Supplementary Information for Targeted Feature Recognition Using Mechanical Spatial Filtering with a Low-Cost Compliant Strain Sensor

In this section, the strain as a function of notch displacement for three shapes is modeled. The triangle example goes through the mathematical model steps of the paper in detail, and then shows a simple geometric approach that gives the same result. This is followed by a hemisphere example in which the parametric equation for the mathematical approach is provided, and then the geometric approach is detailed. Finally, the strain profile is derived for a rectangular feature.

So v increases from 0 to h/2, as is evident from the figure. The value of the reference point f(u + x max ) is h/2. To the left of the apex, for h/2 < x' < 3h/2 (or 0 < which is greater than 0 only for h/2 < x' < h. For 3h/2 < x', v(x',h/2) = 0.
Next any take-off points are found. To the right of x max , this would occur if Just above x' = h/2 (at x = h + ), the slope of the triangle is , and the slope of the straight line from the apex to the corner is Since the former is not less than the latter, the membrane follows the surface. To the left of x max , the condition is instead The slope of the triangle feature there is then while the slope of the straight line from the apex to the corner is given by The condition for take-off is met at the apex, p 1 = h, so the membrane leaves the surface.
Next find the total deformed length of the membrane, given in general by by: For this case, to the right of the apex v is given by equation (3), and to the left of the apex Within the notch, this corresponds to a strain of 0.26/3.0 = 8.6%.
Geometric model. It is often simpler to find the strain using a geometric model. The same triangle is used here as in the previous section, but for convenience we define an x-axis variable x 1 with x 1 = 0 at the left inner edge of the notch (Supplementary Figure S2).

Supplementary
Considering penetration of the triangle into the left half of the notch, the tip penetrates to a maximum of The deformed membrane length is thus given by where x 1 is the distance of the probe tip from the left edge and This is the same result as found in equation (13). To find the strain on the right side of the notch, the results are mirrored by exchanging the definitions of x 1 and x 2 .
Groove dimensions. To gain an intuitive understanding for the presence of the ghost artifacts in the image shown in Figure 4b of the paper, the geometric model was used to evaluate the strain created by a triangular feature. In the experiments the braille dots were 0.7 mm tall, so this value was used for h here. The model was evaluated for values of x 1 between 0 and b. The first groove was wider and taller than the feature, with a width of b = 5 mm. Supplementary Figure S3a shows the strain as a function of contact position. The strain increases until x 1 = h and then decreases again as the feature moves beyond that point towards the center.

Supplementary
The x-positions of the peaks are related to the width of the surface feature. For the triangle, the peaks occur at a distance h from the two edges, when the triangle first (or last) fully indents the membrane. A wider object would therefore result in more closely spaced peaks, reaching the limit of a single peak when the feature size matches the groove, i.e. when 2h = b in this example, as shown in Supplementary Figure S3b. The distance to the ghost signal can therefore in principle be used to determine the size of an object smaller than the groove. The peak amplitudes remain unchanged until the feature becomes wider than the notch, when the amplitude decreases.
Hemisphere Example The tops of the braille dots can be approximated as hemispherical, with a half-circle crosssection.
Mathematical model. Choose u = r/2. To calculate the strain using the mathematical model, the same procedure would be followed as above but using a parametric equation for a circle, putting x = 0 at its left edge:

Supplementary
Find the displacement field v.
This is greater than 0 for 0 < x' < h/2, as shown in Supplementary Figure S5 by the red line, found numerically.
Supplementary Figure S5. Mathematical mode for semi-circle example with r = h = 0.7, b = 3h, u = h/2. Note that x' is shown on the same x-axis.
Find the take-off points and connecting lines. To the right of x max , by inspection of Supplementary Figure S4, there is no p 2 . This is confirmed comparing the slope of f(x) to the slope of a line from the point to the notch inner corner. To the left of x max , we need to find p 1 by comparing the local slope of the function with the connecting line: This was found numerically to be at the top of the semi-circle. The slope is then given by Find the length of v(x',u) and the strain. The length is found by integrating. Here L ex is taken as zero.
The v(x',u) used in this calculation is shown by the red line in Supplementary Figure S6, and its slope is shown by the dashed blue line.
The strain is found to be 0.35%. To map out the strain as a function of u, this process is repeated for each u. The three segments of v(x',u) for two u = 1 and u = 2 are shown in Supplementary Figure S7. The strains in these two cases were 6.37% and 4.12%, respectively.

Geometric model.
Supplementary Figure S8. a) Geometric model for a circular cross section as the feature begins to penetrate into the notch and deflect the membrane. b) When the feature has penetrated its full height into the notch.
A geometric model (Supplementary Figure S8) was used to find the strain as a function of u because of the relative simplicity of this approach. For the case that x 1 < r, when the feature only partially penetrates into the notch, the following relationships hold true.
When r < x 1 < b/2, the feature penetrates to its maximum height into the notch, and these relationships apply instead.

