 0.01 : 1 (more preferably at least 0.02 : 1 , at least 0.03 : 1 or at least 0.04 : 1). The mass ratio of the plurality of non-ferromagnetic conductive platelets in relation to the elastomeric material may be in the range of at most 0.2 : 1 (more preferably in the range of at most 0.15 : 1 , or at most 0.1 : 1 , or at most 0.06 : 1). For example, the mass ratio may be in the range 0.04 : 1 to 0.06 : 1 , or about 0.04 : 1 .The non-ferromagnetic conductive platelets act to bridge the metallic particle chains in the conduction network, and enhance the conductivity of the composite material, enabling the mass ratio of the metallic ferromagnetic particles to be reduced. If the mass ratio of the conductive platelets is less than 0.01 : 1 , the conductivity of the composite material may be unacceptably low. If, however, the mass ratio of the conductive platelets is greater than 0.2 : 1 the pressure sensitivity of the composite material may be unsatisfactory due to saturation of the conduction network.

[0026] The porosity of the composite material of the first aspect may be at least 10%. The porosity of the composite material of the first aspect may be preferably at least 15%, or at least 20%. The porosity of the composite material of the first aspect may be at most 60%. The porosity of the composite material of the first aspect may be preferably at most 50%, or at most 40%. For example, the porosity may be in the range 20-40%. As the porosity increases, the Young’s modulus of the composite material decreases. However, a porosity greater than 60% may disrupt the conductive network in the composite material, resulting in unacceptably low conductivity, electrical stability, and pressure sensitivity. Conversely, for some embodiments, a porosity less than 20% may provide a less advantageous concentration of the conduction network within the composite material, leading to reduced pressure sensitivity, reduced anisotropy of the conduction network, and consequently relatively high pressure sensitivity to lateral deformation that is in some circumstances not wanted. Porosity may be measured by the Archimedes method (determining the theoretical density of the combination of materials in the composite and comparing this with the apparent density).

[0027] The elastomeric material may be a silicone polymer. For example, the elastomeric material may be polydimethylsiloxane (PDMS). For example, the elastomeric material may be any one of Ecoflex, Dragon Skin™, ELASTOSIL®, ExSil 100, and MED-6400. The elastomeric material may be any suitable silicone rubber. The metallic ferromagnetic particles may comprise iron, cobalt, and nickel, and / or alloys containing these elements. For example, the metallic ferromagnetic particles may comprise nickel. Moreover, the metallic ferromagnetic particles may be arranged in the particle chains to permit electrical conduction between the metallic ferromagnetic particles through a quantum tunnelling effect. For example, the plurality of particle chains may be comprised of a plurality of spiked particles. The spiked particles may improve the conductivity and pressure sensitivity of the conduction network.

[0028] The metallic ferromagnetic particles may have an average particle size of at least 0.5 micrometres (more preferably at least 1 micrometre or at least 1 .5 micrometres). The metallic ferromagnetic particles may have an average particle size of at most 20 micrometres (more preferably at most 15 micrometres, or at most 10 micrometres, or at most 5 micrometres).

[0029] The plurality of liquid metal droplets may comprise a eutectic alloy, for example a eutectic alloy of gallium and indium. The liquid metal droplets advantageously combine the deformability of liquid with the high conductivity of metal.

[0030] The liquid metal droplets may have an average droplet size of at least 5 micrometres (more preferably at least 10 micrometres, or at least 15 micrometres). The liquid metal droplets may have an average droplet size of at most 50 micrometres (more preferably at most 40 micrometres, or at least 30 micrometres).

[0031] The conductive platelets may have an average maximum linear dimension of at least 10 micrometres (more preferably at least 20 micrometres or at least 30 micrometres). The conductive platelets may have an average maximum linear dimension of at most 200 micrometres (more preferably at most 150 micrometres, or at most 100 micrometres, or at most 50 micrometres). Conductive platelets with an average maximum linear dimension of less than 10 micrometres may not be able to sufficiently bridge the particle chains to build conductive paths. Consequently, the conduction network may be disrupted, resulting in an almost insulating composite material with low pressure sensitivity.

[0032] The conductive platelets may have an average thickness of at least 1 nanometre (more preferably at least 5 nanometres, or at least 10 nanometres, or at least 20 nanometres, or at least 30nm, or at least 40nm). The conductive platelets may have an average thickness of at most 1 micrometre (more preferably at most 750 nanometres, or at most 500 nanometres, or at most 250 nanometres, or at most 100 nanometres, or at most 90nm, or at most 80nm, or at most 70nm or at most 60nm). This may improve the structural performance of the composite material. For example, the conductive platelets may have an average thickness of about 50 nanometres. The dimensions of the conductive platelets can be assessed via electron microscopy.

[0033] The non-ferromagnetic conductive platelets may comprise graphene. Specifically, the conductive platelets may be multiple layers of graphene. Preferably, the conductive platelets may comprise at least 15 layers of graphene, or at least 30 layers of graphene, or at least 60 layers of graphene, or at least 90 layers of graphene. Preferably, the conductive platelets may comprise at most 600 layers of graphene, or at most 450 layers of graphene, or at most 300 layers of graphene. Preferably, when the conductive platelets comprise graphene, the conductive platelets preferably have an average thickness of at least 5 nanometres, or at least 10 nanometres, or at least 20 nanometres, or at least 30 nanometres. Preferably, when the conductive platelets comprise graphene, the conductive platelets preferably have an average thickness of at most 200 nanometres, or at most 150 nanometres, or at most 100 nanometres.

[0034] The average pore diameter of the composite material may be at least 1 micrometre (more preferably at least 3 micrometres or at least 4 micrometres or at least 5 micrometres). The average pore diameter of the composite material may be at most 20 micrometres (more preferably at most 15 micrometres, or at most 10 micrometres, or at most 8 micrometres, or at most 7 micrometres or at most 6 micrometres). If the average pore diameter of the composite material is greater than 20 micrometres the liquid metal (depending on its surface tension) may enter the pores, affecting the conductive network and reducing the pressure sensitivity of the material. It is therefore preferable that the average droplet size of the liquid metal is greater than the average pore diameter, as the high surface tension of the liquid metal may prevent the droplets from entering the pores.

[0035] In the context of manufacturing the composite material, the curing of the mixture in an applied magnetic field may align the metallic ferromagnetic particles along an alignment axis, causing the conduction network to be anisotropic.

[0036] In the method of manufacturing the composite material, step (a) may additionally comprise one or more of the steps of:

[0037] (a-i) mixing a plurality of metallic ferromagnetic particles, a liquid metal, and a first amount of elastomeric material precursor to form a first mixture,

[0038] (a-ii) mixing a plurality of non-ferromagnetic conductive platelets with a second amount of elastomeric material precursor to form a second mixture, and

[0039] (a-iii) mixing the first mixture of step (a-i) with the second mixture of step (a-ii) to form a third mixture.

[0040] The mixing of step (a-i) may be performed at a higher rotational speed (or more generally, at a higher shear rate) than the mixing of step (a-ii). Mixing the conductive non-ferromagnetic platelets at a lower speed may maintain the average maximum linear dimension of the platelets, as higher-speed mixing may cause the platelets to fragment.

[0041] Step (a) may additionally comprise of mixing a porogen. The porogen creates pores in the composite material. The method may additionally comprise the step (c) of removing the porogen from the cured composite by evaporation of the porogen. Step (c) may be achieved for example either by heating the cured composite to remove the porogen, or by vacuuming the cured composite to remove the porogen, or a combination of heating and vacuuming. Removal of the porogen by heating may be preferred when the porogen are not easily volatile at room temperature. Removal of the porogen by vacuuming may be preferred when the porogen are highly volatile at room temperature. The porogen may accordingly be a sacrificial porogen. The porogen may be an alcohol such as 1 ,2-propanediol, for example. The porogen may also be glycerol, or the porogen may also be isopropyl alcohol. The porogen may be any suitable liquid with a boiling point below 300° C that is not miscible with other components used in the manufacture of the composite material and does not react with the composite material or said components.

[0042] The mass ratio of the porogen in relation to the elastomeric material may be at least 0.1 : 1 (more preferably at least 0.3 : 1 or at least 0.5 : 1). The mass ratio of the porogen in relation to the elastomeric material may be at most 2 : 1 (more preferably at most 1.5 : 1 , or at most 1 : 1 , or at most 0.7 : 1). The mass ratio may be about 0.6 : 1 , for example. The mass ratio of the porogen in relation to the elastomeric material is positively related to the porosity of the composite material. A ratio below 0.1 : 1 may result in high elastic modulus, and the composite material therefore may not have sufficient pressure sensitivity. However, excessive porosity, such as a mass ratio above 2 : 1 may destroy the conductive network, resulting in significantly reduced conductivity and electrical stability.

[0043] The sensor element may have an arrangement of electrodes placed to enable determination of electrical conductivity through different volumetric regions of the sensor element.

[0044] The sensor element may have a tapering shape with a basal region with greater cross sectional area than a force contact region. This may enable the sensor element to further improve the pressure sensitivity and may also provide the sensor element with normal-shear force decoupling capacity.

[0045] The alignment axes of the conductive particle chains may be arranged substantially perpendicular to the basal region. This arrangement may reduce the interference of lateral deformation on the sensor element, which may permit use of the tactile sensing device on curved or flexible surfaces.

[0046] The sensor element may have a pyramidal shape, tetragonal shape, or conical shape. These shapes may act as sensitivity enhancers, amplifying the deformation and resistance changes resulting from pressure incident on the sensor element. The top of the sensor element may be any shape. For example, the sensor element may be flat topped, or spire topped, or domed.

[0047] The arrangement of electrodes may include a plurality of basal region electrodes, permitting a differential conductivity response of the tactile sensing device to pressure including a shear component compared with uniaxial pressure. For example, such an arrangement may facilitate normal-shear force decoupling capacity.

[0048] The arrangement of electrodes may include at least one electrode at the force contact region.

[0049] The tactile sensing device may also include an intermediate layer applied between the composite material and the arrangement of electrodes. This may prevent peeling of the electrodes.

[0050] The tactile sensing device may further include coating a top electrode with a layer to protect the electrode from wear. The layer may be a silicone polymer. For example, the top electrode may be coated with an Ecoflex layer.

[0051] The invention includes the combination of the aspects and preferred features described except where such a combination is clearly impermissible or expressly avoided. Summary of the Figures

[0052] Embodiments and experiments illustrating the principles of the invention will now be discussed with reference to the accompanying figures in which:

[0053] Figs. 1 to 3 illustrate the multi-scale structures of an AGrPE sensor.

[0054] Fig. 1 is a 3D schematic showing the composition and microstructures of the AGrPE.

[0055] Fig. 2 shows a schematic hierarchical diagram of an AGrPE 3D force sensing array with pyramid surface structures mounted on a robot manipulator.

[0056] Figs. 3A to E show scanning electron microscope (SEM) and energy dispersive spectroscope (EDS) images of the cross-section of AGrPE sample. The distribution of Ni, graphene nanosheet, LM droplets, and PDMS are represented by their characteristic elements of Ni, C, Ga and Si, respectively. The EDS image at Fig. 3D shows the aligned Ni particle chains.

