Computational design of capacitive stretch sensors

Abstract

The systems and methods herein relate to a sensor. The sensor includes a first conductive layer including a first conductive region. The first conductive layer is patterned to form the first conductive region having a first design based on a simulation including an elastic simulation and an electrostatic simulation. The sensor includes a second conductive layer including a second conductive region. The second conductive layer is patterned to form the second conductive region having a second design based on the simulation. The sensor includes a dielectric layer positioned between the first conductive layer and the second conductive layer. Deformation of the sensor changes a sensor modality between the first conductive region and the second conductive region based on the first design and the second design.

Description

Atty. Dkt. No.: 046434-0977COMPUTATIONAL DESIGN OF CAPACITIVE STRETCH SENSORS CROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims priority to U.S. Provisional Patent App. No.63 / 748,396 filed on January 22, 2025, the disclosure of which is incorporated herein by reference in its entirety for all purposes.STATEMENT OF GOVERNMENT INTEREST

[0002] This invention was made with government support under 2411349 and 2313156 awarded by the National Science Foundation. The government has certain rights in the invention.TECHNICAL FIELD

[0003] The present disclosure relates generally to computational method and system for sensors, specifically capacitive stretch sensors.BACKGROUND

[0004] Sensors are devices that measure physical quantities by converting them into interpretable signals. Sensor design requires understanding the physical principles underlying the quantity to be measured and creating a system that can reliably transduce that quantity into a usable output. Some challenges with sensor designs includes the need for calibration, a limited range and resolution, and a time needed to reach equilibrium. These are just a subset of properties that can be taken into account and optimized for when designing a sensor.

[0005] Stretch sensors are an alternative to vision-based motion capture systems. They can be fastened to the surface of a soft object and allow estimation of the object’s deformations as it stretches. This has an advantage in settings with frequent occlusions, such as object manipulation by a human hand. An example type of stretch sensor is composed of an elastic ribbon (textile or silicone) with an embedded electronic component whose resistance or capacitance changes when the ribbon is stretched. Capacitive sensors are based on the principal that the capacitance of a capacitor is determined by its geometry. A silicone capacitive sensor is a composite silicone sheets made of a stack of dielectric and conductive layers which form an array of stretchable capacitors. Stretching the capacitors change the14935-7807-0659Atty. Dkt. No.: 046434-0977capacitance, which can be measured directly. While these sensors hold immense potential, they are currently limited to simple, single-dimensional readings.

[0006] A challenge is to recover the geometry of the sensor by reading the capacitance alone. With flat capacitors, which are stretched in one direction, this may be straightforward. In this case, capacitance is proportional to the plates area and inversely proportional to the plates distance. However, treating a generally deformed stretch sensor is not as simple. Estimating the capacitance is difficult, as there are no simple formulas. Additionally, the map between shape and capacitance is not unique in this case. There can be multiple deformations leading to the same capacitance values. This challenge has been tackled before with a data-driven approach, using a calibrated vision-based system to acquire a set of deformations and map them to capacitance values. However, this process is expensive and lengthy and limits the ability to iteratively optimize the sensor layout (i.e., how are the capacitors embedded in the silicone sheet). The systems and methods described herein replace the external system with a simulation. The approach enables calibration and design of stretch sensor layouts without requiring calibration data.SUMMARY

[0007] At least one embodiment relates to a sensor. The sensor includes a first conductive layer including a first conductive region. The first conductive layer is patterned to form the first conductive region having a first design based on a simulation including an elastic simulation and an electrostatic simulation. The sensor includes a second conductive layer including a second conductive region. The second conductive layer is patterned to form the second conductive region having a second design based on the simulation. The sensor includes a dielectric layer positioned between the first conductive layer and the second conductive layer. Deformation of the sensor changes a sensor modality between the first conductive region and the second conductive region based on the first design and the second design.

[0008] At least one embodiment relates to a method for designing a sensor. The method includes determining a model of the sensor. The model includes at least one conductive region separated by a dielectric material. The method includes performing an elastic deformation simulation of the sensor on an object under a boundary condition. The elastic deformation simulation is performed on one or more poses of the object. The method includes performing,24935-7807-0659Atty. Dkt. No.: 046434-0977using the elastic deformation simulation, an electrostatic simulation to determine a capacitance value for each of the at least one conductive region and determining a sensor pattern based on the elastic deformation simulation and the electrostatic simulation.

[0009] At least one embodiment relates to a stretch sensor. A stretch sensor is a device that attaches to objects and measures the amount by which they deform. These sensors have shown great promise as an alternative to vision-based motion-capture systems, and for robotic sensing. Currently, they are generally limited to linear designs, and require a somewhat challenging calibration process. The sensors as described herein use a simulator for a calibration process. Furthermore, sensor layouts of the sensor can be optimized with a shape optimization algorithm.

[0010] Described herein are systems and methods for a differentiable simulator. The simulator can be used for capacitive stretch sensors, that treats both the elasto- and electrostatic parts of the system. The differentiability allows for the optimization of the geometric properties of the sensor in order to improve its design for specific applications. The accuracy of the simulator and the effectiveness of the sensor optimization process is demonstrated for various use-cases, such as human interfaces and robotics.

[0011] It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the subject matter disclosed herein. In particular, all combinations of claimed subj ect matter appearing at the end of this disclosure are contemplated as being part of the subject matter disclosed herein.BRIEF DESCRIPTION OF THE FIGURES

[0012] The foregoing and other features of the present disclosure will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. Understanding that these drawings depict only several implementations in accordance with the disclosure and are therefore not to be considered limiting of its scope, the disclosure will be described with additional specificity and detail through use of the accompanying drawings.

[0013] FIG. 1 shows an initial pattern and an optimized pattern for a sensor design.34935-7807-0659Atty. Dkt. No.: 046434-0977

[0014] FIG. 2A shows an extension experiment, according to an example embodiment.FIG. 2B is a graph of elastic simulation error. FIG. 2C shows a comparison of computing capacitance for a parallel plate capacitor (8 cmx8 cm) under percentages of extension.

[0015] FIGS. 3A and 3B show a 2X2 poking sensor, according to an example embodiment.

[0016] FIG. 3C shows results of the simulation and experiment on a capacitor array, according to an example embodiment.