Intuitive explanation.
Assuming that the finger is in continuous contact with the target surface (the experiments used a fixed vertical offset from the surface), as its x-position varies, so does the part interacting with the surface. In some positions, the bottom-most tip of the probe touches (Supplementary Figure  S10a, pink cases 1 and 3), at other times the rounded edge does (blue case 2), and when the probe is over a small feature, the membrane is in contact and is deflected (green case 4). The probe vertical position therefore changes, as indicated by the bars in Supplementary Figure  S10b, which are color-coded to indicate the cases. The regions that produce a change in resistance (green bars) are boxed. If the signal is proportional to the membrane deflection, neglecting secondary effects, then its appearance will be as shown in Supplementary Figure  S10c. This agrees with the shapes of the peaks shown in Figure 5d,e in the paper.

Nonlinear Amplification
The experiments used a constant offset from the surface, which is equivalent to case 3 (notch less deep than the feature height). To show the effect of increasing the depth of contact (as was done in Figure 6b-

Supplementary Figure S13. Geometric model for a rectangular cross section. Note that the definition of x 1 differs here from the previous cases; the results can be aligned by shifting the xaxis by w/2.
For a rectangle of height h and width w, the feature goes abruptly from being outside the notch (no strain, L d = b) to entirely within the notch. The geometric model (Supplementary Figure  S13) is: The results are shown in Figure 5d of the paper.

Time Course Data for a Single Touch
Data for a single touch are shown in Supplementary Figure S14. There is a baseline voltage before the touch, an immediate rise in voltage when the membrane is strained by the braille dot (corresponding to an increase in resistance R), followed by a graduate drop that does not return all the way to the baseline due to viscoelastic effects.
To form the images in the main text, the baseline voltage before the first touch of the scan was subtracted from the peak voltage. The adjusted voltages were converted to resistance and then normalized by the baseline resistance to yield R/R.

Initial Characterization with an Indenter
Before attempting braille scans, the sensor was characterized by bringing the finger (groovewith-foam variant) repeatedly into contact with a 0.25'' (6.4 mm) diameter wooden dowel (the "indenter"). The finger was positioned to center a single sensing strip above the indenter. The sensor was brought into contact sequentially at three different depths: 0.5 mm, 1 mm, and 1.5 mm, measured from the lowest finger position at which the sensor generated no signal. Touches were separated by 10 seconds, and the series of three touches was repeated 40 times. Supplementary Figure S15 and Supplementary Figure S16 show the response of the sensor over the course of the test. In Supplementary Figure S15, the response is plotted versus time over the duration of the test. In Supplementary Figure S16, the time-series data are partitioned by sets of three touches, with the repetition number indicated by color. Apparent in both is a conditioning effect: the signal decreased as the test progressed. This effect may have been due to the mechanical properties of the foam substrate or the latex skin or both.

Supplementary
In an attempt to correct for the conditioning effect, the baseline resistance at the start of each repetition was subtracted, as shown in Supplementary Figure S17. The conditioning effect was mostly removed. There remained a large drop after the first set of touches, but the decay between subsequent touches was much smaller. The signal in these figures contained notably more noise than the figures in the main paper. This was due to the use of a different power supply (Hantek PPS2116A), which became noisy when it was left on for extended periods.

Zeroing Between Bumps
Based on the indenter tests, the baseline between touches was subtracted from the discrete braille scan. The results, processed from the raw data in Figure 4b, are shown in Supplementary Figure S18.
Supplementary Figure S18. Normalized change in resistance from the baseline before each touch.
The braille pattern was more evident when the baseline was taken only once at the beginning of the scan than before each touch. This was contrary to our expectation. Some key differences might explain this discrepancy. Firstly, the design of the finger was changed between the indenter tests and the braille scan: the foam was removed and the groove was narrowed. Secondly, the 6.4 mm wooden dowel was larger than the 1.5 mm braille bump.
At first glance the image appears noisy, with sharp peaks in places that do not seem to correspond with the braille bumps. However, the pattern was consistently repeated in four independent scans (not shown). It is possible that the sharp points in Supplementary Figure  S18 occurred because, since the grid of points used to scan the braille plate does not coincide with the braille geometry, at some points the braille bump lies more cleanly within the groove of the finger than at others.
In an attempt to recover the overall shape of the braille plate from the moving-baseline data, they were convolved with a 2D Gaussian filter with  roughly corresponding to the size of a braille bump. The result is shown in Supplementary Figure S19. The image improved, but was still inferior to the unprocessed image.
Supplementary Figure S19. Normalized change in resistance from the baseline before each touch after convolution with 2D Gaussian filter ( = 1 pixel).