[0057] Fig. 4 shows an SEM image of the interconnected micropores in AGrPE.

[0058] Figs. 5A to E show (A) SEM and (B to E) EDS images of the cross-section of the AGrPE sample with lower magnification, which clearly shows the aligned Ni particle chain structure as well as the graphene nanosheets and LM droplets bridging them. The distribution of Ni, Graphene nanosheet, LM droplets, and PDMS are represented by their characteristic elements of Ni, C, Ga and Si, respectively.

[0059] Fig. 6 shows the effects of (a-c) Ni content, (d-f) graphene content, and (g-i) LM content on the elastic modulus, initial resistivity, and initial pressure sensitivity of AGrPE.

[0060] Figs. 7A to C show SEM images of graphene nanosheets in the composite material.

[0061] Figs. 8A to F show (A to C) the SEM images of graphene nanosheets in composites prepared using different methods. Effects of graphene nanosheet sizes on the (D) elastic modulus, (E) initial resistivity, and (F) initial pressure sensitivity of AGrPE.

[0062] Fig. 9 shows the porosity of AGrPE samples with different porogen / PDMS mass ratios.

[0063] Figs. 10A to C show the effects of the porogen / PDMS mass ratio (porosity) on the (A) elastic modulus, (B) initial resistivity, and (C) initial pressure sensitivity of AGrPE.

[0064] Figs. 11 to 18 illustrate the electrical and mechanical properties of AGrPE.

[0065] Fig. 11 shows conductivity-strain curves of AGrPE in parallel (0°) and perpendicular (90°) to the alignment direction.

[0066] Fig. 12 shows stress-strain curves of AGrPE in parallel (0°) and perpendicular (90°) to the alignment direction.

[0067] Fig. 13 shows conductivity-pressure curves of AGrPE and AGrHE along 0°.

[0068] Fig. 14 is a schematic diagram illustrating the principle of conductivity change of AGrPE when compressed in different directions. Fig. 15 shows finite element simulations comparing the deformation and stress distribution of AGrPE and AGrHE under a pressure of 513 kPa.

[0069] Fig. 16 shows finite element simulations comparing the conductivity of AGrPE and AGrHE under a pressure of 80 kPa. A larger potential drop (lighter grey colour) corresponds to greater resistivity.

[0070] Fig. 17 shows current density simulations showing conductive paths in AGrPE under pressure.

[0071] Fig. 18 shows the simulated conductivity of AGrPE and AGrHE at different pressures.

[0072] Figs. 19A and B show the stress-strain curves of AGrPE along (a) 0° and (b) 90° under cyclic loading.

[0073] Figs. 20A to D show the effects of the strength of the magnetic field during curing on the (A) elastic modulus, (B) initial resistivity, and (C) initial pressure sensitivity of AGrPE. (D) shows resistance-strain curves of AGrPE samples cured in magnetic field with different strengths.

[0074] Fig. 21 shows the elastic modulus of AGrPE, AGrHE, and their isotropic versions GrPE and GrHE, respectively.

[0075] Fig. 22 shows the conductivity-pressure curves of AGrPE and AGrHE along 90°.

[0076] Figs. 23A to C show SEM images displaying graphene nanosheets and LM droplets bridging within and between Ni particle chains.

[0077] Fig. 24 shows the simulation settings for the electrical conductivity simulation.

[0078] Fig. 25 shows the experimental and simulated elastic modulus of AGrPE and AGrHE. The simulated elastic modulus is calculated based on the simulated stress distribution and model deformation.

[0079] Fig. 26 shows the simulated current density of AGrPE and AGrHE models at 100 kPa pressure. The intensity bar is offset to highlight the current flow in graphene nanosheets.

[0080] Fig. 27 shows a schematic representation of the wavy internal structure of human skin.

[0081] Figs. 28 to 34 shows an AGrPE pyramid sensor unit.

[0082] Fig. 28 shows simulated deformation and stress distribution in the longitudinal section of a pyramid sensor unit under vertical pressure.

[0083] Fig. 29 shows simulated deformation and stress distribution in the longitudinal section of a sensing unit under oblique force.

[0084] Figs. 30A and B show relative conductivity change-pressure curves of the AGrPE sensor unit at (A) 0-30 kPa and (B) 0-500 kPa.

[0085] Figs. 31 A and B show simulated bottom pressure distributions of the AGrPE sensor unit under (A) normal and (B) shear forces.

[0086] Fig. 32 shows relative potential change-pressure curves measured by four electrodes on the bottom of the AGrPE sensor unit at 0-1 .3 kPa Fig. 33 shows relative potential change-pressure curves measured by four electrodes on the bottom of the AGrPE sensor unit at 0-55 kPa.

[0087] Fig. 34 shows the potential-time curve of electrode 1 at the bottom of the sensor unit at 0-1 .6 kPa for 1000 cycles. The insets show the curves in the first 20 cycles and cycles 961-980.

[0088] Figs. 35A and B show the pressure-strain curve of an AGrPE sensor unit, with the inset showing the pressure distribution in a cross section of the sensor unit.

[0089] Fig. 36 shows the sensing performance comparison between the AGrPE sensor and state-of-the-art flexible pressure sensors (Refs. 3-25).

[0090] Figs. 37A and B compare the bottom pressure distribution curve along x=y line of the AGrPE sensor unit under normal and shear forces.

[0091] Figs. 38A and B show (A) the location and (B) a micrograph image of the bottom electrodes of AGrPE sensor unit.

[0092] Fig. 39 show the schematic design of the pressure measurement circuit.

[0093] Figs. 40A and B show potential-pressure curves measured at one electrode (electrode 1) of the sensor unit in circuit with / without a 16-bit analog-to-digital converter at (A) 0-1 kPa and (B) 0-6 kPa.

[0094] Figs. 41 A and B show (A) potential-pressure curves and (B) relative potential change-pressure curves of the electrode 1 of the sensor unit in circuit with a fixed resistor of 100 Q and 5 kQ.

[0095] Figs. 42A and B show relative potential change-time curves measured at electrode 1 of the sensor unit in the (A) first 20 cycles and (B) cycles 961-980 of 1000 cycles of 0-1 .6 kPa cyclic loading test.

[0096] Fig. 43 show the simulated relative potentials of bottom electrodes 2 and 3 of the AGrPE sensor unit under different force directions. Since the positions of electrodes 2 and 3 are symmetric about 0 = 45°, their simulated relative potentials are also symmetric about 0 = 45°.

[0097] Figs. 44 to 52 explain the 3D force sensing of AGrPE sensor unit.

[0098] Fig. 44 shows the decomposition of the oblique force in the spherical coordinate system and different pressure distributions on the four bottom electrodes.

[0099] Fig. 45 shows the simulated relative potential of bottom electrodes under different force directions.

[0100] Fig. 46 shows a comparison of simulation and experimental results of the relative potential vs (p angle curves of the four bottom electrodes when the shear force direction is fixed at 20°.

[0101] Fig. 47 shows a schematic diagram of the oblique force testing device of the AGrPE sensor unit.

[0102] Fig. 48 shows the relative potential change vs force curves of the four electrodes of sensor when the force direction is fixed at q> = 18°, 0 = 40°.

[0103] Fig. 49 compares the force measured by the AGrPE sensor unit with the applied force.

[0104] Fig. 50 compares the angle measured by the AGrPE sensor unit with the set angle. Fig. 51 A is a schematic showing the sliding of the sensor unit on a rough surface. Fig. 51 B is a (i) potential-time curve of electrode 1 when the sensor unit slides on sandpaper.

[0105] Fig. 52 shows the instantaneous changes and subsequent fluctuations in voltage when the sensor slides on different substrates.

[0106] Figs. 53 to 56 demonstrate the AGrPE sensor array.

[0107] Fig. 53 shows a schematic diagram of the AGrPE force sensor array soldered on PCB board.

[0108] Figs. 54A and B show (A) a schematic diagram of a robotic arm equipped with AGrPE sensor array grabbing an A4 paper tube, and (B) normal and tangential forces-time curves detected by the sensor when grabbing A4 paper tube.

[0109] Figs. 55A and B show (A) a schematic diagram of the robotic arm grabbing a steel block, and (B) normal and tangential forces-time curves, as well as the force direction (cp)-time curve detected by the sensor array when transferring the steel block.

[0110] Fig. 56 shows the measured forces on the steel block when it is (ti) sliding, (t2) clamped, and (ta) placed on the ground.

[0111] Fig. 57 shows decomposition of the oblique force in the spherical coordinate system and potentials on the four bottom electrodes.

[0112] Fig. 58 shows representations of the AGrPE sensor unit when pressed in different directions.

[0113] Figs. 59A and B show (A) potential-time curves and (B) calculated forces-time curves of AGrPE sensor unit during a 3D force sensing test.

[0114] Figs. 60A and B show (A) a schematic diagram of the AGrPE sensor unit sliding on the cardboard surface, and (B) the potential-time curves of the electrodes on the front and rear sides along the sliding direction.

[0115] Fig. 61 shows voltage fluctuations of the AGrPE sensor when sliding on 10 substrates with different surface roughness. The linear correlation R2between voltage fluctuation and surface roughness is 0.96. The 10 substrates and their roughness are: Glass (0.007 pm), Plastic (0.17 pm), Steel (0.33 pm), A4 paper (9.1 pm), Cardboard (24.7 pm), Tissue (37.8 pm), Sandpaper (60.7 pm), 3D-printed grooves 0.1 mm (93.3 pm), Fabric (106.7 pm), 3D-printed grooves 0.15 mm (126 pm). Surface roughness is measured by a Bruker Dektak XT Stylus Profilometer.

[0116] Fig. 62 shows the schematic diagram of the pressure measurement and feedback-control circuit of the robotic arm equipped with AGrPE sensor array.

[0117] Fig. 63 shows voltage signal-time curves of two representative electrodes of the AGrPE sensor array during the process of the robotic arm clamping an A4 paper tube. The inset shows the location of two selected electrodes. The ti and t2 correspond to ti and t2 in Fig. 5d. Fig. 64 shows voltage signal-time curves of two representative electrodes of the AGrPE sensor array during the process of the robotic arm transferring a steel block. The inset shows the location of two selected electrodes. The ti to U correspond to ti to t4 in Fig. 5h.

[0118] Fig. 65 shows a photograph and SEM images of the AGrPE microsensor array. The white areas in SEM images are due to charges on the PDMS matrix.

[0119] Fig. 66 shows a schematic diagram of the AGrPE microsensor array bonded on glass wafer with patterned electrodes, as well as the measured pressure distribution on the bottom of four microsensor units in contact with a metal ball.

[0120] Figs. 67A and B show the measured average (A) normal force and (B) force direction generated by gold and indium balls of different diameters.

[0121] Fig. 68 shows the preparation of the AGrPE microsensor array film, (a) 3D schematic diagram and optical photo of the silicon mould for curing microsensor array film, (b) Optical photo of the microsensor array film with a unit side length of 200 pm. (c) SEM images of the AGrPE microsensor array deposited with 100 nm gold layer as the top electrode.

