# Optimizing Multi-Touch Textile and Tactile Skin Sensing
Through Circuit Parameter Estimation

Bo Ying, Su1, Yuchen Wu1, Chengtao Wen2, Changliu Liu1 1Carnegie Mellon
University, Pittsburgh, PA. Contact: {boyings, ywu7,
<EMAIL_ADDRESS>Corporate Technology, Berkeley, CA, 94704, USA

###### Abstract

Tactile and textile skin technologies have become increasingly important for
enhancing human-robot interaction and allowing robots to adapt to different
environments. Despite notable advancements, there are ongoing challenges in
skin signal processing, particularly in achieving both accuracy and speed in
dynamic touch sensing. This paper introduces a new framework that poses the
touch sensing problem as an estimation problem of resistive sensory arrays.
Utilizing a Regularized Least Squares objective function—which estimates the
resistance distribution of the skin—we enhance the touch sensing accuracy and
mitigate the ghosting effects, where false or misleading touches may be
registered. Furthermore, our study presents a streamlined skin design that
simplifies manufacturing processes without sacrificing performance.
Experimental outcomes substantiate the effectiveness of our method, showing
26.9% improvement in multi-touch force-sensing accuracy for the tactile skin.

Figure 1:  An overview of our proposed tactile skin sensing method. (a) Two
textile pieces with conductive stripes are separately knitted. (b) The two
textile pieces are sewn together orthogonally to create a grid of sensing
cells. The light pink fabric is made of Nylon Stretchy Yarn and the red
vertical fabric stripes are made of Acrylic Yarn. (c) The skin is modeled as a
resistive sensory array. Our approach predicts force applied on the skin by
estimating cell resistances $R^{C}$ using the Arduino board.

##  I INTRODUCTION

As robotics become increasingly integrated into everyday life, tactile and
textile skins have emerged as essential technologies for ensuring safe and
nuanced human-robot interactions [1]. While textile-based skins offer benefits
like scalability, low cost, and adaptability [2], they present signal
processing challenges, including nonlinearity and signal ghosting, that hinder
their practical application.

This paper introduces a new signal-processing framework designed to improve
the accuracy and reliability of the multi-touch force sensing of textile-based
tactile skins. We proposed the very first solution to achieve accurate multi-
touch textile-based tactile sensing relying entirely on textile materials. We
formulate the textile-based tactile sensing problem as a parameter estimation
problem for a resistive sensor array, which can be solved via optimization
techniques. This work focuses on the resistive sensing approach on textiles
due to its simplicity and robustness against deformation. Our framework
requires only one single-point force calibration in the beginning and can make
accurate multi-touch force predictions afterward. Our approach also
effectively mitigates ghosting by assuming that any sensing cell can influence
another, irrespective of the touch patterns.

Due to the enhanced multi-touch sensing capability, we further simplified the
tactile skin to a two-layer structure. The two-layer skin is subject to a more
serious ghosting effect due to direct contact between two conductive layers
despite its advantage of a much lower minimum detectable force. As our
solution considers a more general multi-touch scenario, our signal-processing
framework has significantly mitigated the undesired ghosting effect for the
two-layer skin, and therefore, unleashed its potential for lower minimum
detectable force. Experiments later demonstrated the lower detectable force
based on our integrated hardware-software solution.

The remainder of this paper is organized as follows: Section II reviews
related work in tactile skins and existing resistance estimation methods;
Section III describes our novel design for 2-layer textile-based tactile skin;
Section IV outlines our problem statement and proposed methodology; Section V
presents and discusses our experimental results; Section VI concludes the
paper.

##  II BACKGROUND AND RELATED WORK

###  II-A Textile and Tactile Skin

Tactile skins provide robots with the capability to sense pressure,
facilitating a wide range of applications from nuanced human-robot interaction
to advanced safe control mechanisms [3, 4]. Various fabrication techniques of
tactile skins have been proposed, including capacitive units featuring
flexible polyethylene terephthalate (PET) substrates [5], and piezoresistive
arrays with star-shaped strain gauges [6]. A detailed review of different
manufacturing techniques and effective utilization of tactile skins can be
found in this survey [6583342].

Recent advancements in textile-based tactile skins offer benefits like
scalability, cost-effectiveness, and stretchability [2, 7]. However, they
introduce unique challenges in signal processing. One significant issue is the
non-negligible wire resistances in conductive textiles, which makes the
accurate estimation of contact forces more complex. Another distinct challenge
arises from the alternate paths of current, which can lead to false touches or
ghosting when multiple simultaneous contacts occur.