[0017] FIG. 4A shows a 2 X 2 poking sensor, according to an example embodiment. FIG.4B shows an optimized 2X2 poking sensor, according to an example embodiment. FIG. 4C shows capacitance change from rest (pF) for various poses in the simulation compared to reality.

[0018] FIG. 5A shows an optimized 2X2 poking sensor, according to an example embodiment. FIG. 5B shows a ball pressing down on a sensor, according to an example embodiment. FIGS. 5C and 5D show capacitance change from rest (pF) for various poses in the simulation compared to reality.

[0019] FIGS. 6A and 6B show a poking sensor, according to an example embodiment.FIG. 6C shows results of an optimized joystick sensor via capacitance change from rest (pF) for various poses in the simulation compared to reality.

[0020] FIGS. 7A and 7B show an inflation sensor, according to an example embodiment.FIG. 7C shows results of an optimized joystick sensor via capacitance change from rest (pF) for various poses in the simulation.

[0021] FIG. 8 shows a parallel plate capacitor, according to an example embodiment.

[0022] FIG. 9 illustrates a computer system for use with certain implementations.

[0023] FIG. 10 illustrates a schematic diagram of the sensor simulation algorithm.

[0024] FIG. 11 illustrates a multi-start optimization, according to an example embodiment.44935-7807-0659Atty. Dkt. No.: 046434-0977

[0025] FIG. 12A shows a fabricated sensor design. FIG. 12B shows the fabricated sensor design in simulation. FIG. 12C shows the fabricated sensor design for experimental use. FIG.12D shows results of the fabricated sensor design for various poses in the simulation compared to reality.

[0026] FIG. 13A shows a baseline sensor pattern for a joystick. FIG. 13B shows an optimized sensor pattern for the joystick.

[0027] FIG. 14A shows a starting sensor pattern for a glove. FIG. 14B shows the optimized sensor pattern for the glove. FIG. 14C shows a number of poses for the glove with the optimized sensor pattern.

[0028] Reference is made to the accompanying drawings throughout the following detailed description. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. The illustrative implementations described in the detailed description, drawings, and claims are not meant to be limiting. Other implementations may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented here. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the figures, can be arranged, substituted, combined, and designed in a wide variety of different configurations, all of which are explicitly contemplated and made part of this disclosure.DETAILED DESCRIPTION

[0029] Embodiments described herein relate generally to systems and methods for multidimensional and free-form deformation sensing. The systems and methods provide a simulation approach to accurately estimate the capacitance of a deformed sensor in a virtual environment. The simulation approach can be a hybrid elastostatic and / or electrostatic differentiable simulation approach. Boundary conditions (e.g., poses) can be scripted in a simulated environment and the simulator can then compute the deformed sensor pose and the corresponding capacitance using a volumetric electrostatic simulation. The simulation can then be optimized for a sensor layout automatically in a number of ways. For example, the simulation can be optimized by using shape optimization and looking for the layout that will maximize the entropy of the sensor reading over all poses, i.e., that will lead to maximally different reading between the poses, thus increasing an accuracy of a reconstruction using the simulation. Once the sensor layout is computed, the simulator is used to generate a map from54935-7807-0659Atty. Dkt. No.: 046434-0977capacitance to geometry, which is then compressed in a neural network for real time reconstruction.

[0030] The systems and methods described herein enable the design of sensors that are able to sense deformations of geometrically complex objects. The computational method can be applied on a number of deformable objects. For example, in a medical application, the sensors can be used for joint tracking or to understand how tissues deform. In a virtual reality environment, predicting and optimizing the sensors can used for hand tracking. Other applications can include for sensing with gloves and soft robotic arms.

[0031] The systems and methods include an elastic and electrostatic differentiable simulator. The simulator is configured to accurately simulate sensor deformation and capacitance reading. As described herein the simulator is validated by comparing it with real-world experiments. In various embodiments, the simulator enables an entirely virtual calibration of silicon capacitive sensors, forfeiting the use of motion capture systems. Additionally, a sensor design optimization process (e.g., a shape optimization algorithm) is used to optimally design sensor layouts for capturing a prescribed set of poses. As shown in FIG. 1, the systems and methods can be applied to real-world and simulated soft robots equipped with an optimized (e.g., automatically optimized) capacitive sensor on their surface that enables state estimation. As described herein, the systems and methods provide application in graphics and robotics, among other fields, for differentiable simulation.

[0032] Various stretch sensing technologies have emerged in recent decades. The predominant approaches utilize resistive and capacitive sensing mechanisms. These sensors operate based on their respective electrical principles. Resistive sensors utilize an elastic, conductive material that exhibits changes in electrical resistance when stretched. By measuring these resistance changes, the degree of deformation can be determined. Capacitive stretch sensors function as deformable capacitors, in which mechanical strain induces measurable changes in capacitance. Alternative sensing approaches include optical, piezoelectric, and triboelectric mechanisms. An optical sensor can made of an optical fiber. For example, the optical sensor can be made with an element known as Fiber Bragg Grating. Transmission of light passing through the fiber changes as the fiber is stretched, due to changes in the spacing between the grating. Piezoelectric sensors exploit the property of certain materials to generate voltage when subjected to mechanical strain. Triboelectric sensors are based on the tribelectric effect, colloquially known as “static electricity”, which64935-7807-0659Atty. Dkt. No.: 046434-0977is a transfer of charge that can happen when two surfaces touch. This creates a temporary potential difference that can be measured and used in order to estimate strain. As described, sensors differ in properties such as stretchability, durability, sensitivity, measurement accuracy, linearity, response time, and hysteresis effects. Additionally, fabrication costs, duration, and customizability can all be factored in.

[0033] Recovering strains from capacitance measurements requires a calibration process, which presents a significant challenge. Simple, cord- or ribbon-like capacitive sensors tend to respond linearly to stretching. For these sensors, calibration involves stretching them by a predefined, measurable amount, recording the corresponding capacitance, and applying a linear regression model. However, more complex cases require more sophisticated models. As an example, due to the high degree of hysteresis resistive sensors exhibit, a long shortterm memory (LSTM) model can be used to calibrate such sensor by essentially training a time dependent model. Complex geometries require multiple, spatially distributed sensors, or sensor arrays, in order to estimate the deformation across the entire surface. In these cases, an external tracking system is used to capture the geometry and fit it to the measurements. The widespread use of deep neural networks in these works suggests that the relationship between sensor measurements and actual deformation is too complex for traditional regression models.