[0122] Figs. 69A and B show the force sensing performance of a single AGrPE microsensor unit with the side length of 200 pm. Fig. 69A shows the average relative potential change-force curve measured by four bottom electrodes of the AGrPE microsensor unit. Fig. 69B shows the average potential measured by the four bottom electrodes of the microsensor unit under normal forces of 0, 0.9, 1 .8, and 2.7 pN.

[0123] Fig. 70 demonstration the AGrPE microsensor array with sensor unit side length of 200 pm. (a) shows photolithographically patterned electrodes on the glass wafer, (b) shows a gold ball prepared by melt solidification method, and (c) shows the experimental setup for metal ball detection test.

[0124] Fig. 71 shows the direction of the shear force measured by the microsensor unit.

[0125] Figs. 72 and 73 show raw relative potential data measured by the bottom electrodes of the microsensor unit under (Fig. 72) gold and (Fig. 73) indium balls of different diameters. See the definition of force direction and Ui ~ LU in Fig. 44.

[0126] Fig. 74 illustrates the force analysis of the microsensor unit under the metal ball.

[0127] Detailed Description of the Invention

[0128] Aspects and embodiments of the present invention will now be discussed with reference to the accompanying figures. Further aspects and embodiments will be apparent to those skilled in the art. All documents mentioned in this text are incorporated herein by reference.

[0129] In embodiments of the present invention, a composite material is incorporated into a multi-structured force sensor array. Fig. 1 shows in the central view a schematic illustration of a pressure sensing conductive elastomeric composite material 10. The material comprises a polymer matrix 12, comprising an elastomeric material 14 with pores 16 (the microporous structure of the matrix is shown in the schematic enlarged view in the left side of Fig. 1). A conduction network is formed within the polymer matrix, the conduction network comprising a plurality of particle chains 18, each particle chain comprising a plurality of metallic ferromagnetic particles 20, shown in the schematic enlarged view at the right hand side of Fig. 1 . The metallic ferromagnetic particles 20 in this embodiment are spiked Ni particles, enabling a quantum tunnelling effect for conduction between them. The particle chains 18 are aligned along direction A. The composite material also includes a plurality of liquid metal droplets 22. In this embodiment, the composite material also includes a plurality of non-ferromagnetic conductive platelets 24, such as graphene platelets. In other embodiments, it may not be necessary to include a plurality of non-ferromagnetic conductive platelets 24, such as graphene platelets.

[0130] In more detail, in relation to Fig. 1 , the composite material includes a polymer matrix and incorporates a hybrid filler comprising metallic ferromagnetic particles forming particle chains, non-ferromagnetic conductive platelets, and liquid metal (LM) droplets, forming a solid-liquid hybrid conduction network with LM droplets as deformable hubs and non-ferromagnetic conductive platelets as bridges. The metallic ferromagnetic particles are preferably spiked nickel (Ni) particles, which form a conductive chain which is sensitive to the applied pressure along its chain alignment. The non-ferromagnetic platelets are preferably graphene nanosheets. The liquid metal is preferably eutectic gallium-indium (EGain, 75% gallium and 25% indium), which combines the deformability of liquid with the high conductivity of metal (44, 45). The elastomeric material which comprises the polymer matrix may be polydimethylsiloxane (PDMS). The composite material may introduce a porogen during the preparation process, which, through curing in a magnetic field provides an interconnected porous structure, as best shown in Figs. 11 to 18. The porogen may be 1 ,2-propanediol. The porogen may alternatively be glycerol or isopropyl alcohol, for example. The composite material can achieve high pressure sensitivity along its alignment direction. Through controlled variable experiments and numerical simulations, the composite material’s composition and structural parameters were further improved, as reported here, enhancing its sensing performance.

[0131] As described above, in a preferred embodiment the composite material incorporates a conduction network into an interconnected porous structure, with the conduction network comprising spiked Ni microparticles forming a conductive chain with LM droplets as deformable hubs and graphene nanosheets providing interchain conductivity. This preferred embodiment is collectively termed an anisotropic graphene-enabled porous conductive elastomer (AGrPE).

[0132] Preparation, Characterisation and Simulation of AGrPE

[0133] The 3D microstructures of AGrPE are illustrated in Fig. 1. Its detailed preparation process is given in the Methods Section. To prepare AGrPE, Ni particles and LM are first mixed into liquid PDMS through highspeed stirring. The mixture is then mixed with 1 ,2-propanediol and graphene-PDMS dispersion at low speed, with 1 ,2-propanediol serving as a sacrificial porogen for micropore structure formation in AGrPE. The dispersion of graphene into PDMS is done separately to control graphene nanosheet size. The final mixture is poured into a 3D printed mould and solidified in a uniform magnetic field at 80 °C. Finally, AGrPE samples are obtained by heating the cured composite at 140 °C for 3 hours to remove 1 ,2- propanediol. The interconnected micropores facilitate porogen evaporation, with the result shown in Fig. 4.

[0134] The SEM image of Fig. 4 shows the interconnected micropores structures in AGrPE samples. Due to its high volume fraction, the porogen forms contacted micro-droplets in the composite mixture during mixing process. After curing in an oven, these droplets remain contacted in cured AGrPE samples. During the high temperature heating process, the porogen droplets are evaporated and escape the AGrPE sample from these connected pores, leaving behind an interconnected microporous structure. The diameters of these pores are typically in the range 3 to 8 pm.

[0135] In an embodiment, the mass ratio of raw materials Ni / LM / graphene / 1 ,2-propanediol / PDMS is 1 .4 / 0.6 / 0.04 / 0.6 / 1 (see composition discussion in the next section). AGrPE has a porosity of 27.9% and a Ni / LM / graphene / PDMS volume ratio of 0.154 / 0.092 / 0.017 / 1. Scanning electron microscope (SEM) and energy-dispersive X-ray spectroscopy (EDS) images of the cross-section of the AGrPE sample such as those presented in Figs. 3A to E and Figs. 5A to E were used to measure the diameters of graphene nanosheets, LM droplets, and pores to be 25 to 50 pm, 15 to 30 pm, and 3 to 8 pm, respectively. The aligned Ni microparticle chains together with the graphene nanosheets and LM droplets bridging them construct an anisotropic conductive network within the microporous elastomer, as evident in low- magnification SEM and EDS images shown in Figs. 5A to E. In more detail, Figs. 5A to E show the SEM and EDS images of the cross-section of AGrPE sample with lower magnification, which clearly shows the aligned Ni particle chain structure as well as the graphene nanosheets and LM droplets bridging them. The distribution of Ni, graphene nanosheet, LM droplets, and PDMS are represented by their characteristic elements of Ni, C, Ga and Si, respectively. The microporous structure, quantum tunnelling effect between Ni particles (Refs 46-48), and anisotropic particle network collaboratively improve the pressure sensitivity of AGrPE.

[0136] Importantly, mimicking the structure of dermis, a pyramidal surface structure is established on the AGrPE film for pressure sensing array creation (Fig. 2). This macrostructure imparts the AGrPE sensor not only extraordinary sensitivity and range but also capabilities beyond traditional pressure sensors, including three-axis force sensing, slip detection, and roughness identification. Accordingly, as shown in Fig. 2, embodiments of the present invention use pyramidal structure 60 formed of the composite material 12 with the particle chain alignment along direction A. The pyramidal structure 60 has an array of electrodes 62 as described in more detail later. The pyramidal structure 60 are provides in an array 80 on a suitable substrate surface. In the illustrated embodiment, two such arrays 80 are provided on opposing faces of a vice-type manipulator 100, capable of bringing the arrays 80 together to grip an objection (not shown). With this approach, it is possible for the manipulator to provide sensing of the forces and direction caused by the interaction between the object and the manipulator, and also to provide slip detection and roughness detection. A variety of AGrPE samples were prepared with variation in their raw material compositions and processing methods. The samples’ electrical and mechanical properties were subsequently characterised to adapt their characteristics for heightened pressure sensitivity and wide sensing range.

[0137] The following Equation (1) defines the pressure sensitivity S of the composite, where o, and p denote conductivity, initial conductivity, and pressure, respectively. Specifically, S represents the ratio of the slope of the conductivity-pressure curve to the initial conductivity.

[0138] 1 Aff 1 (T — (Tn

[0139] S = - = - -(1)

[0140] (T0p (T0p

[0141] The effects of Ni, graphene, and LM content on AGrPE properties were investigated. To investigate the influence of the conductive filler contents on the pressure sensing performance of AGrPE, a set of AGrPE samples with different Ni, graphene, and LM contents were prepared, and their elastic modulus, initial resistivity, and initial pressure sensitivity were compared. Since the surface structure has not yet been created on AGrPE samples, their conductivity increases nonlinearly with pressure. The conductivity at an applied pressure of 80 kPa was incorporated into Equation (1) to calculate the initial pressure sensitivity S.

[0142] As the Ni content increases, the elastic modulus and electrical conductivity of AGrPE rise, as shown in Figs. 6A and B. High Ni content significantly increases the stiffness of AGrPE and hinders its deformation and resistance reduction under pressure, resulting in lower pressure sensitivity. However, the pressure sensitivity does not change much (around 0.38 kPa-1) as the Ni / PDMS mass ratio increases from 1 to 1 .4, as shown in Fig. 6C. This is because at low Ni content, the conductive particle network in AGrPE is sparse and is less likely to form a large number of conductive paths under deformation, resulting in an insignificant reduction in resistance under deformation. When the Ni / PDMS mass ratio exceeds 1 .4, the conductive particle paths in AGrPE are dense and thus result in high initial conductivity. This makes the conductive paths more likely to saturate upon compression and limits the room for resistance to drop, resulting in significantly reduced sensitivity (0.223 kPa-1for a Ni / PDMS mass ratio of 1 .8).

[0143] A similar pattern can be found for the graphene content, except that the modulus of AGrPE is less affected by the graphene content because graphene nanosheets are much more flexible than Ni particles and have a much lower volume fraction in the composite, as shown in Fig. 6D. Note that the graphene- free composite is electrically insulating (resistivity > 100 MQ»m), demonstrating the irreplaceable role of graphene in enhancing conductivity and reducing the Ni content required, as shown in Fig. 6E. For similar reasons as in the case of Ni particles, the pressure sensitivity of AGrPE fluctuates around 0.38 kPa-1when the graphene / PDMS mass ratio is lower than 0.04, and drops by 32% to 0.259 kPa-1as the graphene / PDMS mass ratio increases to 0.06, as shown in Fig. 6F, due to an order of magnitude lower initial resistivity and more stable initial resistance (as evidenced by the shorter error bars), AGrPE with a graphene / PDMS mass ratio of 0.04 exhibits better electrical properties than the case of 0.02.

[0144] In addition, liquid metal is also an integral part of the conductive network in AGrPE. Although graphene nanosheets can bridge Ni particle chains to enhance conductivity, excess graphene can severely weaken the pressure sensitivity of the composite as shown in Fig. 6F. Therefore, the introduction of LM droplets can not only significantly improve the conductivity of AGrPE by more than two orders of magnitude, as shown in Fig. 6H, but also reduce the elastic modulus and enhance pressure sensitivity by around 14%, as shown in Figs. 6G and I.