Images from Strips on Same Membrane
Supplementary Figure S20 shows images from all three strips on one sensing skin; the center strip produced Figure 4b in the main paper. While the outer strips malfunctioned slightly at the end of the scan, the same basic response is visible in all three. The relative lateral offset of the images corresponds to the distance between the sensing strips.
Supplementary Figure S20. Results from three strips on same membrane during same scan.

Images from Finger with an Insert
Another type of finger was fabricated after the finger with the 5 mm wide groove and before the 3D printed finger. In this finger, the foam was replaced with an insert that reduced the width of the groove to 1.6 mm, comparable to the width of one braille bump (Supplementary Figure S21). The rigid insert was laser-cut from Delrin, and then ground on a bench grinder to its final profile. The groove in the insert was left empty.

Supplementary Figure S21. Schematic illustrating the finger with an insert.
Images were produced with the second finger from four sensing skins using the same discrete scan procedure. The best result is shown in Supplementary Figure S22b. The peak positions again perfectly corresponded to the braille pattern. The peaks had a larger diameter, close to the diameter of the braille dots. As shown in the main text, this indicates that the depth of contact was greater in this scan. There was significant streaking, with the signal not returning to the baseline for quite some time after the membrane was deflected by a dot, also consistent with the greater indentation. It should be emphasized that using materials with lower viscoelasticity would reduce or eliminate the streaking, but regardless, the pattern could still be readily identified.
There was again a ghost image, albeit fainter than for the first finger, offset in the y-direction by 2.0 mm. The hypothesis for the ghost features in this image is illustrated in the corresponding schematic, Supplementary Figure S22a. A strong signal was generated from the good localization produced with the narrow groove. However, the machined insert had been handmade and inserted, and it did not fit perfectly flush with the surface. Therefore, there were sections over which the membrane was not fully supported, but was suspended with a gap between the insert and the rest of the finger. When the dot deflected the membrane at this location, a faint ghost image resulted.
To test this supposition, the depth of contact was reduced by decreasing the distance travelled by the z-actuator. This was expected to eliminate the contact of the braille dot with the membrane suspended over the outer edge of the insert. The resulting image is shown in Supplementary Figure S22d. The ghosting was considerably reduced, without significantly diminishing the primary signal, and the dot diameter decreased slightly. The resolution between dots also improved by reducing the horizontal streaking: smaller deflections result in less viscoelastic deformation. The two closely spaced dots on the lower left slightly blended together, indicating their separation was approaching the limit of the resolution. The resolution could be improved by making the groove narrower, although that would also reduce the signal amplitude. For this application, in which the size of the dots is known, the presence of two features is clear.
These results corroborate the conclusion that if the underlying geometry allows for strains in more than one place, a ghosted image will be generated. A smooth finger is thus required that perfectly supports the membrane so that no artifacts are introduced.

Discussion of the Materials
Robustness is important for tactile sensors. The particular latex membranes used here are a shortcoming of the current prototypes. Both types of membrane use in this work degraded rapidly (within a week) upon clamping, becoming sticky and soft. Latex is also known to wear away under extended contact 1 . In future work, the latex sheet should be replaced with a more robust membrane material.
The membranes used in this work experienced viscoelastic deformation, leading to streaky images. Appropriate corrections to the baseline based on the scanning history may mitigate this (Supplementary Figure S17), or the viscoelastic effect could be handled with software 2 , but a more elastic material may be preferable. We had previously characterized the sensing membrane 3 , but in future work, researchers will no doubt use other types of sensors, other elastomeric materials, and other methods of fabricating the cavity. Therefore, instead of focusing on the sensor performance, we focused on understanding how the finger geometry and interaction with the surface affected the images, and we provided general guidelines for design and materials.
Although rubber fingertips provide advantages in gripping tasks, stickiness is not ideal for scanning, since it leads to membrane strain, and thereby interfering signals. The combination of stretchability and the ability to slide has been achieved in silicone rubber skin by creating a matte surface finish 4 . Coatings or an inherently less tacky membrane material could also be implemented.
The membranes were held taut over the finger surface with two metal clamping plates ( Figure  2d). At times the handling and clamping process damaged the sensors or the connections, rendering some of the sensing strips inoperable. The clamping method should be further investigated.

Possible Future Directions
The cavity shape under the membrane could be specialized to target shapes of a given size, such as a hexagonal bolt head, or an interior occlusion could be added for detecting rings. This shape recognition would not require an array. There is also a practical consideration concerning wiring. A strip sensor permits electrical connections to be made at the back or side of the finger.
In the variation of the device illustrated in Figure 8c, a round bump would likely be the most typical. However, the spatial matching could in principle be made different along the x and y axes by using an oval-shaped bump. Such a sensor would additionally detect steps, since it would compress one side of the membrane, which the current configuration cannot do. In principle one could combine bumps and divots on the same fingertip.