[0034] To eliminate the need for calibration, the systems and methods described herein simulate a deformation and capacitance for the sensor. This approach allows for the generation accurate data without depending on external sources. Furthermore, a stretch sensor is simulated in terms of both its elastic properties and electrostatics.

[0035] Optimization of the sensor could lead to sensor designs with improved precision and performance. A canonical problem related to sensor design is an optimal sensor placement problem, going back to earlier work on information theory an optimal experimental design. This problem addresses how to position sensors to maximize information gain about the system or optimally distinguish between different states. Optimal sensor design and placement has since been investigated across numerous domains. In structural engineering, researchers optimize sensor placement to maximize information gain for structural health monitoring. For antenna design, various optimization techniques have been developed to enhance signal reception and transmission patterns. There have been several attempts to optimize stretch sensors for robotics and human interfaces in particular. Some attempts74935-7807-0659Atty. Dkt. No.: 046434-0977include approaching sensor optimization via information theory, using joint entropy -based optimization. The idea is that maximizing the entropy of the distribution of measurements would a better utilization of measurement space. However, the approach only treats cord-like sensors and does not consider the full electromagnetic simulation of capacitive sensors.

[0036] Most existing approaches either rely on experimental data collection or simplified physical models for optimization. The systems and methods described herein differs fundamentally by leveraging a differentiable physics simulator that can model both the mechanical deformation and capacitive response of the sensor. This enables continuous, principled design optimization without requiring expensive physical prototyping or external tracking systems. This approach allows for a much larger design space than previous methods while maintaining physical accuracy.

[0037] Generally, a common model for a (rigid) capacitor is two parallel, conductive plates, separated by a dielectric material. A capacitance is a function of area and distance between the plates. As such, if the plates could stretch and change their area, it would be possible to tell how much the area changed by measuring the capacitance. In various embodiments, stretchable capacitors are made out of silicone. Silicone capacitive sensors are composed of interleaved conductive and dielectric layers of silicone. To make silicone conductive, it is dispersed with carbon particles. Certain manufacturing processes allow for control of a layout of the conductive layers, effectively forming an elastic Printed Circuit Board (PCB). Furthermore, while single capacitor sensors exist, controlling the layout of the layers allows for the use of a grid-like layout that effectively creates many capacitors within a single silicone sheet and enables localized stretch sensing. Different layouts lead to different capacitances and different changes when the sensor is deformed. By designing the pattern, it is possible to target different design objectives.

[0038] As described herein, an external source is not required for calibration. Rather, a physical simulation of the sensor is conducted. This enables testing layouts in simulation, avoiding fabrication and data collection. The systems and methods described herein utilize a coupling between the electrodynamics and sensing modality (i.e., electrostatics) to model deformable sensing systems. As described herein, a one-way coupling between the electrodynamics and the electrostatics may be used as it can be undesirable for the electrostatics to affect the deformation (e.g., the electrostatics exerting forces on the sensor) to sense deformation.84935-7807-0659Atty. Dkt. No.: 046434-0977

[0039] A layout design of the conductive layer is used to build a volumetric mesh representing the layers of silicone. In various embodiments, the layout design is two-dimensional (2D). The mesh can be virtually attached to other simulated objects, forming boundary conditions and other constraints. Repositioning these objects then drives the deformation of the sensor, which is computed using a numerical method. For example, the Finite Element Method (FEM) can be used. An electrostatic simulation can then be used to compute the capacitances in the deformed pose. For example, FEM can then be used to solve an electrostatics problem, as described herein, from which the capacitance can be computed.

[0040] In various embodiments, the simulator can be used to optimally design a sensor to capture a prescribed set of poses. Since the simulation steps are differentiable, it can be possible to define a bi-level optimization and solve using the adjoint method. Although the adjoint method was used herein, it can be appreciated by those skilled in the art that other numerical methods for computation and optimization can be used. A high-level objective can be adjusted depending on a goal, user, purpose, etc. For example, a goal can be to use the measured capacitances to distinguish between different poses. As such, it can be opted to make the capacitances for different poses as different as possible from each other, by maximizing their pairwise distances. However, many other objectives are possible, as described herein.

[0041] To perform the elastic simulation, an open source framework is used. PolyFEM, an open source FEM framework, which is based on the Incremental Potential Contact (IPC) formulation was used. Although PolyFEM is used, it can be appreciated by those skilled in the art that other frameworks can be used to perform elastic simulation.

[0042] The sensor includes a capacitive part. The capacitive part includes a number of layers. For example, the sensor may include five layers. The layers include conductive silicone layers separated by dielectric silicone layers so that the conductive silicone layers on are not electrically connected. For example, the main capacitive part may include two conductive layers separated by a dielectric layer. The two conductive layers are then encased on top and bottom by two dielectric layers to protect against mechanical forces and prevent electrostatic discharge. In such embodiment, the total number of layers are five and the order of layers are: a dielectric layer, a conductive layer, a dielectric layer, a conductive layer, a dielectric layer. In various embodiments, the conductive layer is patterned, and the dielectric94935-7807-0659Atty. Dkt. No.: 046434-0977layer is not patterned. The conductive layer may be patterned using a stencil cutter and curing a sample on the stencil cutter.

[0043] A thickness of the i ’th layer of silicone is referred to as tj. In an example, ttcan be tens on the order of tens of microns. As described herein, a top, middle and bottom layer (e.g., the dielectric layer) of the sensor are non-conductive. In various embodiments, at least one of the top, middle, or bottom layer is made (e.g., entirely made) of cured silicone. The remaining two layers (e.g., the conductive layer), which contain the plates of the capacitors, have both conductive and non-conductive silicone parts. In various embodiments, the layers with the plates do not physically contact each other, such that the non-conductive layer are positioned between the layers with the plates. Since the sensor is flat, the sensor can be described by 2D domains. A shape of the entire sensor is denoted by £1 and the conductive region by £lc£ fl, both represented by sets of polygons. In various embodiments, this region is the same for both conductive layers. The region being the same for both conductive layers is valid since non-overlapping conductive parts do not contribute to capacitance considerably and can be neglected. £lcis the union of several connected components, each representing a single capacitor. Before fabricating, the components are connected with non-overlapping “bridges” in order to create a capacitor.