[0145] Therefore, the Ni / graphene / LM / PDMS mass ratio was set at 1 .4 / 0.04 / 0.6 / 1 to achieve a particularly suitable pressure sensing performance of AGrPE.

[0146] The processing method also influences the electromechanical properties of AGrPE. Considering the thinness of graphene nanosheets (which are approximately 50 nm in some embodiments) and their diameter typically exceeding 30 pm, as shown in Figs. 7A to C, careful mixing methods are used to prevent breakage, therefore maintaining the high conductivity of AGrPE. Dispersing graphene sheets separately in PDMS at low mixing speed achieves this goal.

[0147] In more detail, due to their high aspect ratio, graphene nanosheets are easily broken during stirring, especially under high shear forces, and therefore require careful mixing methods in order to prevent breakage, and consequently maintain the high conductivity of AGrPE. When graphene nanosheets were mixed with Ni particles, LM, and PDMS, and stirred at a speed of 350 rpm, the high viscosity of the mixture and rapid stirring resulted in high shear forces, causing the majority of graphene nanosheets to be broken to less than 10 pm, as shown in Fig. 8A. As a result, the broken graphene sheets cannot bridge the Ni particle chains well to build conductive paths, resulting in AGrPE being almost insulating, with resistivity > 30 MO m, and possessing a low pressure sensitivity of 0.287 kPa1. Dispersing graphene sheets separately in PDMS at low mixing speed addresses this problem. When preparing AGrPE, we pre-dispersed graphene in PDMS and mixed it with the Ni-LM-PDMS mixture at a low speed to maintain the large size of the graphene nanosheets. As can be seen in Figs. 8B and C, the lowest premixing speed can maintain the size of most graphene nanosheets above 30 pm, which significantly increases the conductivity of AGrPE and enhances its pressure sensitivity by 33% to 0.382 kPa1.

[0148] Porosity, another significant factor affecting AGrPE performance, is adjustable through porogen content. Because composites shrink during high-temperature evaporation of the porogen, it is difficult to calculate their porosity according to the volumes of porogen and other raw materials in AGrPE. Without wishing to be bound by theory, we speculate that this is due to the shrinkage stresses occurring within the porous PDMS at high temperature. Therefore, we calculated the porosity of AGrPE using the mass difference method. Specifically, we measured the mass of non-porous AGrHE and porous AGrPE composites with the same volume, recorded as Mi and M2, respectively. The porosity of AGrPE consequently calculated from Equation (2) below:

[0149] The calculated porosity of AGrPE for varying porogen / PDMS mass ratios is shown in Fig. 9. Higher porosity enhances composite flexibility for improved pressure sensitivity but compromises conductivity and electrical stability. As the porosity (positively related to the porogen / PDMS mass ratio) increases, the elastic modulus of AGrPE decreases (shown in Fig. 10A), which theoretically contributes to enhanced pressure sensitivity. However, excessive porosity will destroy the conductive particle network in the composite, resulting in significantly reduced conductivity and electrical stability (as shown in Fig. 10B). These micropores will also hinder the formation of conductive paths under pressure, which in turn weakens the pressure sensitivity of AGrPE (shown in Fig. 10C). However, the porosity range can be very wide. For sufficiently soft polymer matrices, even nonporous materials (with a porosity of 0%) are possible. Composites can also be processed into flexible aerogels to achieve extremely high porosity. After investigation, AGrPE with a porogen / PDM mass ratio of 0.6 (porosity of 27.9%) exhibits low resistivity (~1 kOm) and the highest sensitivity (-0.38 kPa1). A suitable sensitivity is therefore achieved with a porogen / PDMS mass ratio of 0.6 (porosity of 27.9%).

[0150] The electrical conductivity-strain and stress-strain curves of the optimised AGrPE are presented in Figs. 11 and 12. The directions parallel and perpendicular to the Ni particle chains are designated as 0° and 90°, respectively. AGrPE shows notable anisotropy attributed to aligned particle chains. Its electrical conductivity and elastic modulus along 0° (724.8 pS»m1and 5.62 MPa) are 24 times and 5.4 times those along 90° (30.0 pS»m1and 1.05 MPa), respectively.

[0151] In cyclic loading tests, AGrPE shows good mechanical stability and elastic hysteresis in both parallel and perpendicular to the alignment directions of Ni particle chains, as shown in Figs. 19A and B. The directions parallel and perpendicular to the Ni particle chains are defined as 0° and 90°, respectively. For both cases, the sample exhibits a more pronounced elastic hysteresis (larger elastic hysteresis loop) in the first cycle. Their stress curves almost overlap in subsequent cycles, showing good mechanical stability as shown in Figs. 19A and B. However, the elastic hysteresis of AGrPE in the first cycle along 0° is particularly significant and exhibits a stiffness softening phenomenon that decreases with strain. This is because the closely contacted Ni particles in the aligned Ni particle chains hinder the initial compression of the sample. When the compressive strain exceeds 5%, some Ni particles are extruded from the particle chains, resulting in a decrease in sample stiffness, significant energy dissipation and elastic hysteresis. This phenomenon no longer occurred in subsequent cycles because the mechanical properties of the sample stabilised.

[0152] Along 0°, AGrPE demonstrates markedly higher sensitivity, with a six-order-of-magnitude surge in conductivity at 20% compressive strain. Conversely, its resistance along 90° remains stable with a fluctuation of < 10% during 20% compression. This characteristic is achieved by adjusting the curing magnetic field strength. When cured in a 500 mT magnetic field, AGrPE attains not only high conductivity and sensitivity along 0°, but also nearly constant resistance along 90°.

[0153] We investigate the influence of the curing magnetic field strength on the pressure sensing performance of AGrPE, as shown in Figs. 20A to D. The isotropic sample cured without a magnetic field (strength of 0) is insulating (resistivity > 100 MQ»m), demonstrating the necessity of the anisotropic particle network to enhance the conductivity of the sample. As the magnetic field strength increases, the elastic modulus and electrical conductivity of the obtained AGrPE samples increase, yet their pressure sensitivity does not decrease significantly. The pressure sensitivity of AGrPE samples cured in 300 / 500 / 700 mT magnetic fields differed by only 4%. More importantly, the magnetic field strength can adjust the anisotropy ratio of AGrPE and the effect of lateral deformation (along 90°) on the sample resistance, which is useful to avoid interference caused by lateral strain (along 90°) when the sensor is working. When cured in a magnetic field of 500 mT, AGrPE exhibits nearly constant resistance along the 90° direction (<3.5% variation within 17% strain). Even with 5% compression along 90°, the change in conductivity along 0° is less than 5%. As a comparison, when AGrPE is compressed by 5% along 0°, its conductivity increases 2000 times, showing a change that is 4 orders of magnitude higher. This insensitivity to lateral deformation is important for AGrPE sensors as it avoids signal interference caused by working on curved surfaces or being stretched.

[0154] To demonstrate the improvement of microstructures on AGrPE's pressure sensing performance, we compare its conductivity-pressure curves with that of a non-porous anisotropic graphene hybrid filler elastomer (AGrHE, see Methods section for preparation method) without adding porogen. As shown in Fig. 13, AGrPE exhibits a sensitivity of 0.382 kPa1along 0°, 13.6 times that of AGrHE. This is because the porous structure of AGrPE significantly reduces its elastic modulus, enhancing deformation under pressure, especially at low pressures. The greater deformation of the conductive particle network in AGrPE results in a sharp rise in conductivity, indicative of heightened sensitivity.

[0155] In more detail, Fig. 21 compares the elastic modulus of AGrPE and AGrHE along 0° and 90°, as well as the modulus for isotropic porous (GrPE) and nonporous (GrHE) composites. It can be seen that the porous structure significantly reduces the elastic modulus of the composites along 0° by 68% (17.5 MPa for AGrHE to 5.62 MPa for AGrPE). As a result, the deformation of AGrPE is > 3 times that of AGrHE under the same pressure. More importantly, in non-porous AGrHE, a large amount of stress and deformation during compression are shared by the PDMS matrix; while in porous AGrPE, the porous structure between Ni particle chains cannot share the pressure, causing almost all stress to be concentrated on the Ni particle chains. These result in more pronounced filler network deformation and conductive particles contact, resulting in significant conductivity changes and extremely high sensitivity.

[0156] Note that isotropic porous or nonporous composites with identical filler content but not cured in a magnetic field are insulators.

[0157] In addition, AGrPE also exhibits more significant stiffness anisotropy (anisotropic ratio of 5.4). This is because most of the deformation during compression along 90° is achieved through the deformation of 0- stiffness micropores, which greatly reduces the elastic modulus along 90° (1.05 MPa).

[0158] Contrary to the sensitivity enhancement along 0°, AGrPE exhibits a sensitivity of only 0.0012 kPa1along 90°, less than 10% of that of non-porous AGrHE (as shown in Fig. 22). In more detail, Fig. 22 compares the conductivity-pressure curves of AGrPE and AGrHE along 90°. Along 0°, AGrPE has a pressure sensitivity more than ten times higher than that of AGrHE (Figs. 30A and B). However, along 90°, AGrPE shows a sensitivity of almost 0 (0.0012 kPa1), which is only 9% of that of AGrHE (0.013 kPa1). The sensitivity of AGrPE along 0° is 320 times higher than that along 90°, which significantly reduces the interference of lateral deformation (along 90°) on the AGrPE sensor, as explained above regarding the influence of the curing magnetic field strength. The conductive network changes in AGrPE under deformation, illustrated in Fig. 14, explain this opposite effect. In AGrPE, graphene nanosheets and LM droplets are filled within and between Ni particle chains as pivotal components of the conductive network. They bridge Ni particles to form conductive paths and enhance conductivity, as shown in Figs. 23A to C. Along 0°, abundant conductive paths bring high conductivity. Upon compression, the proximity of Ni particles significantly reduces the particle contact resistance and enhances conductive paths, resulting in high pressure sensitivity. In contrast, along 90°, the serpentine conductive path is composed of transverse Ni particle chains and the graphene / LM between them (as shown in Fig. 14). Fig. 14 also shows that there are fewer conductive paths along 90° than there are along 0°. When compressed, the micropores between Ni particle chains absorbs most of the deformation. The contact resistance of particles remains essentially unchanged, ensuring stable conductivity of AGrPE when compressed along 90°.

[0159] Finite element simulations validated our hypothesis, demonstrating the much lower elastic modulus (Fig. 15) and resistance (Fig. 16) of the porous composite under pressure (see the Methods section for simulation settings). The simulated elastic modulus of AGrPE and AGrHE aligns with experimental results with an error of < 6% (Fig. 25). The simulated elastic modulus shown in Fig. 25 is calculated based on the simulated stress distribution and model deformation. Current density simulations visually depict the conductive paths in AGrPE, with high current density in graphene and LM confirming their role in bridging Ni particles (as shown in Fig. 17). Fig. 26 provides a clearer visualisation of current flow in graphene nanosheets. Due to the extremely high aspect ratio of graphene nanosheets, they are very thin and difficult to see in the 2D finite element model. Therefore, we enlarged the current density simulation images of AGrPE and AGrHE, and changed the colour bar value range of the current density (from 10-1000 Am2, to 100-100000 Am2) to highlight the high current density flowing through graphene nanosheets. Simulated conductivity-pressure curves, as shown in Fig. 18, further validate the experimental fundings, showcasing AGrPE's sensitivity an-order-of-magnitude higher than AGrHE.