This paper aims to address these specific challenges through a novel signal-
processing framework, thereby improving the performance and reliability of
textile-based tactile skins.

###  II-B Readout of Resistance Sensor Arrays

Our approach to estimating multiple contact forces relies on accurately
determining the resistance in each cell of a tactile skin array, connected in
rows and columns as shown in Figure 1(c). The challenge of accurately reading
resistance sensor arrays has been extensively studied along with many
different approaches [8, 9, 10].

Existing solutions to the readout problem generally fall into two categories.
The first involves the addition of extra electrical components to the array
for better resistance estimation. For example, Snyder et al inserted diodes to
calculate the current in each column’s sensitive elements and, subsequently,
their resistance [11]. Tanaka et al introduced transistors into a 128×128
resistive array for the same purpose [12]. While effective, these hardware
modifications introduce complexities, inflate costs, and compromise the skin’s
flexibility and stretchability.

The second approach employs a resistance matrix, first suggested in [13] and
later refined in [14], to estimate individual resistances. While this approach
is less complex than hardware modifications, it fails to account for wire
resistances and the uneven resistance distribution of textile-based tactile
skins.

In light of these limitations, we propose the first optimization-based
approach for textile-based tactile skins. Unlike conventional approaches, our
method does not assume constant wire resistances, which can change due to
stretching or bending. As a result, our approach enhances the accuracy of
contact force estimation, a claim substantiated by our comprehensive
experimental results.

##  III TEXTILE AND TACTILE SKIN:
DESIGN AND PROPERTIES

Our design builds upon the tactile skin model proposed by Si. et al [2], but
incorporates several modifications. Unlike the three-layered construction
suggested in their work, we employ a simplified two-layer construction by
removing the insulating layer. Our two-layer construction was chosen for its
ease of manufacturing and lower minimum detectable force. The readout
frequency of the tactile skin depends on the grid dimensions of the skin,
where 8x8 skin runs at a 90Hz readout rate.

###  III-A Working Principle

The functionality of our tactile skin is dependent on the interaction between
its two layers of conductive fabric. Upon applying pressure, these layers come
into contact, inducing a change in resistance. This change influences the
voltage across an associated resistor network, which can be measured through a
resistance measurement circuit. As more pressure is exerted, the contact area
between the layers expands, reducing the resistance and consequently altering
the voltage drop across the resistor network. This voltage drop serves as an
estimator for the applied force.

###  III-B Skin Material and Fabrication

Our tactile skin is made from three different types of fabrics, each serving a
specific purpose: Acrylic Yarn, the red portion shown in Figure 1 (b) offers
structure and durability. Nylon Stretch Yarn (MaxiLock Stretch Textured
Nylon), adds stretchability, and Bekinox-polyester Stainless Steel Yarn
(Baekert BK 9036129) provides conductivity. The Nylon Stretch Yarn and
Stainless Steel Yarn are co-knitted to form the conductive stripes of the
textile skin, which can be seen in the light color portion in Figure 1 (b). By
executing the knitting program written in the knitout language [15], the
skin’s top and bottom layers are first knitted individually with stripe
patterns. They are then joined along the edges of the conductive stripes using
a sewing machine, as illustrated in Figure 1.

###  III-C Properties and Characteristics

The skin’s minimum detectable pressure is primarily determined by two factors:
the inherent resistance of the conductive yarn, which is specified as
$20\,\Omega/\text{cm}$ for Baekert BK 9036129, and the deformation of the skin
under applied pressure. The stretchable properties of the yarn, combined with
the selected knitting pattern, confer bidirectional stretchability to the
skin. It should be noted that the resistance within the skin exhibits spatial
variations. Specifically, the resistance per unit length tends to be lower
along the yarn compared to that between stitches, resulting in a non-uniform
distribution of resistance. The resistance is generally lower in the course
(horizontal) direction compared to the wale (vertical) direction [16].
Furthermore, the resistance values lower as the skin stretches, adding
complexity to the skin’s resistance profile [16]. In this work, it is not
required to measure actual resistances of the skin as it is solved
numerically.