[0044] To simulate with high accuracy, volumetric FEM was used, which requires generation of a volumetric tetrahedral mesh. Since the layers are extremely thin, existing meshing tools are likely to fail. Due to this, a compatible triangulation of £1 and £lccan be generated and the triangles that are inside £lcare marked. The triangulation is extruded out of plane to create a triangular prism mesh. Each prism can then be split into three tetrahedra, while ensuring that compatibility across prisms is maintained. This process generates a tetrahedral mesh for one layer. To generate all layers, the process is repeated, the thickness of the mesh is adjusted accordingly, and overlapping vertices between layers are merged. All the elements that correspond to elements of £lcin the two conductive layers are marked.

[0045] As described, in this example, PolyFem was used to simulate elastic deformation, where the deformation is driven by defining Dirichlet boundary conditions, or by applying external forces through contact, using inductively coupled plasma (ICP). The simulation is differentiable, which allows for the sensor designs to be optimized via continuous optimization.104935-7807-0659Atty. Dkt. No.: 046434-0977

[0046] In order to achieve an accurate simulation, material parameters must be identified. Standard material testing requires bulk material and is not well suited for thin sheets. Standard material testing is particularly not well suited when a purpose is to perform volumetric simulation. Producing standard samples (i.e., cubes of material) was attempted, but silicone mixed with carbon black does not cure in this form. As a result, a uniaxial extension test was conducted using an Instron column testing machine, as shown in FIG. 2A. Two thin layer samples made of clear silicone and layered silicone / silicone were tested with carbon black. The clear silicon represented a dielectric silicone material and the layered silicone tested with carbon back represented a conductive silicone material. A neo-Hookean material model to the data was fitted, for both the clear silicone and the dark carbon / silicone compound. It was found that Poisson’s ratio is 0.47 for both, while Young’s modulus is 570 kPa for the clear silicone, and 1100 kPa for the carbon black silicone. The models appears to match to experimental data well for up to 70% extension.

[0047] The model was further validated by performing an extension test on a thin sheet, for up to 100% extension. In this example, the thin sheet was 90mm><75mm><0.7mm. Markers were placed on a 14^15 grid on the sample and their positions were recorded using a calibrated camera for 25 extension cycles. The positions were matched with a simulation and the error per extension step was computed (FIG. 2B). The maximal error was around 1 mm, or 2% indicating that the model agrees with the measurements.

[0048] Following elastic simulation, a next challenge is to calculate capacitance using FEM. For this calculation, we abstract away the electronic circuitry and assume ideal capacitors. Electrostatics is a study of how charged particles or distributions interact. Two like chargesand q2exert a repulsive force on one another which follows an inverse square law, F oc E oc — where F is the force, E is the electric field and d is the distance between the dcharges. This phenomenon is modeled by Poisson’s equation:where (p = —VE is the electric potential, p is the charge density, and e0is the vacuum permittivity. In order to increase the capacitance, capacitors are usually embedded in a dielectric medium, which effectively changes the permittivity to a different value e that depends on the specific dielectric.114935-7807-0659Atty. Dkt. No.: 046434-0977

[0049] A conductor is defined by its ability to allow charges to move freely within it. In an electric field, charge will redistribute until reaching equilibrium, where there is no net electric field inside the conductor, i.e., the magnitude of the electric field must be zero. This means that the electric potential must be constant inside a conductor, and in particular on its boundary surface. Therefore, in a charge-free space, outside of a conductor, Poisson’s equation shown in Eq. (1) turns into a Laplace equation with boundary conditions:eV2= 0(2)where we used £lcagain to denote the volume of the conductor, and u is the surface potential. Setting u can be easily done in practice connecting the conductor to a voltage source.

[0050] Capacitance is an ability of system to store electric charge. The mutual capacitance of two conductors is defined as the charge stored divided by the difference in electric potential, C = q / 4V. This measure of capacitance depends purely on the geometry of the conductors, and the dielectric, since q and AV are related linearly. Capacitors also store energy, given by:[7 = |c(4V)2, (3) The energy stored in an electric field is also the Dirichlet energy electric potential:U = ( e||V ||2dx. (4) J a.Thus, using Eq. (3), two conductors at potentials= 0V and < >an2= IV, have the capacitance:

[0051] To compute the capacitance in simulation, the permittivity of the silicone is measured. This can be done by fabricating a simple parallel plate capacitor (FIG. 8). The capacitance in this case is known to be:C = e^, (6) where A is the area of the plates and d is the distance between them. To find the permittivity, a rectangular silicone capacitor is fabricated with known dimensions and the capacitance is measured. Cross sections of the capacitor is then taken and an average distance between the plates on a calibrated microscope is measured. The permittivity in this example was found to be e = 2.84e0.124935-7807-0659Atty. Dkt. No.: 046434-0977

[0052] To then compute the capacitance, the Poisson’s problem in Eq. (2) is solved using PolyFEM to obtain < >, and then the Dirichlet energy is computed as required in Eq. (5). As shown in FIG. 2C, the volumetric simulation is necessary to compute capacitance. Although a simple approximation can be gathered using the formula for parallel plates, it is not as accurate as shown by the difference in the full simulation and the non-physical and physical estimation. This is because the thickness of the dielectric layer changes as the sensor deforms, and this happens in a complicated and non-uniform way.

[0053] In simulation, the capacitance for each element is determined by setting all conductors to 0V, except for one conductor of the target capacitor, which is set to IV. The electrostatic solution is then obtained through Eq. (2), and the capacitance is computed using Eq. (5). This process is repeated for each capacitor element.

[0054] The fabricated sensor presents constraints in terms of available wire routing area on the silicone and microcontroller pin count. To address these limitations, we employ a multiplexing technique. For an n n capacitor grid, top conductors are connected columnwise while bottom conductors are connected row-wise, reducing the required wire count from 2n2to 2n. Capacitor formation is achieved by partitioning the wires into two groups with shared connections within each group. While a single capacitor cannot be addressed individually, different capacitor combinations can be activated, and the individual capacitance values can be obtained by solving a linear system, assuming negligible interference between capacitors. Single Pole Double Throw (SPDT) array ICs is utilized in this approach, which can introduce parasitic capacitance. This requires augmenting the linear system to account for the parasitic contributions of switches in both ON and OFF states, assuming uniform parasitic capacitance within each state.