[0160] AGrPE Pyramid Sensor Unit- Incorporation of the Composite Material into a Tactile Sensing Device

[0161] By further establishing a pyramidal macrostructure that mimics human epidermis on the composite surface and depositing patterned electrodes, we create a 3D force sensor array with extremely high linear sensitivity and a wide detection range. Integrated into a robotic gripper, it demonstrates high-precision real-time sensing in force magnitude and direction, slippage, and roughness, showing promising application prospects in prosthetics and industrial manipulation.

[0162] In more detail, to further improve pressure sensitivity and enable normal-shear force decoupling capability in the micro-structured AGrPE, we incorporate human skin-like surface structures on it. In human skin, the wavy epidermis structure concentrates pressure on baroreceptive cells for heightened sensitivity (Ref 49). As shown in Fig. 27, in human finger skin, the rete pegs of the papillary layer on the uppermost dermis extend into the epidermis, forming a wavy interface. Under pressure, the pressure is concentrated on baroreceptive cells at the bottom of the wave structure, resulting in high pressure sensitivity of the skin (Ref S2). The macrostructures of AGrPE sensor are designed by imitating this natural structure. Drawing inspiration from this natural structure, we designed a pyramid-shaped AGrPE sensor unit. The pyramid structure demonstrates substantial deformation and resistance changes under tiny pressure, as illustrated in the numerical simulation (Fig. 28) and the pressure-strain curve shown in Figs. 35A and B.

[0163] At the beginning of compression, the sensor is only stressed at the tip with obvious stress concentration, which can produce large deformation and resistance changes under small pressure, as illustrated in the numerical simulation (Fig. 28) and the pressure-strain curve (Figs. 35A and B). As the pressure increases, the contact area between the sensor tip and the contact surface increases significantly, resulting in a gradual increase in the equivalent compression modulus (Fig. 35B).

[0164] While an AGrPE cubic block sample requires 80 kPa to produce a 1 .4% compression, the pyramid sensor unit achieves the same deformation and resistance change under only 1 .0 kPa, exhibiting an initial sensitivity enhancement of 80 times. With further compression, the tip of sensor unit gradually flattens, resulting in increased modulus and a rapid rise in pressure. This provides the AGrPE sensor with a broad pressure sensing range, overcoming a main limitation of narrow operating ranges of previous high- sensitivity pressure sensors.

[0165] More importantly, the nonlinear conductivity-strain curve of the sensor unit can synergise with its nonlinear conductivity-strain curve to yield a perfectly linear conductivity-pressure response, as shown in Figs. 30A and B. Below 175 kPa, the sensor unit exhibits a high sensitivity of 93.0 kPa1and an extraordinarily linear response (R2=0.9991). As pressure exceeds 200 kPa, sensitivity further increases to 122.7 kPa1, maintaining commendable linearity (R2=0.9983). Such exceptional linear pressure sensitivity and a response range up to 500 kPa surpass state-of-the-art flexible pressure sensors. As shown in Fig. 36, compared with existing flexible pressure sensors, AGrPE demonstrates not only the highest pressure sensitivity (122.7 kPa1) but also the largest pressure sensing coefficient (PSC, the product of pressure sensitivity and linear sensing range). The PSC of most flexible pressure sensors is around 10, with a few reaching 1 ,000. Combined with both high sensitivity and wide working range, AGrPE exhibits an astonishing PSC of > 60,000, far exceeding state-of-the-art alternatives.

[0166] In addition to sensitivity enhancement, the pyramid structure plays an important role in decoupling normal and shear forces. When an oblique force acts on the sensor unit's tip, asymmetric stress distribution occurs due to shear force, as shown by the simulated stress distribution of the longitudinal section in Fig. 29. The average and difference of the pressures at two symmetrical points at the bottom of the sensor will be proportional to normal and shear forces, respectively. Figs. 31 A and B show the pressure distribution at the bottom of sensor unit under a normal or shear force of 0.1 N respectively.

[0167] Since the four electrodes on the bottom of the sensor unit are symmetrical about the centre and distributed on the diagonal line (x = ±y), we plot the pressure distribution on the x = y line on the sensor bottom under the normal and shear forces based on the simulation results to select the appropriate electrode positions. At x = ±0.5 mm, both normal force and shear force can produce large pressure. The pressure generated by shear force at these points is close to the peak and relatively stable. According to the curves shown in Figs. 37A and B, a normal force of 0.1 N can produce an equal pressure of 15.87 kPa at these two points; while a shear force of 0.1 N (along the x-axis) can produce a pressure of ±16.69 kPa at x = ±0.5 mm. Therefore, we select the centre coordinates of the four bottom electrodes at (x, y) = (±0.5 mm, ±0.5 mm) to evaporate gold electrodes for pressure measurement (as shown in Figs. 38A and B). The force effects are linearly superimposable, enabling the calculation of normal and shear forces from the pressures on four electrodes (see details in next Section).

[0168] Building upon the AGrPE sensor unit, Fig. 39 shows a pressure measurement circuit based on an AGrPE sensor unit controlled by an Arduino UNO. First, the high potential (5V) of the Arduino is connected to the four bottom electrodes of the sensor through a 16-way Decoder. The output potentials of different channels of the Decoder are switched by the Arduino program to traverse the four electrodes (frequency of 100 Hz). A diode is connected in series between the Decoder and each bottom electrode to prevent the remaining three electrodes from interfering with the measurement. The top electrode of the sensor unit is connected in series with a fixed resistor and then connected to ground. The divided voltage on the fixed resistor is read by Arduino through a 16-bit analog-to-digital converter (16-bit ADC) as the output signal of the AGrPE sensor. The sensor unit is connected in series with a fixed resistor. As pressure increases, the sensor resistance decreases, causing the potentials of four bottom electrodes to rise. A 16-bit analog-to- digital converter is incorporated in the circuit to improve voltage reading accuracy by 64 times. Without the 16-bit ADC, the reading resolution of Arduino UNO is only 10 bit. In this case, the voltage resolution of the circuit is 4.88 mV, corresponding to a poor pressure resolution of 0.09 kPa. As shown in Figs. 40A and B, after using the 16-bit ADC, the theoretical voltage resolution of the measurement circuit is increased 64 times to 0.0763 mV, with an actual pressure resolution of < 0.01 kPa. Figs. 32 and 33 show relative potential change-pressure curves recorded on four bottom electrodes of sensor unit under pressures of 0-1.3 kPa and 0-55 kPa, respectively.

[0169] The resistance of the fixed resistor will significantly affect the sensitivity and detection range of the AGrPE sensor. For a sensor with an initial resistance of about 1 MQ, using a fixed resistor of 100 Q results in an initial voltage signal of ~0.5 mV, as shown in Fig. 41 A. The output voltage can rise linearly within a wide pressure range with a high sensitivity, as shown in Fig. 41 B. When using a fixed resistor of 5 kQ, the initial voltage signal of the sensor increases to 25 mV, and the output voltage rises rapidly as the pressure increases and tends to saturation after exceeding 2 V (Fig. 41 A), resulting in nonlinear response and low sensitivity (Fig. 41 B), as shown in Fig. 41 .

[0170] With the resistance of fixed resistor set to 0.01 % of that of AGrPE sensor, a low initial voltage signal of approximately 0.5 mV provides the sensor with not only a linear voltage-pressure response but also a wide sensing range. Referring to Equation (1), we define the pressure sensitivity of the sensor as Equation (3):

[0171] Where Ui is the potential of the electrode numbered i.

[0172] As pressure increases, the sensitivity of the sensor increases from 72.3 kPa-1(0-1 kPa) to 110.3 kPa-1(>3 kPa) with high linearity (R2=0.997). Due to the same pressure on the four electrodes in the absence of tangential force, their relative potential curves almost overlap (deviation <1.5% at 5055 kPa, see the inset of Fig. 33), showing high precision. Additionally, the sensor exhibits exceptional stability under cyclic loading. Fig. 34 shows the potential-time curve of electrode 1 under a cyclic load of 1 .6 kPa for 1000 cycles. Although the maximum voltage in each cycle decreases by 9.1% in the first 20 cycles due to increased sensor resistance, it stabilises after 400 cycles. Notably, the relative potential change in each cycle remains constant. Owing to the self-calibration function of the sensor system, it can record the voltage at 0 kPa as the initial potential before measurement. There is almost no change in the relative potential-pressure curve and sensitivity of the sensor before and after 1000 cycles, reflecting its stable sensing performance.

[0173] In more detail, as illustrated in Fig. 42A and B, after cyclic load testing at 1.6 kPa for 1000 cycles, the output voltage signal of the sensor decreases due to the increase in initial resistance. However, the ratio of its output potential at 1 .6 kPa to that at 0 kPa remains basically unchanged. The program's selfcalibration feature allows recording the output voltage at 0 kPa as the initial potential before measurement. Therefore, the relative potential-pressure curve of the sensor during 1000 cycles is almost unchanged with a stable sensitivity of ~69 kPa1, reflecting a stable sensing performance.

[0174] 3D Force Sensing of Tactile Sensing Device

[0175] Benefiting from the force decoupling capability of the AGrPE pyramid sensor unit, it achieves high- precision spatial force direction identification, sliding detection, and roughness identification on the contact surface. We employ the spherical coordinate system to define the force F (unit: N) applied to the tip of sensor unit (Fig. 44). The angle between the force and the z-axis is denoted as <p, and the angle between the horizontal component (shear force) Fs and the x-axis is 0. According to the bottom pressure distribution under normal and shear force in Figs. 37A and B, the average pressures on the four electrodes Pi are shown in Equation (4):

[0176] P^fcPa) = 158.7 ■ F ■ cos(<p) + 166.9 ■ F ■ sin(<p) [cos(0) + sin(0)] (i = 1,2, 3, 4) (4)

[0177] For Pi to P4, the values of the two positive / negative signs are (+,+), (+,-), (-,-), and (-,+) respectively.

[0178] According to the bottom electrode setup as discussed above (as displayed in Figs. 37A and B), with the centre coordinates of the four bottom electrodes at (x,y) = (±0.5 mm, ±0.5 mm), the pressure on the four bottom electrodes in Fig. 44 is equal to 158.7 kPa under a normal force of 1 N. Under a tangential force of 1 N applied along the x-axis, the pressure on electrodes 1 and 2 (Pi and P2) is 166.9 kPa, and the pressure on electrodes 3 and 4 (P3 and P4) is -166.9 kPa. An analogy can be made for the case of shear force applied along the y-axis. Under small force, AGrPE can be regarded as a linear elastic material, and the bottom surface pressure distribution under different forces can be superimposed. Based on this, we can get the average pressure Pi to P4 on the four bottom electrodes under the force in Fig. 44 (the unit of force F is N).