###  III-D Challenges in Tactile Sensing

Multi-touch tactile sensing in textile-based sensors presents multiple
challenges, including undesired ghosting effects and fluctuations in skin
resistance. Moreover, to preserve key attributes like manufacturability,
stretchability, and flexibility, it’s crucial to avoid adding extraneous
components. Maintaining a fabric-only composition not only ensures the
washability of the tactile skin but also minimizes the risk of electronic
damage. Given these design considerations, the following challenges are
intrinsic to the development of textile-based tactile sensors.

####  III-D1 Ghosting Effects

As shown in Figure 2 (a), false positive detections occur due to alternate
electrical paths between the skin layers. When three or more touches align on
a rectangle’s corners, the untouched corner mistakenly registers a touch, a
result of currents flowing an alternate path between the layers.

####  III-D2 Adaptation to varying skin resistance distribution

The tactile skin’s stretchability and flexibility introduce resistance
variations along the conductive stripes, which skews the skin output in multi-
touch scenarios. Traditional resistor matrix methods, designed to combat
ghosting, operate under assumptions that may not apply to textile and tactile
skins. Changes in resistance, due to stretching or bending, challenge accurate
force estimation.

((a))

((b))

Figure 2: (a): Ghosting effects occur when an alternate path of current (shown
in green) is formed for the sensing cell at the upper left corner, bypassing
it completely. (b): Ohmmeter Configurations. Details are provided in Section
IV(C). Algorithm 1 Resistance Estimation

1:procedure Resistance Estimation

2:$\triangleright$ Step 1: Take voltage measurement

3: $V_{s},V_{r}\leftarrow\text{four measurements for each cell}$

4:$\triangleright$ Step 2: Calculate initial circuit states

5: $R^{t},R^{b}\leftarrow 0$

6: $R^{c}\leftarrow\text{results solved with Ohm's law}$

7: $V^{t},V^{b}\leftarrow Simulation(V_{s},V_{r},R^{t},R^{b},R^{c})$

8: $P\leftarrow\\{V_{s},V_{r},R^{t},R^{b},R^{c}\\}$

9:$\triangleright$ Step 3: Solving WithOUT Regularization

10: $P\leftarrow solveLeastSquares(P)$

11:$\triangleright$ Step 4: Solving With Regularization

12: $P\leftarrow solveRegularized(P)$

13:end procedure

##  IV Algorithms for Multi-Touch Sensing

###  IV-A Modeling

We model the physical tactile skin structure as a simplified circuit
comprising resistors and voltage sources shown in Figure 1(c). This circuit
model mirrors the tactile skin’s construction, where both the top and bottom
layers consist of conductive stripes. These conductive stripes are represented
as resistors connected in series with unknown resistances, $R_{i,j}^{t}$ for
the top layer and $R_{i,j}^{b}$ for the bottom layer where $i$ is the row
index and $j$ is the column index. The point of contact between the top and
bottom stripes is similarly modeled as a grid of resistors with unknown
resistances $R_{i,j}^{c}$, whose value changes when different contact forces
are applied. A voltage source $V_{dd}$ is connected through a reference
resistor, multiplexed to one input to the skin resistor network, and is then
linked to another reference resistor before reaching the ground. The problem
of contact/force estimation problem is formulated as a parameter estimation
problem, where we aim to solve unknown sensing cell resistances $R_{i,j}^{C}$.
By applying different voltages to the top and bottom layers, we obtain the
total voltage drop across the skin’s resistor network from pairs of electrodes
across rows and columns. We then employ optimization techniques to estimate
these unknown resistances, which are subsequently used to predict the force
applied to the skin.

###  IV-B Overview of the Solution Approach

Our approach to multi-touch force sensing using textile-based tactile skin
comprises two stages. The first stage performs one-time single-touch force
calibration. Given the readout data acquired from the Ohmmeter circuit, we
estimate the cell resistances $R_{i,j}^{c}$ of the skin using the proposed
resistance estimation algorithm shown in Algorithm 1 and fit them to simple
linear regression models for each cell, which predicts the applied force. The
second stage is the estimation stage, where the skin cell resistances are
solved online using the same optimization program. Multi-touch forces are
predicted by the regression model created in the first stage using the solved
resistances.

###  IV-C Readout Process

In the readout process, we first take four distinct measurements for each cell
using different ohmmeter configurations. The four distinct ohmmeter
configurations, labeled A, B, C, and D, are employed for each sensing cell as
shown in Figure 2(b). This dual-layer strategy effectively compensates for
reference resistor tolerances and addresses the non-ideal behavior of tactile
skin by eliminating systematic errors.