[0055] The method was validated by performing a uniaxial extension test of a soft capacitor array (FIG.3A) and comparing it with simulation (FIG.3B). For the capacitor, a 3 by 3 array of square parallel capacitors of dimension 2 centimeters (cm) *2 cm each was chosen. From earlier estimations of layer thicknesses, a capacitance of around 70 pF per square capacitor was estimated. Uniaxial extension beyond 100% of its width, as shown in FIGS. 3A and 3B, for three samples was performed, recording individual capacitances.

[0056] This experiment was repeated in simulation and computed individual capacitances at each extension level. P2 order elements was used for both the elastic and electrostatic134935-7807-0659Atty. Dkt. No.: 046434-0977simulations. The results of the simulation and experiment for each of the nine capacitors are shown in FIG. 3C. As shown in FIG. 3C, simulation result 310 are relatively similar to the experimental results 320. In general, a good agreement is shown between the simulation results 310 and experimental results 320. A calculated error in the worst case is around 20%, but this is under extreme extension. In various embodiments, a better fabrication procedure of the samples may reduce the error. Additionally, a slight error increase as we moved vertically along the capacitor (along each row of the figure), but not horizontally, suggests that there might be other artifacts in the fabrication process leading to incorrect assumptions regarding the thickness.

[0057] Additionally, the simulator can be used to virtually calibrate a sensor. For example, the sensor can be a planar poking sensor. A 2^2 capacitor grid on a 10 cm 10 cm silicone sheet, as shown in FIG. 4A, is used. The capacitors 402 (e.g., first capacitor 402a, second capacitor 402b, third capacitor 402c, fourth capacitor 402d) are shown as circles. The deformations can be restricted to poking on top of the capacitors 402 to know when each capacitor 402 is pressed given capacitance readings of the sensors. As shown in FIG. 4B, pressing capacitor 402a can be fabricated in a simulation using a virtual sensor and pressing one of the virtual capacitors 404 (e.g., first virtual capacitor 404a, second virtual capacitor 404b, third virtual capacitor 404c, fourth virtual capacitor 404d), shown as first virtual capacitor 404a being pressed. While it may seem obvious that the capacitance of the pressed capacitor will increase, it is not known by how much the capacitance will increase. It is also not known whether the other capacitors will change and / or to what extent the other capacitors will change.

[0058] The method, as described herein, is used to create the virtual sensor and gather readings for each of the virtual capacitors 404 (e.g., first virtual capacitor 404a, second virtual capacitor 404b, third virtual capacitor 404c, fourth virtual capacitor 404d) in different poses. Readings were gathered in the different poses by pressing the virtual capacitors 404 down by a distance in simulation. In this example, the distance is 1.3 cm and the virtual sensor was pressed with a small 2 cm ball. At rest, the capacitance of each node (e.g., the virtual capacitors 404) is computed to be approximately 57 pF. When pressed, the capacitance of that node is predicted to increase by around 9 pF while the capacitance of the rest of the nodes by 1.3 pF each. When the experiment is conducted, it is found that the capacitor values of the capacitors 402 at rest are 59.7 pF, 60.4 pF, 53.4 pF, 59.5 pF (i.e., all are within 6% of144935-7807-0659Atty. Dkt. No.: 046434-0977predicted values). Each of the nodes (e.g., the capacitors 402) are poked by hand, trying to match the displacement seen in simulation. An average of around 10.5 pF increase for the pressed sensor and around 1.5 pF increase in all other sensors is seen. FIG. 4C shows a comparisons between the simulated results (labelled “Sim”) and the experimental results (labelled “Real”) for the different poses (e.g., different capacitors 402, 404 being pressed) The procedure is repeated three times and the values are averaged. As shown in FIG. 4C, the measured capacitances for the simulation results matches the experimental results for the poses showing that the experimental results are consistent with simulation predictions.

[0059] With the simulator, the problem of optimizing the conductive layouts to increase the effectiveness of the sensor, i.e., its ability to distinguish between different poses, can be considered.

[0060] Problem Formulation. FIG. 10 shows a schematic diagram of the sensor simulation algorithm. As described herein, £2 is the 2D domain represents the shape of the sensor. Uj £1c. = Q.c£ fl can be represent an initial shape of the capacitors and the conductive late. Optimization can be used to deform Flcinto an optimized shape. The deformation is expressed using a displacement map q £1 -> £1, where q(x) = x + u(x). As further described below q = q(x) is defined using a planar deformed (e.g., a liner blend skinning planar deformer). In various embodiments, q represents a degree of freedom and M = M(q) is the mesh (e.g., the volumetric mesh) generated from q(£2). Mcis a sub-mesh of the mesh M and represents the mesh for the conductor. Mcis the complement of Mcand represents the dielectric medium (e.g., the dielectric layer, the non-conductive silicone).

[0061] As described herein, the sensor is coupled (e.g., adhered, glued, etc.) to a deformable object to detect specific poses. This application can be simulated by selecting a triangle mesh representing the object K and deforming it into various poses Kt, as shown in FIG. 10. The sensor can then be optimized for the various poses. In an elastic simulation, one side of the sensor, represented by M, is attached to the object K at various poses. For example, the bottom boundary Mbof M is attached to the object K to compute a mapping from Mbto Ktas shown in FIG. 10. Interpolation may be used to obtain the mapping of the meshes (e.g., a Clough-Tocker interpolant). To generate multiple sensor deformations, this process occurs for a set of poses P of the object K. The mappings can be defined b)) G P. The mappings are used to define boundary conditions for the elastic simulator (e.g., q(x) ->154935-7807-0659Atty. Dkt. No.: 046434-0977Plq x)y). The deformation obtained for the object in various poses using the mappings is shown in FIG. 10 and denoted herein as boundary condition:

[0062] The deformation for the object Mldepends on q(x) as the sensor affects the deformed pose and the rest post. Since the sensor is thin and flexible, it can be assumed that the object can deform freely as the additional elastic force exerted by the sensor is negligible.

[0063] With the boundary condition related to the elastic simulation, for each pose Ml, the capacitance cj of each capacitor can be computed using the electrostatics simulator described herein. The electrostatic potential for Mland Cj can be computed asas shown in FIG. 10. The capacitance cj(q) can then be found through integration of Eq. (8), as described with reference to Eqs. (3)-(6).