[0179] As the electrode potential is proportional to the pressure on electrodes, Fig. 45 plots the relative potential of each bottom electrode under different force directions but constant force magnitude according to Equation (4), where 0 ranges from 0 to 90° (shear force in the first quadrant). Note that the data of electrode 2 is omitted for clarity as its potential is symmetrical to that on electrode 3 with respect to 0 = 45°, as shown in Fig. 43. Assuming the electric potential at p = 0° (no shear force) as the initial potential, with the rise in shear force, Ui (the potential on electrode 1) increases due to the increased pressure Pi. At <p = 35°, 9 = 45°, U4 almost drops to 0, indicating that the resultant pressure of normal and shear forces acting on electrode 4 is 0. Fig. 46 compares the simulated and experimental relative potential changes of four electrodes as <p increases (force gradually tilts with constant force magnitude) when 9 = 20° (constant shear force direction). As the force tilts, the error in measured potentials increases (larger error bars) but remains generally consistent with the simulation results (deviation < 5.3%).

[0180] Since the electrode potential can be calculated from force direction through Equation (4), conversely, the direction and magnitude of the force can also be determined based on measured potentials Ui as set out in Equations (5) to (8): where Vi is the relative potential changes of bottom electrodes, and SF is the force sensitivity of sensor unit under normal force, calculated from Fig. 33. It is evident that the force direction is solely related to the relative magnitude of the four electrode potentials.

[0181] Using the device depicted in Fig. 47, forces of various directions are applied to the sensor unit. In more detail, Fig. 47 shows the schematic diagram of the oblique force testing device of the AGrPE sensor unit. The sensor unit is mounted on a 3D printed tilted platform and compressed by the tensile tester. The potential-time curves on four bottom electrodes (recorded by Arduino UNO) and force / displacement-time curves (recorded by the tensile tester) are recorded during the test. The angle between the platform slope and the horizontal plane is the angle <p between the force F and the z-axis in Fig. 44, while the angle between the sensor unit and the edge of the platform is the angle 9 between the shear force Fs and the x- axis. Therefore, this experimental device can conveniently adjust <p and 9 to test the force response curve of the sensor unit.

[0182] Fig. 48 gives the relative potential change vs force curves of four electrodes at p = 18°, 9 = 40°. The curves reveal consistent proportions among potentials as the force increases, indicating no impact of force magnitude on force direction measurement. Fig. 49 compares the applied force and force calculated from Fig. 48, showing a maximum deviation of only 3.1 %. The force angles <p and 9 calculated from electrode potentials at different forces also show high precision and accuracy, with short error bars and <2.7% deviation from set angles (Fig. 50). Furthermore, forces with time-varying magnitudes and directions are applied on the sensor unit to demonstrate its accurate real-time 3D force sensing capability, as shown in Figs. 57 to 59. The force on the sensor can be divided into normal force (FN) along the z axis and shear forces along the x-axis (Fsx) and y-axis (Fsy) (Fig. 57). We continuously applied three forces with different magnitudes and directions on the sensor unit to demonstrate its real-time 3D force sensing capability. The three forces are the normal force, the oblique force to the right and the oblique force to the left, as shown in Fig. 58. It can be seen from Fig. 59A that the signals Ui to LU of the four bottom electrodes of the sensor basically overlap under normal force, but there are differences under oblique force. The three component forcetime curves calculated in real time based on the electrode potential-time curves are shown in Fig. 59B.

[0183] In addition, the sensor unit can detect sliding with the contact surface and identify surface roughness. This is because the static friction coefficient of most materials surpasses their kinetic friction coefficient (50). When sliding occurs, the shear force on sensor unit instantaneously decreases while the normal force remains relatively stable, leading to a sudden change in electrode potentials. During sliding, the sensor tip induces frictional vibrations on the rough surface, causing electrical potential fluctuations positively related to surface roughness. Taking the sensor unit sliding on 120-grit sandpaper as an example (see the Method section below for experimental details), assuming electrode 1 bears the maximum pressure (Fig. 51 A), its potential Ui drops sharply by 10.7% at the onset of sliding, followed by a potential fluctuation of -4.3% during subsequent sliding (Fig. 51 B). Note that the electrode potential on the side along sliding direction will increase when sliding occurs, avoiding misjudgements of sliding caused by a sudden decrease in overall force.

[0184] In more detail, when the sensor unit slides to the right on the contact surface (Fig. 60A), the pressure on the left electrode (P1) will momentarily decrease while the pressure on the right electrode (P2) will increase simultaneously due to the sudden drop in friction. This causes potential jumps in opposite directions but similar amplitudes on the left and right electrodes (Fig. 60B). This can avoid the misjudgement of sliding caused by a sudden reduction in normal force.

[0185] Fig. 52 shows the instantaneous changes and subsequent fluctuations amplitude of Ui when the sensor unit slides on various materials with increasing roughness. The instantaneous change amplitude of Ui correlates positively with the difference between the static and kinetic friction coefficients of the material. The subsequent fluctuations depend on the roughness of the contact surface. As the roughness increases from nearly 0 (smooth glass) to 126 pm (grooves structure), the voltage fluctuation increases from -1% to 6.5%, with a linearity R2of 0.96. In more detail, Fig. 61 shows voltage fluctuations of the AGrPE sensor when sliding on 10 substrates with different surface roughness. The linear correlation R2between voltage fluctuation and surface roughness is 0.96. The 10 substrates and their roughness are: Glass (0.007 pm), Plastic (0.17 pm), Steel (0.33 pm), A4 paper (9.1 pm), Cardboard (24.7 pm), Tissue (37.8 pm), Sandpaper (60.7 pm), 3D-printed grooves 0.1 mm (93.3 pm), Fabric (106.7 pm), 3D-printed grooves 0.15 mm (126 pm). Surface roughness is measured by a Bruker Dektak XT Stylus Profilometer. Hence, this sensor proves effective in identifying surface roughness and even material type. Demonstration ofAGrPE

[0186] We prepared and assembled the AGrPE sensor array onto a robotic arm gripper to demonstrate its high pressure sensitivity, real-time 3D force sensing and sliding detection capabilities. The AGrPE sensor array shown in Fig. 53 comprises of 4 sensor units, which is sufficient for object clamping and demonstrates the scalability of the sensor array. The sensor array features a top layer of evaporated gold electrode and 16 bottom electrodes (4 per unit). It is soldered on a designed PCB, so that the bottom electrodes of the sensor array are in register with the electrode array on the PCB. The PCB has a low melting point alloy and is encapsulated with an Ecoflex layer on top to safeguard the electrodes (see the Methods section for details). The sensor array with PCB is mounted on the robot arm gripper / manipulator. The voltage signals of the sensor array read by Arduino control the movement of the manipulator in real time. The sensor voltage signal interfaces with the Arduino control board of the robotic arm for real-time feedback control.

[0187] Fig. 62 shows the real-time control circuit of the robotic arm equipped with AGrPE sensor array controlled by an Arduino board. First, the high potential (5V) of the Arduino is connected to the 16 bottom electrodes (4 sensing units) of the sensor array through a 16-way Decoder. The output potentials of different channels of the Decoder are switched by the Arduino program, traversing 16 electrodes (frequency of 250 Hz). A diode is connected in series between the decoder and each bottom electrode to prevent the remaining electrodes from interfering with the measurement. The top electrode of the sensor array is connected in series with a fixed resistor and then connected to ground. The divided voltage on the fixed resistor is read by Arduino through a 16-bit ADC as control signals for the robotic arm. Arduino calculates force magnitude and direction in real time through pre-written programs, and controls the movement of 5 pre-programmed servos according to set trigger conditions, such as reaching the pressure threshold and the occurrence of sliding.

[0188] The robotic arm executes pre-programmed movements guided by sensor inputs to pick up objects and transfer them to another platform. In an A4 paper tube gripping demonstration (Fig. 54A), the sensor array exhibits high force sensitivity and low detection limit. Upon grasping and contacting the paper tube, the sensor swiftly detects a force of only 11 mN to avoid tube deformation and control the robotic arm to execute the lifting procedure (ti in Fig. 54B). Moreover, the sensor array even accurately measures the weight of the paper tube (0.74 g) through the sensed tangential force of 7.3 mN (t2 in Fig. 54B). In comparison, a commercial force sensor with a high detection limit of 180 mN causes serious paper tube deformation during clamping (see the voltage signal-time curve in Fig. 63). Fig. 63 shows the voltage signal-time curves of two representative electrodes of the AGrPE sensor array during the process of the robotic arm clamping an A4 paper tube. The inset shows the location of two selected electrodes. The ti and t2 correspond to ti and t2 in Fig. 54B.

[0189] The robotic arm further demonstrates the 3D force sensing and sliding detection abilities of the sensor array by transferring a steel block (Fig. 55A). Fig. 64 provides voltage signal-time curves and changes in force direction during the transfer of the steel block. The inset shows the location of two selected electrodes. The ti to t4 correspond to ti to t4 in Fig. 55B. When the steel block is clamped, the sensor promptly recognises the object contact (1 .9 s in Fig. 55B). During attempts to lift the steel block, the sensor detects increased shear force caused by gravity. When the steel block slips due to insufficient friction, the sensor instantly recognises the sliding state through a sudden ~5% drop in shear force (ti in Fig. 55B), subsequently tightening the gripper to clamp the steel block. The angle <p between the force and the normal direction at ti , which is the friction angle between the sensor and the steel block, is approximately 32° (Fig. 56). At t2, the steel block is lifted with a shear force (0.38 N) equal to its gravity, and a force direction <p of 18.7°. When placing the steel block down, the sensor identifies ground contact through the reduction of tangential force and <p (t3 in Figs. 55B, 56), triggering the gripper to release the steel block (t4 in Fig. 55B). In comparison, a robotic arm equipped with a commercial force sensor failed to detect the sliding of the steel block or its contact with the ground.

[0190] The demand for miniaturised 3D force sensing technologies is growing, particularly for developing micro haptic devices and achieving tactile spatial resolution comparable to human skin. To demonstrate the miniaturisation potential of the AGrPE sensor, we prepared a microsensor array consisting of 200 pm sensor units (see Fig. 65, Fig. 68 and the Methods section below for more details).

[0191] The AGrPE microsensor array film has pyramid sensor units with a side length of 200 pm and a space of 100 pm, exhibiting a spatial resolution of 300 pm. The pyramid sensor is 140 pm high and the bottom layer of the microsensor film is 100 pm thick. Because the Ni particles are aligned along the magnetic field direction perpendicular to the film surface, the film is translucent along this direction (Fig. 68). This also facilitates the alignment of the microsensor film and the patterned electrodes on the glass wafer. After aligning the microsensor array and the bottom patterned electrodes, a 100 nm gold layer was deposited on top of the microsensor array film as the top electrode. After compression of 25% strain (corresponding to a normal force of about 11 mN), the gold electrode on the surface of the microsensor unit wrinkled but did not break (Fig. 68). There are cracks in the gold layer at the tip of the micro-pyramid unit, but it does not affect the operation of the sensor.