###  IV-D Resistance Estimation

In both calibration and estimation stages, we are using the same procedure to
solve for unknown sensing cell resistances $R_{i,j}^{C}$, as shown in
Algorithm 1. The process of resistance estimation is as follows: Given the
measurements for each cell using different ohmmeter configurations in the
readout process, we create circuit state variables by applying the circuit
model of the skin shown in Figure 1(c), aiming to find a set of unknown
resistance and voltage values $R_{ij}^{T}$, $R_{ij}^{B}$, $R_{ij}^{C}$,
$V_{ij}^{T}$, and $V_{ij}^{B}$ that best explains the observation. We
bootstrap the optimization program by calculating initial resistances for each
cell assuming zero wire resistances. Following this, we run circuit
simulations using the estimated resistances to obtain the initial voltage at
each circuit node. These initial values provide a starting point for an
optimization program designed to refine the estimated resistances and
voltages. The optimization process consists of two stages: the first focuses
on finding a least squares solution that complies with Kirchhoff’s Law and
Ohm’s Law shown in step 3, while the second stage aims to regularize wire
resistances to yield regularized values shown in step 4.

###  IV-E Proposed Optimization Program

We define the decision variables to the proposed optimization program as a set
of circuit states, each of which corresponds to one measurement using the
Ohmmeter circuit. A circuit state of each measurement consists of 5 sets of
variables: $R_{ij}^{t}$, $R_{ij}^{b}$, $R_{ij}^{c}$, $V_{ij}^{t}$, and
$V_{ij}^{b}$.

Our optimization program enforces circuit equality constraints for each
circuit state based on Kirchhoff’s Current Law and Ohm’s Law. This ensures any
feasible solution the solver returns to also be a valid solution to the
circuit model.

###  IV-F Least Squares Objective Function

We design the objective function to be the sum of the squared discrepancies
between the resistance values among the circuit states. We define two least
squares objectives. The first objective $Cost_{f}$ is the sum of discrepancies
between the $A$ and $B$ configuration and the sum of discrepancies between the
$C$ and $D$ configuration. Let

${}^{k}P=\\{^{k}R^{t}\cup\ ^{k}R^{b}\cup\ ^{k}R^{c}\cup\ ^{k}V^{t}\cup\
^{k}V^{b}\\}$ (1)

be the set of unknown variables in the circuit states with ohmmeter
configuration $k$. We define

$Cost_{f}=\sum_{p\in P}(^{A}p\ -\ ^{B}p)^{2}+(^{C}p\ -\ ^{D}p)^{2}$ (2)

Since $A$ and $B$ configurations and $C$ and $D$ configurations consist of
consecutive measurements with the same input voltage configuration, we assume
both the voltages and resistance values would not change much between the two
measurements.

The second objective $Cost_{c}$ is the sum of discrepancies between the
circuit states over measurements in all the cells with the same ohmmeter
configurations. Let

${}^{ij}Q=\\{^{ij}R^{t}\cup\ ^{ij}R^{b}\cup\ ^{ij}R^{c}\\}$ (3)

be the set of unknown resistance variables in the circuit states when
measuring the cell at column $i$ and row $j$. We define

$Cost_{c}=\sum_{i=1}^{n}\sum_{j=1}^{m}\sum_{q\in Q}(^{ij}q\ -\
^{i(j+1)}q)^{2}$ (4)

Note that the comparison is conducted in column-major order, which aligns with
the readout sequence. For example, when solving a $2\times 2$ skin, a squared
cost is defined for the discrepancy between the circuit state when measuring
the cell at (1, 1) using ohmmeter configuration $A$ and the circuit state
measuring (2, 1) under the same ohmmeter configuration $A$. This approach is
based on our assumption that the resistances remain stable between consecutive
measurements. The full least squares objective function is defined as follows:

$Cost_{lsq}=\alpha Cost_{f}+\beta Cost_{c}$ (5)

where $\alpha$ and $\beta$ are hyper-parameters where we set both to 1.0e6.