[0064] Advantageously, as is differentiable with respect to q, anysmooth objective function of cj(q) can be optimized. For example, a general objective function can be defined aswhere C;( ) = (c}(q))7and represents a vector of capacitances for pose Ml. In other words, the vector may be a feature vector to characterize Ml. d is a dissimilarity measure and R Mc,q~) is a regularizations term that regularizes the shape of the capacitors. In various embodiments, the regularization term also regularizes q.

[0065] A goal for the dissimilarity measure may be to improve the quality of the sensor. For example, given a pose space with a sampling of poses, the goal may be for the capacitance readings to be sufficiently spaced apart to reduce errors. As a result, the minimum distance between any two pairs of capacitance vectors from the poses are maximized to optimize the sensor. A number of methods can be used to create a smooth function of the dissimilarity measure d and maximize the distance. For example, “LogSumExp”, which calculates a log of the sum of exponentials of the input elements of d (e.g., Cq), C2(q)), may be used to space capacitance vectors apart. Although “LogSumExp” was used, other smooth maximum and / or smooth approximation functions may be used. For example, simpler objective functions, such164935-7807-0659Atty. Dkt. No.: 046434-0977as maximizing the squared distances between the capacitance pairs may be used. Advantageously, “LogSumExp” allows for capacitance degeneracy to be removed making the capacitances distinguishable. In various embodiments, an assumption for the algorithm includes that the poses are sufficiently well spaced out in the pose space.

[0066] Note that the simulation steps described herein depend on the shape of the conductive layers. The elastic deformation is affected as the material properties of the conductive and non-conductive layers are different, while the electrostatic simulation is affected as the simulation domain changes.

[0067] To optimize / , the shape derivates VQ / is computed, which requires a gradient of the capacitance of each capacitor in each pose:The first term of the chain rule is the change in capacitance with respect to the change of shape in the deformed pose (e.g., electrostatic simulation) and the second term is the change of shape in the deformed pose with respect to the change in q (elastic simulation). The term may be trivial because M(q) are duplicates of q, such that the term is effectively the identity.gpi

[0068] To evaluate — , the map Plis defined by establishing a correspondence usingbarycentric coordinates between two meshes of the same connectivity. These two meshes can be obtained either via a direct simulation or by creating the poses using other deformations techniques such as linear blend skinning. The derivatives of the two meshes with respect to the parameters q can be computed using finite differences.

[0069] To evaluate the elastic shape derivatives, deformation techniques may be used.(IM'and are elastic shape and Dirichlet derivatives, respectively. The derivatives can be computed using the adjoint formulation, introduced with reference to the bi-level optimization. This step requires solving an adjoint problem for each pose, which can then be reused to compute the shape derivatives for each capacitor. The adjoint formulation, as described herein, is used for computational optimization.174935-7807-0659Atty. Dkt. No.: 046434-0977

[0070] To evaluate the electrostatic shape derivatives, the electrostatic system reduces to a Poisson equation, as described with reference to Eq. (1). In this case, the shape derivatives of the Dirichlet energy, ^4, can be computed according to the derivations set out in [Huang et al. 2024],

[0071] To parametrize q, the hierarchical linear blend skinning approach is used. In the approach, a set of points are uniformly distributed over the boundary, linear blend skinning weights are automatically computed, and a translation attached to each point is used as a solution space. During the optimization, the sample density can be increased to provide additional degrees of freedom after the optimize is close to the optimum. Although the linear blend skinning approach is used, as described herein, other deformation techniques may be used to deform the mesh.Optimization Algorithm.

[0072] / (q) is minimized using an optimization method. For example, the L-BFGS algorithm can be used and the optimization can be interleaved with a remeshing algorithm to control mesh distortion under large deformations.

[0073] For the L-BFGS algorithm, an initial mesh for the sensor is generated using the meshing algorithm described herein, and an LBS basis is computed for each initial control points. In various embodiments, the LBS bases is computed with 10 control points. The translations parameters of the control points form the q vector. L-BFGS is used on / (q) to provide an explicit evaluation of dqJ to the solver. Each evaluation of the shape derivatives requires solving i adjoint solves for elasticity and i * k adjoints for electrostatic, where i is the number of poses, and k the number of capacitors.

[0074] After every iteration, the quality of the mesh used for £1° is checked, and remeshed if any internal angles are less than a predetermined angle. For example, the predetermined angle can be 10°. After the optimization converges (e.g., out of iterations for each cascade level), the number of LBS samples is doubled and the optimization continues with a larger space of parameters q. This process is stopped when the optimization runs out of cascade steps.184935-7807-0659Atty. Dkt. No.: 046434-0977Multi-Start Optimization.

[0075] In various embodiments, a multi-start optimization strategy may be used to determine more optimal designs. The multi-start optimization utilizes different initial configurations. To obtain different initial configures, a number of capacitors in the array can be randomly and / or systematically chosen. The initial location of the capacitors can be randomly sampled. Particularly, for k e [2, m] number of capacitors, n initial configurations can be initialized randomly or uniformly (e.g., using an algorithm). In various embodiments, 80% of the initial configurations are initialized randomly and 20% are initialized uniformly. In various embodiments, m is 6 and n is 25.

[0076] Using a minimum L1norm between all poses as a metric, an optimal final configuration for each number of capacitor can be chosen. To choose among different numbers of capacitor, the smallest number of capacitors beyond which the L1norm exhibits minimal change is chosen. Since there may be a limited capacitor area and capacitors need to be separated by some distance, the L1norm generally decreases as more capacitors are added.FIG. 11 shows a multi-start optimization on a biaxial stretch experiment (top) and a joystick experiment (bottom). As shown in the figure, the optimal configuration for the biaxial stretch experiment is k = 4 and the optimal configuration for the joystick experiment is k = 3.

[0077] In various embodiments, the sensor may be automatically sampled and optimized (e.g., via a control system). In such embodiments, rather than receive a set of discrete poses, the algorithm may utilize a parameterized pose space to sample and optimize the sensor.Optimization on Poking Sensor.