[0192] We applied a normal force load on the microsensor unit and measured the output potentials of its four bottom electrodes. Fig. 69A gives the average potential versus normal force curve, showing a high force sensitivity of 670 mN1. To measure the detection limit of the microsensor unit, we prepared 0.8x0.8x0.6 mm PDMS blocks as weights. The PDMS weight is stably placed on the four micro-sensor units, and each sensor unit is subject to a normal force of 0.9 pN when one weight is placed. We recorded the change in the average potential of the sensor bottom electrodes when weights were gradually added to the microsensor array, as shown in Fig. 69B. It can be seen that the sensor can accurately detect a single PDMS weight, showing an extremely low detection limit of 0.9 pN.

[0193] To demonstrate the 3D force sensing abilities of the microsensor array, we placed gold and indium balls with diameters from 0.6 to 2.8 mm sequentially on it. The forces on the four sensor units in contact with the metal balls are detected through photolithographic patterned electrodes on glass wafer, as shown in Fig. 66 and Fig. 70.

[0194] We used a laser writer and electron beam evaporator to create patterned gold electrodes on a glass wafer (Fig. 70). The electrodes distribution is as shown in Fig. 38. Gold and indium balls were then placed on the microsensor film to demonstrate its 3D force detection capabilities. Gold balls were made by melting then solidifying gold particles on the evaporation boat in a thermal evaporator (Fig. 70). Fig. 70 also shows photos of the experimental setup. The microsensor array film is aligned and bonded with the patterned electrodes on the glass wafer under a microscope after plasma treatment. A 3D printed bracket is used to hold the spring pin connectors to connect the microsensor array with the Arduino UNO board. The Arduino UNO board calculates the force and direction on the four sensor units in contact with the metal ball in real time.

[0195] Figs. 67 and 71 show the measured forces and directions generated by gold and indium balls of different diameters, respectively (see the raw relative potential data in Figs. 71 to 73). The mass and diameter of metal balls can therefore be calculated to distinguish their material types through density (as explained below and in reference to Fig. 74).

[0196] When placed on the microsensor array film, the metal balls come into contact with the vertices of the four microsensor units, generating tilting forces. Due to the symmetrical distribution of microsensor units, the theoretical normal force on a single sensor unit is one-quarter of the weight of the metal ball. The direction of the shear force remains unchanged but its value depends on the diameter of the metal ball. Taking the sensor unit in the first quadrant marked in Fig. 74 as an example, its shear force direction 0 is 45° (see the measured shear force direction in Fig. 71). Assuming that the force on the sensor unit is perpendicular to the surface of the metal ball, the angle (p between the force and the z-axis satisfies:

[0197] Z / ? 424.3

[0198] Where D is the diameter of the metal ball, and I is the horizontal distance between the vertices of the two diagonally opposite sensor units. Since the distance between adjacent sensor vertices is 300 pm, I is around 424.3 pm.

[0199] Considering the friction force, the actual force direction (p will be smaller, but it still basically satisfies that the sine of (p is inversely proportional to the diameter of the metal ball, as proven in Fig. 67B. Therefore, the microsensor array can calculate the mass and diameter of the metal ball through the measured normal force and force direction respectively, and further identify the metal type through the calculated density.

[0200] Additionally, by analysing the force direction distribution, the sensor array can also distinguish the geometry of weights on it, such as spheres, plates and cylinders. Such a small size allows the sensor to be used in limited spaces such as micromanipulators or microrobots.

[0201] These experiments demonstrate the low detection limit, high sensitivity, and 3D force sensing capabilities of the AGrPE sensor array. Furthermore, when using a PDMS-based flexible PCB, the sensor array can operate on curved surfaces and withstand lateral stretching. As discussed above (regarding Figs. 20A to D), the anisotropic porous structure of AGrPE endows the sensor with extremely low sensitivity to lateral deformation, ensuring its stable response when working on curved surfaces. Further work -

[0202] The present inventors have further investigated the enhancing effect of graphene on the flexibility and long-term stability, as well as on the conductivity and sensitivity of composites according to embodiments of the present invention. For composite materials without graphene, a Ni / PDMS mass ratio of 1 .6 is used to achieve suitable sensitivity of the composite.

[0203] The embodiments described above are based on a composite material composition which includes a PDMS matrix and a hybrid filler composed of liquid metal, nickel microparticles, and graphene nanosheets. When this is modified so that graphene is not included, but the Ni content is increased as mentioned above, the performance of the composite material changes. The elastic module decreases by 45.1% (from about 10 MPa to about 5.5 MPa). Furthermore, the long-term reliability of the composite decreases significantly, by 83.3%. This is assessed in terms of the AU / Uo deviation over 10K cycles.

[0204] Without graphene, the initial conductivity is about 4 x 106Snr1, and the sensitivity is about 0.1 kPa1. With graphene, the initial conductivity is about 340 times higher, at about 103Snr1, and the sensitivity is about 270% higher, at 0.4 kPa1.

[0205] Accordingly, although composite materials without graphene exhibit a significant decrease in conductivity and can even lead to sample insulation, it is still possible to achieve significantly reduced but still usable conductivity and sensitivity in the absence of graphene by increasing the content of nickel particles in the material. For composite materials without graphene, a Ni / PDMS mass ratio of 1 .6 was needed to balance electrical conductivity and elastic modulus and achieve suitable sensitivity of the composite. As a cost, this damages the long-term stability and pressure sensitivity of the composites.

[0206] It can therefore be seen that the use of graphene in the composite significantly reduces the need for Ni in composites and enhances their overall sensing performance.

[0207] Further work - sensor configuration

[0208] In the work described above, the sensors use a square pyramidal configuration. A side length of 4mm is used. Such a square-pyramid sensor employs a four-electrode base configuration to detect pressure distribution, where the averaged pressure correlates with normal force and the pressure gradient reflects the magnitude and direction of tangential force.

[0209] The inventors have contemplated different configurations.

[0210] Although triangular pyramids could theoretically achieve force decoupling with three electrodes, their inherent error sensitivity severely limits practical reliability. This limitation arises because single-point measurement errors in triangular configurations propagate linearly into force calculations, introducing substantial deviations. By contrast, our four-electrode square-pyramid design leverages statistical oversampling, reducing random error variance by 25% (o2 / 4 vs. o2 / 3 for triangular systems) through redundancy-weighted averaging. Furthermore, the symmetrical four-electrode arrangement allows residual-based outlier detection, which is absent in three-electrode systems with insufficient degrees of freedom. Other shapes can be used. For example, pentagonal or hexagonal pyramids with additional electrodes could marginally enhance stability. However, their nonlinear benefit scaling renders them impractical. Specifically, using complex geometric shapes and increasing electrode count compromises manufacturing feasibility and amplifies computational complexity in solving high-dimensional forcedecoupling equations. We therefore adopt the square-pyramid configuration as the suitable compromise, achieving robust force discrimination with minimal electrodes while maintaining fabrication and operational simplicity.

[0211] Conclusions

[0212] This work creates a three-dimensional force sensor array founded on a graphene-LM anisotropic porous composite. The bionic surface pyramid array structure on the sensor achieves decoupling of normal and shear forces, enabling precise real-time measurement of feree magnitude and direction, alongside detection of sliding and roughness. Following development through experimental and simulation approaches, the sensor exhibits a few detection limit of ~1 mN, exceptional sensitivity of 110 kPa1, a wide linear response range of 500 kPa, and a force direction measurement deviation of < 1.1 °, far outperforming the state-of-the-arts. Applied to a robotic hand, this sensor array enables intelligent grasping of unknown objects with dynamic force adjustment through real-time 3D force and sliding detection. Our work bridges human multi-dimensional tactile sensations into force sensors, offering a pragmatic solution for precise tactile perception and dexterous grasping in prosthetics, industrial grippers, and soft robotics.

[0213] Methods

[0214] The graphene nanoplatelets (25 pm particle) and 1 ,2-propanediol (98+% purity) were purchased from Sigma-Aldrich, UK. The EGain (75 wt% gallium, 25 wt% indium) and Field's metal alloy (51 wt% indium, 32.5 wt% bismuth, 16.5 wt% tin) were purchased from Magnametals, UK. The spiked nickel microparticles (2 - 5 pm in diameter) were purchased from APC Pure, UK. The SYLGARD 184 Silicone Elastomer (PDMS) Curing Agent and SYLGARD 184 Silicone Elastomer (PDMS) Base were purchased from Univar Specialty Consumables, UK. The Ecoflex 00-30 silicone rubber was purchased from 4.2 Bentley Advanced Materials, UK.

[0215] To prepare the AGrPE, we first put the Ni particles (2.8 g), EGain (1 .2 g), and liquid PDMS (1 .2 g, PDMS base / curing agent mass ratio of 9:1) in a plastic cup with a mass ratio of Ni:EGaln:PDMS of 1 .4:0.6:0.6. Then mixed them using a flat plastic stick (cross section of 2 x 5 mm) equipped on an electric stirrer at 350 rpm for 5 minutes. We then mixed 0.08 g graphene nanosheets with 0.8 g PDMS (mass ratio of 0.04:0.4) using the electric stirrer at 120 rpm for 5 minutes. The two mixtures were then mixed with 1 .2 g 1 ,2-propanediol at 120 rpm for 5 minutes. Next, the obtained mixture (Ni / EGaln / graphene / 1 ,2- propanediol / PDMS mass ratio of 1 .4 / 0.6 / 0.04 / 0.6 / 1) was poured into a 3D printed plastic mould (material: thermoplastic polyurethane, TPU 95A) and solidified in a 500 mT uniform magnetic field at 80 °C for 12 hours. Finally, the cured AGrPE samples were removed from the mould and heated in an oven at 140 °C for 3 hours to remove the 1 ,2-propanediol. The final AGrPE sample has a porosity of 27.9% and a Ni / EGaln / graphene / PDMS volume ratio of 0.154 / 0.092 / 0.017 / 1.

[0216] The methods for preparing nonporous AGrHE and other isotropic porous or nonporous composites are based on those for AGrPE. For AGrHE, the only differences are the absence of 1 ,2-propanediol and the heating step after sample curing. As for isotropic composites, the only difference between them and AGrPE or AGrHE is that they were not solidify in a magnetic field.

[0217] In some embodiments, graphene was not included. In order to provide a suitable balance of electrical conductivity and elastic modulus, a Ni / PDMS mass ratio of 1 .6 was used.

[0218] To fabricate the 4 mm AGrPE sensor unit and array, we first printed a pyramid-shaped mould with an Ultimaker S5 3D printer using TPU 95A filament with a precision of 0.06 mm for curing the sensor. The 3D printed masks were then used to evaporate electrodes on the top and bottom of sensors using an electron-beam evaporator. A 5 nm chromium was firstly evaporated on the AGrPE surface, and then 15 nm gold was evaporated. The function of the chromium intermediate layer is to enhance the adhesion of the electrode to avoid peeling. Detailed electrode dimensions and distributions are provided in Figs. 38A and B. The gold-plated electrode on the top of the sensor array is then drop-cast with an Ecoflex layer to encapsulate and protect the electrode from wear. When mounted on the gripper of a robot manipulator, the sensor array is soldered on a self-designed PCB (printed circuit board) to ensure stable electrical contact. The electrodes on the PCB correspond to the bottom electrodes of the sensor array. The top electrode of the sensor array is also soldered to the PCB board through via holes. Field's metal with a melting point of 61 °C is used as solder to prevent high temperature damage to the sensor and electrodes.