###  IV-G Regularization

Since the circuit states create underdetermined systems of equations, we add a
regularization term to the objective function to ensure the solution is
unique. We applied the $L_{2}$ regularization term to the objective function
that penalizes large wire resistances in the top and bottom stripes. For each
circuit state, a regularization term is added, defined as

$Cost_{r}=\sum_{i=1}^{n}\sum_{j=1}^{m}(R_{ij}^{t})^{2}+(R_{ij}^{b})^{2}$ (6)

As a result, the optimization program ensures both the circuit is feasible by
complying with Kirchhoff’s current law, and the wire resistances are small for
each circuit state, as the force signal would be more likely to be attributed
to changing cell resistances. The regularized objective function is defined as

$Cost_{reg}=\alpha Cost_{f}+\beta Cost_{c}+\lambda Cost_{r}$ (7)

where $\lambda$ is the regularization weight where we set it to 1.0e9. We also
set $\alpha=1$, $\beta=1$. In practice, we found that as long as the skin
itself is not stretched or bent too violently in a short time, the solver can
find local optimum solutions quickly using the previous solution as a starting
point.

###  IV-H Optimization

In our optimization process, we employ the interior-point algorithm to find
the best-fitting circuit parameters using the Ipopt solver [17]. Given the
initial resistances obtained using Ohm’s Law and initial voltages obtained
using a circuit simulator [18], we first solve the optimization program
without the regularization term for least squares objective $Cost_{lsq}$, then
solve the program with the regularization objective $Cost_{reg}$. We scale the
resistance values close to 1 to maximize machine floating-point precision and
use the inverse of resistance to represent constraints in the optimization
problem.

###  IV-I Force Prediction

In the calibration stage, we collect single-point calibration data using a
robotic arm with a Robotiq FT 300-S Force Torque Sensor attached to its end
effector, which the force sensor has a signal noise of 0.1 N. We create linear
regression models for each sensing cell using the calibration data. We rely on
the single-point calibration models to predict force given the solved
resistance values in the estimation stage, where multiple touches may present.

Ground
Truth
---
Naive
Solution
Feasible
Solution
Optimal
Solution
0.00010.00050.0010.0210.041$0$$0.5$$1$Wire Resistance $(M\Omega)$RMSENaive
Error $(M\Omega)$Least Squares Error $(M\Omega)$Regularized Error $(M\Omega)$
Figure 3: Simulation results for varying wire resistances in tactile skin.
Brighter colors denote lower resistances, ranging from $0\Omega$ to
$1.0M\Omega$. The pressed cells are assigned a lower$0.001M\Omega$ resistance,
while unpressed cells have higher$1.0M\Omega$. Wire resistances vary as
$0.0001-0.041M\Omega$ from left to right. These values are typical for our
setup. Ground
Truth
---
Naive
Solution
Feasible
Solution
Optimal
Solution
0.010.070.090.50.7$0$$0.5$$1$Cell Resistance $(M\Omega)$RMSE $(M\Omega)$Naive
Error $(M\Omega)$Least Squares Error $(M\Omega)$Regularized Error $(M\Omega)$
Figure 4: Simulation results for tactile skin with variable cell resistances.
Brighter colors denote lower resistances, ranging from $0\Omega$ to
$1.0M\Omega$. The pressed cells are simulated with resistances of
$0.01-0.7M\Omega$ displayed from left to right. Unpressed cells have a fixed
resistance of $1.0M\Omega$, and wire resistances are $0.001M\Omega$. These
values are typical for our setup.

##  V EXPERIMENTAL EVALUATION

To validate our method, we have conducted several experiments in simulation
and with real robots.

###  V-A Simulation Validation

We use the circuit simulation tool [18] to assess our optimization algorithm
for cell resistance estimation. Using the prior circuit model, we simulate the
ghosting effect by varying wire resistances between 0.0001 $M\Omega$ to 0.041
$M\Omega$ and cell resistances from 0.01 $M\Omega$ to 0.7 $M\Omega$.

Results on the effects of wire resistance variation are in Figure 3. Here,
three cells with lower resistances were pressed, revealing anticipated
ghosting, especially in the top-right cell as shown in Figure 3 Naive Solution
row. In comparison, our algorithm reduces ghosting, evident in the lower Root
Mean Square Error (RMSE) in Figure 3 Feasible Solution row. While the
regularized solution in the Optimal Solution row introduces a regularization
term to further reduce RMSE, it underperforms in scenarios with high wire
resistances.

To gauge accuracy in varying cell resistances with constant wire resistances,
results are in Figure 4. The naive approach struggles with high cell
resistances as depicted in Figure 4 Naive Solution row. Conversely, our method
recovers resistances with low RMSE, shown in Figure 4 Feasible Solution row.
The solution in the Optimal Solution row further optimizes RMSE but struggles
when cell resistances are below wire resistances, aligning with prior wire
resistance findings.