[0078] To highlight the utility of our inverse design algorithm, we again consider the sensor we used to register poking as described herein with reference to FIGS. 4A-4C. If a top of the capacitors is poked, the stretching will be localized to where we have the capacitor. If instead we want to poke in a cross pattern, the sensor is ineffective at detecting poking in other locations (e.g., the cross pattern). Poking on the cross pattern of the designs in FIGS.4A and 4B increases the capacitances by a few pF uniformly, which in practice is barely distinguishable. This mirrors the real-world behavior of the capacitor under this set of poking locations, as can be seen from the poses of FIG. 5C.194935-7807-0659Atty. Dkt. No.: 046434-0977

[0079] The systems and methods described herein can be run on his algorithm to obtain an optimized pattern. The fabricated optimized result is shown in FIG. 5A-5D. This pattern leads to distinct measurements for all the poses. The predicted capacitances at rest are 294.9 pF, 287.6 pF, 286.5 pF, 301.5 pF, while the measured capacitances from the fabricated sensor are 296.0 pF, 303.9 pF, 267.7 pF, 320.8 pF, respectively (all within 6.5%). The results from poking the sensor are given in FIG. 5D. We can see that the patterns in capacitance in experiment mirror those in simulation, even if the total magnitude may vary a little due to differences between simulation and experiment.Optimization on Biaxial Stretch Sensor.

[0080] The systems and methods described herein can be used for designing and optimizing a sensor for biaxial stretch. The sensor can distinguish in-plane stretch in the vertical and horizontal direction. As described with reference to FIG. 11, the multi-start optimization method can be used to explore the design space and k = 4 can be determined as an optimal design. As shown in FIGS. 12A-12C, the determined design of the sensor can be fabricated and simulation and experimental stretching can be conducted in a vertical direction (pose 1) and a horizontal direction (pose 2). As shown in FIG. 12D, the fabricated sensor matches closely with the simulated sensor indication that the optimal design allows biaxial stretch to be distinguished and measured from rest.Optimization on Joystick Sensor.

[0081] A joystick-like object is designed that can sense the direction in which the end effector is moved. To estimate a state, sensors are placed entirely outside the cantilever, which can be beneficial in settings where there is not full control of the fabrication process for the actuator. This also means that an actuator, used in previous methods, can be replaced for a complex but general sensor fabrication method, although the method requires a developable surface.

[0082] We optimize a sensor to discriminate between different simulated poses of a joystick. For example, the sensor can be optimized to discriminate between nine principle poses representing the main directions of movement of the capacitor (e.g., center, up, down, left, right, and four diagonals). FIG. 13A shows a baseline sensor pattern for the joystick and FIG. 13B shows an optimized sensor pattern for the joystick. The baseline sensor pattern is determined using the initial simulation model described herein and the optimized sensor204935-7807-0659Atty. Dkt. No.: 046434-0977pattern is determined using the systems and methods described herein related to the optimization. The optimized sensor is more accurate and stable in comparison to the baseline sensor.Optimization on Inflating Cylinder Sensor.

[0083] The method can be used for sensing inflation by augmenting a soft actuator with sensing capabilities, such as with a pneumatic sensor. The actuator can include a silicone cylinder with an offset cylindrical cavity inside, as shown in FIGS. 6B and 7B. As the inside cavity is pressurized, differences in wall thickness leads to the actuator bending to one side as it expands from the internal pressure. While simulation can predict the inflation behavior of the cylinder, sensing capabilities are needed to determine if there are other objects in the scene that the actuator collides into.

[0084] FIGS. 6A-6B shows the baseline sensor pattern for the cylinder sensor (e.g., the pneumatic sensor) and FIG. 6C shows the corresponding results comparing the simulation and the experimental data. As shown in FIG. 6C, although the experimental and simulation data match, there are areas (e.g., poses) in which the sensor is ineffective at detection, shown in pose 2. A sensor wrapped outside of the cylindrical actuator can be optimized to determine if the cylinder has collided with a ball in the scene. The ball takes two positions, pushing the cylinder either to the left or to the right once it is inflated. The goal of the sensor is to determine whether the cylinder inflated normally or was pushed to either side. The results of the optimization are given in FIGS. 7A-7C. The results show that there are significantly senses differences of inflation from rest in the different poses. Further, the optimized pneumatic sensor can be used to sense if he Fiactuator was disturbed from its inflation path and predict the magnitude of this deviation.Optimization on Wrist and Glove Sensors.

[0085] The systems and methods described herein can be used for designing and optimizing a sensor for a human wrist and / or for a glove. In various embodiments, a preexisting human body model may be used to generate different wrist poses for optimization and evaluation. As the wrist may have complex deformation, a starting configuration for the optimization may not be obvious. As a result, the multi-start optimization may be beneficial to find an optimized layout. As shown in FIG. 11, the multi-start optimization shows that k =2 is the optimal sensor pattern.214935-7807-0659Atty. Dkt. No.: 046434-0977

[0086] A glove can be sensorized for purposes of hand pose estimation. To produce an optimal design, a dataset of hand poses can be used, and sensors can be placed over a hand in the rest pose. FIG. 14A shows the starting capacitor design. The starting capacitor design may be determined based on known information on how the hand deforms. FIG. 14B shows the optimized sensor pattern using the systems and methods described herein. The optimization of the sensor pattens allows the sensors to distinguish between a number of different poses, including the poses shown in FIG. 14C, better than the starting capacitor design.

[0087] Advantageously, the configuration of the sensors along with the simulation and optimization algorithm allows for a way to sense deformations of a number of objects, including geometrically complex objects. Rather than conducting calibration with an external source, a simulation can be conducted with a simulator that enables virtual calibration of sensors. As described herein, the virtual simulations are validated with real-world experiences showing a substantial accuracy with the simulations. Additionally, although described with capacitive stretch sensors, arbitrary capacitive sensors (e.g., for traction, for compression, etc.) could be modeled using the systems and methods described herein. Furthermore, other sensing modalities such as resistive, magnetic, and electromagnetic, may utilize the systems and methods, making the optimization algorithm further applicable to a wide range of sensors.Definitions.

[0088] As used herein, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, the term “a member” is intended to mean a single member or a combination of members, “a material” is intended to mean one or more materials, or a combination thereof.

[0089] As used herein, the terms “about” and “approximately” generally mean plus or minus 10% of the stated value. For example, about 0.5 would include 0.45 and 0.55, about 10 would include 9 to 11, about 1000 would include 900 to 1100.

[0090] It should be noted that the term “exemplary” as used herein to describe various embodiments is intended to indicate that such embodiments are possible examples, representations, and / or illustrations of possible embodiments (and such term is not intended to connote that such embodiments are necessarily extraordinary or superlative examples).224935-7807-0659Atty. Dkt. No.: 046434-0977

[0091] As used herein, the terms “coupled,” “connected,” and the like mean the joining of two additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate members being attached to one another.