[0219] To fabricate the AGrPE microsensor array with sensor unit side length of 200 pm, a silicon wafer with anisotropically etched pyramid pit array was used as the mould. We used AZ5214E photoresist to laser write a mask on a glass wafer and evaporate the electrode pattern (5 nm chromium and 100 nm gold) as the bottom electrode of the microsensor array, as shown in Fig. 70. The reason for using the glass wafer is to facilitate the alignment of electrode patterns and the microsensor array under the microscope. The microsensor array and the glass wafer are plasma treated and then bonded together to achieve stable electrical contact. After aligning the microsensor array and the bottom patterned electrodes, a 100nm gold layer was deposited on top as the top electrode. The assembled microsensor array is connected to the Arduino UNO board through spring pin connectors. The rest of the preparation process is the same as the 4 mm AGrPE sensor array.

[0220] An FEI Quanta 3D FEG Dual Beam Electron Microscope was used to obtain the SEM and corresponding EDS images of the composite in Figs. 3A to E and Figs. 5A to E, all other SEM images were taken using a secondary Magellan 400 SEM.

[0221] The COMSOL Multiphysics 5.2 software package (Burlington, MA, USA) was used for finite element numerical simulation. We used COMSOL finite element software to simulate the resistivity of the AGrPE and AGrHE 2D models (100 x 100 pm) during a compression process. The thickness of the model is set at 1 pm. The models are established based on the SEM images. The sizes of the Ni (2~5 pm), pores (3~8 pm), graphene nanosheets (25-50 pm), and LM (15-30 pm) particles are equal to those in the actual composites. We use an electrical-mechanical coupled multi-field to simulate the mechanical deformation and resistivity of the model. The material parameters of the fillers and PDMS matrix (mainly including the elastic modulus, Poisson's ratio, conductivity, and dielectric constant) are consistent with the COMSOL material library. In the simulation model, we omit the gallium oxide layer on the surface of the EGain droplet. This is because the thickness of this gallium oxide film is only 1-3 nm (Ref S1), which is much smaller than the diameter of LM droplets. Such a thin oxide layer does not affect the mechanical deformation of the LM droplets. Additionally, since the conductivity of both the LM droplet and the gallium oxide is much higher than that of the PDMS matrix, this extremely thin oxide layer also does not affect the simulation for the resistivity of the composite. The mechanical deformation and microstructure change of the model are simulated by applying a fixed displacement or pressure load to the upper side of the model. Fig. 24 shows the boundary conditions in the simulation of electrical conductivity. The left and right sides of the 2D model are electrically insulated, the lower side is grounded, and the current density through the upper side is fixed at 100 A. nr2. The resistivity of the model can be calculated based on the drop in electrical potential.

[0222] An Ultimaker S5 3D printer was used to print the plastic moulds for curing AGrPE samples and sensors, as well as masks for electrode evaporation, and plastic parts in testing device (Fig. 47). An Instron 68TM- 50 Universal Testing Machine was used to compress composite samples (5x5x5 mm) and sensors at a speed of 5%«mim1to measure their stress-strain curves. A Keithley 2400 Standard Series Source- Measurement Unit (SMU) with a resistance range of 1 GQ was used to measure the sample resistance. The final resistance is the measured resistance minus the internal resistance of the circuit with no sample present. An Electron-beam Evaporator (PVD 200 Pro, Kurt J. Lesker) was used to evaporate gold electrodes on the AGrPE samples and sensors. An Arduino Uno Rev 3 was used to control the sensor measurement circuit. An ADS1115 16-Bit analog-to-digital converter and another MCP3008 8-Channel analog-to-digital converter were also used in this circuit. A self-designed PCB board with an electrode array was used to fix the AGrPE sensor on it for measurement. The sensor is soldered on the PCB board at a low temperature of 80°C using the Field's metal (indium-bismuth-tin alloy, melting point 62°C) to avoid burning the AGrPE. To measure the sliding of the sensor unit on different substrates, the sensor unit was fixed on the PCB board under a pressure of 5 kPa that applied using the INSTRON Testing Machine. The substrate was clamped between the sensor tip and the jig of the Testing Machine and pulled by a screw guide at 2 mnrs~1. A Bruker Dektak XT Stylus Profilometer was used to measure the surface roughness of various substrates. An ALSA 4 Degrees of Freedom Robotic Arm controlled by BotBoarduino used for the demonstration of AGrPE sensor array was purchased from Robotshop Inc., Canada.

[0223] ***

[0224] The features disclosed in the foregoing description, or in the following claims, or in the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for obtaining the disclosed results, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof.

[0225] While the invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art when given this disclosure. Accordingly, the exemplary embodiments of the invention set forth above are considered to be illustrative and not limiting. Various changes to the described embodiments may be made without departing from the spirit and scope of the invention.

[0226] For the avoidance of any doubt, any theoretical explanations provided herein are provided for the purposes of improving the understanding of a reader. The inventors do not wish to be bound by any of these theoretical explanations.

[0227] Any section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.

[0228] Throughout this specification, including the claims which follow, unless the context requires otherwise, the word “comprise” and “include”, and variations such as “comprises”, “comprising”, and “including” will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

[0229] It must be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by the use of the antecedent “about,” it will be understood that the particular value forms another embodiment. The term “about” in relation to a numerical value is optional and means for example + / - 10%.

[0230] References

[0231] A number of publications are cited above in order to more fully describe and disclose the invention and the state of the art to which the invention pertains. Full citations for these references are provided below. The entirety of each of these references is incorporated herein.

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Claims

Claims:1 . A pressure sensing conductive elastomeric composite material, the material comprising: a polymer matrix, comprising an elastomeric material, and a conduction network within the polymer matrix, the conduction network comprising: a plurality of particle chains, each particle chain comprising a plurality of metallic ferromagnetic particles, a plurality of liquid metal droplets, and a plurality of non-ferromagnetic conductive platelets, wherein the conductivity of the composite material varies as a function of the pressure applied to the material.

2. The composite material according to claim 1 , wherein the composite material is porous.

3. A pressure sensing conductive elastomeric composite material, the material comprising: a polymer matrix, comprising an elastomeric material, and a conduction network within the polymer matrix, the conduction network comprising: a plurality of particle chains, each particle chain comprising a plurality of metallic ferromagnetic particles, a plurality of liquid metal droplets, optionally, a plurality of non-ferromagnetic conductive platelets, wherein the composite material is porous, and wherein the conductivity of the composite material varies as a function of the pressure applied to the material.

4. The composite material according to any one of claims 1 to 3, wherein each particle chain is arranged substantially along an alignment axis, the alignment axes of the plurality of particle chains being arranged so that the conductivity response of the composite material is anisotropic, dependent on the direction of the pressure applied to the composite material.

5. The composite material according to any one of claims 1 to 4, wherein the Young’s modulus of the material in at least one direction is between 1 MPa and 20 MPa.

6. The composite material according to any one of claims 1 to 5, wherein: the mass ratio of the plurality of metallic ferromagnetic particles in relation to the elastomeric material is in the range 1 : 1 to 2 : 1 , the mass ratio of the plurality of liquid metal droplets in relation to the elastomeric material is in the range 0.2 : 1 to 2 : 1 , the mass ratio of the plurality of non-ferromagnetic conductive platelets, when present, in relation to the elastomeric material is in the range 0.01 : 1 , to 0.2 : 1 , and the porosity of the composite material is in the range 10-60%.

7. The composite material according to any one of claims 1 to 6, wherein the metallic ferromagnetic particles are arranged in the particle chains to permit electrical conduction between the metallic ferromagnetic particles through a quantum tunnelling effect.

8. The composite material according to any one of claims 1 to 7, wherein the metallic ferromagnetic particles have an average particle size of 0.5 to 20 micrometres.

9. The composite material according to any one of claims 1 to 8, wherein the liquid metal droplets comprise a eutectic alloy of gallium and indium.

10. The composite material according to any one of claims 1 to 9, wherein the liquid metal droplets have an average particle size of 3-50 micrometres.

11. The composite material according to any one of claims 1 to 10, wherein the conductive platelets have an average maximum linear dimension of 10-200 micrometres.

12. The composite material according to any one of claims 1 to 11 , wherein the conductive platelets, when present, have an average thickness of 1 nanometre to 1 micrometre.

13. The composite material according to claim 2 or claim 3, or according to any of claims 4 to 12 as dependent on claim 2 or claim 3, wherein the average pore diameter is 1-20 micrometres.

14. A method of manufacturing the composite material of any of claims 1 to 13, the conductivity of the material being configured to vary as a function of pressure applied to the composite material, wherein the method comprises performing the steps of:(a) providing a mixture of a plurality of metallic ferromagnetic particles, a liquid metal, optionally a plurality of non-ferromagnetic conductive platelets and an elastomeric material precursor, and(b) curing the mixture in an applied magnetic field to form the composite material.

15. The method according to claim 14, wherein step (a) additionally comprises:(a-i) mixing a plurality of metallic ferromagnetic particles, a liquid metal, and a first amount of elastomeric material precursor to form a first mixture,(a-ii) mixing a plurality of non-ferromagnetic conductive platelets with a second amount of elastomeric material precursor to form a second mixture,(a-iii) mixing the first mixture of step (a-i) with the second mixture of step (a-ii) to form a third mixture, wherein the mixing of step (a-i) is performed at a higher rotational speed than the mixing of step (a-ii).

16. The method according to claim 14 or claim 15, wherein step (a) additionally comprises mixing a porogen, and wherein the method additionally comprises:(c) removing the porogen from the cured composite by evaporation of the porogen.

17. The method according to any of claims 14 to 16, wherein the mass ratio of the porogen in relation to the elastomeric material is in the range 0.1 : 1 to 2 : 1 .

18. A tactile sensing device comprising a sensor element formed of the composite material of any one of claims 1 to 13.

19. A tactile sensing device according to claim 18, wherein the sensor element has an arrangement of electrodes placed to enable determination of electrical conductivity through different volumetric regions of the sensor element.

20. A tactile sensing device according to claim 18 or claim 19 wherein the sensor element has a tapering shape with a basal region with greater cross sectional area than a force contact region.

21. A tactile sensing device according to claim 20 wherein the alignment axes of the chains are arranged substantially perpendicular to the basal region.

22. A tactile sensing device according to claim 20 or claim 21 , wherein the sensor element has a pyramidal shape, tetragonal shape, or conical shape.

23. A tactile sensing device according to any one of claims 20 to 22, wherein the arrangement of electrodes includes a plurality of basal region electrodes, permitting a differential conductivity response of the tactile sensing device to pressure including a shear component compared with uniaxial pressure.

24. A tactile sensing device according to any of claims 20 to 23, wherein the arrangement of electrodes includes at least one electrode at the force contact region.

25. A method of operating the tactile sensing device of any one of claims 18 to 24, the tactile sensing device comprising the composite material, the conductivity of the material varying as a function of the pressure applied to the composite material, wherein the method comprises: contacting the device with an object, the device sensing the object, through the pressure of the object on the device causing a change in the conductivity of the composite material, the device measures the change in conductivity of the composite material.

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