((a))

((b))

((c))

Figure 5: The Force Estimation experiment setup. (a) flat surface experiment
setup and (b)curved surface experiment. (c) two-layer design of the skin
allows the detection of tiny forces as low as 1N. Blue dots represent a
single-point training set. Red dots represent a multi-touch test set.

(1, 1)(2, 1)(1, 2)(2, 2)$0$$2$$4$$6$$8$Cell Index (Row, Column)RMSE (N)Naive
Calibration$(M\Omega)$Solved Calibration$(M\Omega)$Naive
Estimation$(M\Omega)$Solved Estimation$(M\Omega)$

Figure 6: Flat Surface Experiment. Single-touch force calibration is performed
once to create a calibration set for the linear regression model. Our method
achieved lower multi-touch error compared to the naive approach which predicts
force from with raw voltage.

(1, 1)(2, 1)(1, 2)(2, 2)$0$$2$$4$$6$$8$Cell Index (Row, Column)RMSE (N)Naive
Calibration$(M\Omega)$Solved Calibration$(M\Omega)$Naive
Estimation$(M\Omega)$Solved Estimation$(M\Omega)$

Figure 7: Curved Surface Experiment. Single-touch force calibration is
performed to create a calibration set for the linear regression model. Our
method achieved lower multi-touch error compared to the naive approach which
predicts force from with raw voltage. Figure 8: Time series data of 4 seconds
with the robot tip pressing cell (2, 2). For the middle and bottom figures,
Blue: cell (1, 1) and Red: cell (2, 1). Black: cell (1, 2). Gray: cell (2, 2).
Top: Force Torque sensor readings at cells (2, 2). Middle: Raw voltage from
the readout of the skin. Bottom: Solved conductance.

###  V-B Force Estimation

We conducted real-robot experiments using a Kinova Gen3 robot with a force-
torque sensor to evaluate our method’s force estimation accuracy, comparing it
to ground truth measurements and an existing approach.

In the first experiment, the tactile skin was set on a flat surface and
pressed by a robot’s flat tip. The robot’s tip moves gradually toward the
skin, incurring varying levels of pressure. The pairs of data from both the
force sensor and the tactile skin are used for calibration. After calibrating
the sensor, single-point touches formed a calibration set through linear
regression. Using this model, we estimated forces on cells (1, 2) upon placing
two 100g weights on cells (1, 1) and (2, 1). With known ground truth forces,
our method reduced the RMSE by 27.3% compared to the existing “Naive”
approach, which directly estimates forces from voltages. The results are
displayed in Figure 6.

The skin was placed on a curved surface for the second experiment, altering
its resistance distribution. Comparisons with the Naive approach revealed our
method enhanced accuracy by 26.4%, as seen in Figure 7.

###  V-C Time Series

We evaluated the tactile skin’s time-series data using our algorithm. The
force reading results shown in Figure 8 indicate that the algorithm
effectively mitigates the ghosting effects caused by force applied on the same
row or column, as evident from the reduced correlated noise in cells (1, 2)
(Black) and (2, 1) (Red) due to the pressing cell (2, 2) (gray).

###  V-D Minimum Detectable Force

Attributed to the two-layered design which removes the physical threshold
presented by the middle layer, our proposed method could detect tiny force as
low as 1N in the presence of multiple touches, shown in Figure 5.

###  V-E Scalability

Our algorithm runs at 11 samples/second, on an AMD 7940HS Laptop CPU for a 2x2
skin, taking on average 30 iterations and 40ms for a least squares solution
and 25 iterations and 50ms for the regularized solution. Textile skins as
large as 16x16 have been manufactured and shown robust single-touch
performance. However, on larger skins, such as 3x3 as shown in simulation, we
are unable to achieve real-time performance due to the non-linear programming
nature of the problem.

##  VI CONCLUSION

In this paper, we formulated multi-touch force sensing using textile-based
tactile skins as a circuit parameter estimation problem. By employing a
Regularized Least Squares objective function and optimization techniques, we
mitigated the ghosting effects while achieving accurate multi-touch cell
resistance estimations in both simulated and experimental environments. Our
approach improved existing methods by reducing error rates in force prediction
by 27.3% on flat surfaces and 26.4% on curved surfaces in multi-contact
scenarios.

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