[0092] As shown in FIG. 9, e.g., a computer-accessible medium 120 (e.g., as described herein, storage members directly or indirectly to one another. Such joining may be stationary (e.g., permanent) or moveable (e.g., removable or releasable). Such joining may be achieved with the two members or the two members and any device such as a hard disk, floppy disk, memory stick, CD-ROM, RAM, ROM, etc., or a collection thereof) can be provided (e.g., in communication with the processing arrangement 110). The computer-accessible medium 120 may be a non-transitory computer-accessible medium. The computer-accessible medium 120 can contain executable instructions 130 thereon. In addition or alternatively, a storage arrangement 140 can be provided separately from the computer-accessible medium 120, which can provide the instructions to the processing arrangement 110 so as to configure the processing arrangement to execute certain exemplary procedures, processes and methods, as described herein, for example. The instructions may include a plurality of sets of instructions.

[0093] System 100 may also include a display or output device, an input device such as a keyboard, mouse, touch screen or other input device, and may be connected to additional systems via a logical network. Many of the embodiments described herein may be practiced in a networked environment using logical connections to one or more remote computers having processors. Logical connections may include a local area network (“LAN”) and a wide area network (“WAN”) that are presented here by way of example and not limitation. Such networking environments are commonplace in office-wide or enterprise- wide computer networks, intranets and the Internet and may use a wide variety of different communication protocols. Those skilled in the art can appreciate that such network computing environments can typically encompass many types of computer system configurations, including personal computers, hand-held devices, multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. Embodiments of the invention may also be practiced in distributed computing environments where tasks are performed by local and remote processing devices that are linked (either by hardwired links, wireless links, or by a combination of hardwired or wireless234935-7807-0659Atty. Dkt. No.: 046434-0977links) through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0094] Various embodiments are described in the general context of method steps, which may be implemented in one embodiment by a program product including computerexecutable instructions, such as program code, executed by computers in networked environments. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Computer-executable instructions, associated data structures, and program modules represent examples of program code for executing steps of the methods disclosed herein. The particular sequence of such executable instructions or associated data structures represents examples of corresponding acts for implementing the functions described in such steps.

[0095] Software and web implementations of the present invention could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various database searching steps, correlation steps, comparison steps and decision steps. It should also be noted that the words “component” and “module,” as used herein and in the claims, are intended to encompass implementations using one or more lines of software code, and / or hardware implementations, and / or equipment for receiving manual inputs.

[0096] It is important to note that the construction and arrangement of the various exemplary embodiments are illustrative only. Although only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter described herein. Other substitutions, modifications, changes and omissions may also be made in the design, operating conditions and arrangement of the various exemplary embodiments without departing from the scope of the present invention.

[0097] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what may be claimed, but rather as descriptions of features specific to particular implementations of244935-7807-0659Atty. Dkt. No.: 046434-0977particular inventions. Certain features described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.254935-7807-0659

Claims

Atty. Dkt. No.: 046434-0977WHAT IS CLAIMED IS:

1. A method for designing a sensor, comprising:determining a model of the sensor, the model comprising at least one conductive region separated by a dielectric material;performing an elastic deformation simulation of the sensor on an object under a boundary condition, the elastic deformation simulation performed on one or more poses of the object;performing, using the elastic deformation simulation, an electrostatic simulation to determine a capacitance value for each of the at least one conductive region; and determining a sensor pattern based on the elastic deformation simulation and the electrostatic simulation.

2. The method of claim 1, wherein the elastic deformation simulation is differentiable with respect to a deformation of the object based on the one or more poses.

3. The method of claim 1, wherein the boundary condition is based on a mapping between the sensor and a representation of the object.

4. The method of claim 1 , wherein each of the at least one conductive region has a design and the method further comprises optimizing the design based on the elastic deformation simulation and the electrostatic simulation.

5. The method of claim 4, wherein optimizing the design comprises:determining a difference in the capacitance value for each of the at least one conductive region; andadjusting the design of the at least one conductive region to maximum the difference in the capacitance value.

6. The method of claim 4, wherein optimizing the design comprises:generating a plurality of initial sensor layouts, each of the plurality of initial sensor layouts comprising a different number of capacitorsoptimizing each of the plurality of initial sensor layouts based on the elastic deformation simulation and the electrostatic simulation; anddetermining the sensor pattern to be one of the plurality of initial sensor layouts based on a metric.264935-7807-0659Atty. Dkt. No.: 046434-09777. The method of claim 6, wherein the plurality of initial sensor layouts are randomized or uniformly distributed.

8. The method of claim 6, wherein the metric is a minimum L1norm.

9. A sensor comprising:a first conductive layer comprising a first conductive region, the first conductive layer patterned to form the first conductive region having a first design based on a simulation including an elastic simulation and an electrostatic simulation;a second conductive layer comprising a second conductive region, the second conductive layer patterned to form the second conductive region having a second design based on the simulation; anda dielectric layer positioned between the first conductive layer and the second conductive layer;wherein deformation of the sensor changes a sensor modality between the first conductive region and the second conductive region based on the first design and the second design.

10. The sensor of claim 9, wherein the sensor is a capacitive stretch sensor.

11. The sensor of claim 9, wherein at least one of the first conductive layer, the second conductive layer, or the dielectric layer is manufactured by silicone.

12. The sensor of claim 9, wherein the first design includes a size, shape, or a position of the first conductive region.

13. The sensor of claim 9, wherein the first design of the first conductive region and the second design of the second conductive region is based on an optimization process configured to maximize a minimum difference between a capacitance measurement of the first conductive region and the second conductive region.

14. The sensor of claim 13, wherein the capacitance measurement is obtained from a set of target object poses of the sensor.

15. The sensor of claim 13, wherein the capacitance measurement is obtained from a parametrized pose space of the sensor.274935-7807-0659Atty. Dkt. No.: 046434-097716. The sensor of claim 9, wherein the sensor modality is capacitance.

17. The sensor of claim 9, wherein the deformation includes at least one of stretch, traction, or compression.

18. The sensor of claim 9, further comprising a second dielectric layer positioned on a side of the first conductive layer distal the second conductive layer and a third dielectric layer positioned on a side of the second conductive layer distal the first conductive layer.284935-7807-0659

Images