Evaluating the use of a tactile sensor for measuring carton compliance

Paperboard packages

The packages used throughout this study were manufactured on a flatbed cutter (Esko-Graphics, Gent, Belgium). The packages were all made from clay-coated virgin paperboard, in a range of grammages from 239–486 g/m². The material was manufactured on an industrial scale paperboard machine. All in all, 8 different materials and 3 different package designs were tested. The packages labeled I–III are summarized in Table 1. Material data for the materials A–H are summarized in Table 2. Values for bending resistance geometric mean (BR GM in Table 2) were used to distinguish the package materials (plotted on X-axis of Figures 4–5).

Exploratory procedure

The design of the EP for this experiment was based on a pre-study. Subjects were presented with a set of packages of the types I and II and were asked to fill out a simple questionnaire about the package. The packages used were plain white, and subjects were given no other information about the product or the market segment targeted. Package I was filled with two layers of chocolate (weight 530 g) of the type Aladdin (Mondelēz Sverige AB, Upplands Väsby, Sweden). Package II was filled with a bottle of Blossa Glögg (750 ml, 1260 g) (Altia Sweden, Kungsängen, Sweden).

Subjects (n=44) were recruited at a supermarket in Sweden. They were first asked to state their gender, age, and dominant hand. There were 28 female and 16 male participants with median age of 59. Three had a dominant left hand and the remaining 41 had a dominant right hand. They were then requested to pick one out of four words describing each package. The words were stable, unstable, durable, and weak. These words were chosen so that the subjects would employ relevant EPs. Furthermore, the subjects could give a free-text answer.

By studying how the subjects explored the packages during this exercise, it was possible to identify loading directions that are important for the consumers’ perception of the package. From the identified load cases, we defined a simplified EP. We chose to simplify the EP by excluding tangential forces. This is justifiable because a paperboard package is a shell structure, and hence can cope well with membrane stresses. The implemented EP is designed to mimic the compression of a package with one finger while the package is resting on a flat rigid surface, see Figure 1.

Figure 1

The modeled exploratory procedure.

BioTac sensor

The tactile sensor used in phase two was a BioTac 2P (SynTouch Inc., Los Angeles, CA, USA)(Wettels et al. 2008). The BioTac is modeled to mimic the sensory capabilities of the human finger. The BioTac consists of a rigid epoxy core, surrounded by an elastomer skin, with a conducting liquid filling the void. A total of 19 Electrodes embedded in the core measure the changes in impedance caused by displacement of the liquid. The signals from the electrodes are digitized at 100 Hz. Figure 2 shows the distribution and numbering of the electrodes on the BioTac.

Figure 2

Photos of the BioTac fully assembled (A) and the BioTac core with electrode numbering (B).

Additionally, the BioTac has a pressure sensor and a thermistor. The pressure sensor measures the pressure inside the liquid. This signal is filtered through a low pass filter and digitized at 100 Hz on the PDC channel. The pressure sensor is also high pass filtered, amplified and digitized at 2200 Hz on the PAC channel. The thermistor is also digitized and provided in a low pass filtered version and a derivative version.

The BioTac has been used successfully for force and compliance determination in the previous experiments (Ciobanu et al. 2014, Wettels and Loeb 2011), which made it a good candidate for this experiment.

Experimental setup

The setup (Figure 3) consisted of the BioTac with data acquisition hardware and software, an AMTI six-axis force plate with DAQ (NI6218) and data acquisition software (NI LabView). The BioTac was mounted on an aluminum bar with screws that replaced the ones that normally hold its fingernail. The angle of the aluminum bar to the vertical line was 79°. This angle caused the flat part of the core of the BioTac (see further discussion below) to be parallel to the package before deformation. The aluminium bar was attached to a manipulator that allowed vertical movement. A thick plywood sheet was fixed to the force plate using double sided tape. This extended the area that packages were placed on in order to make sure that the entire package was supported.

Figure 3

Experimental setup from the side (A) and front (B).

The BioTac was used with the standard sampling sequence. The order is low pass filtered pressure (PDC), temperature derivative (TAC), temperature (TDC), and electrode impedances (E1−E19). Between each sample from these channels, the high pass filtered pressure (PAC) is sampled. The total sampling frequency was 4400 data points per second.

The BioTac was slowly pushed against the top surface of the package until a static vertical force of 4 N was recorded. The distance from the edge of the package a was varied between two values (18 and 22 mm) reflecting a likely range of variability in human exploration. BioTac sensory data at 4 N force were generally overlapping for these two distances, as illustrated in Results.

The data acquisition was conducted on two different computers. One acquired the signal from the BioTac and one acquired the signal from the force plate. These signals were synchronized using a custom programmed BioTac board that sent out a 100 Hz clock signal that was used to trigger the acquisition on the NI6218 board.

In some experiments, the trigger function failed for unknown reasons, which lead to the force plate data lagging behind the BioTac data. The external clock still managed to maintain equal spacing of samples. In these cases, the data was realigned by visual inspection of the graphs of the vertical force and BioTac pressure signal. The accuracy was estimated to be 20 ms (two samples), which is slightly worse than the automatic synchronization which should be accurate to at least ±5 ms (half a sample).

BioTac measurements

Only the electrodes and the PDC signal from the BioTac were analyzed. PAC was not studied because it was completely dominated by variations in the compression rate. The thermistor signal was not of interest for this work. We paid particular attention to electrodes 7–10, which are located on a flat region of the rigid core that mimics the apical tuft of the human distal phalanx. The voltages measured by these electrodes are inversely related to the impedance of the conductive liquid that is squeezed between the electrodes and the overlying skin. These voltages have been shown to be strongly influenced by small tilts of flat surfaces against which the finger is pressed, similar to the presumed sensory function of the apical tuft during precision grip in humans (Su et al. 2016). This is particularly true for small tilts around parallel alignment between the flat on the BioTac core and the surface against which it is pressed.

Su et al. (2012) showed that PDC is dependent on the compliance of the surface. In the current case, we must consider the structural stiffness of the paperboard. This depends on the bending resistance of the material as well as the geometry of the package. Because both grammage and SCT are strongly correlated with bending stiffness of the material, we did not expect to distinguish among the three in a regression model. Because compliance has been shown to correlate with PDC, it makes sense to include the bending resistance and not SCT, grammage, or another correlated quantity. Our first attempt was the ordinary least squares model

where the hat indicates an estimated value, w, d and a are defined in Figure 3 and BR is the geometric mean bending resistance. Inspecting the data of Su et al. (2012) more closely, it looks like the pressure has a linear relationship with durometer A. For a homogenous material, durometer A has an approximate linear relation with the logarithm of Young’s modulus (Qi et al. 2003). In the case of thin paperboard packages, Young’s modulus is not relevant, but we can use the structural stiffness instead. If we consider a simplified model of the panel as a simply supported beam of length L and bending stiffness EI, the compliance, i. e. the inverse of stiffness, at a point a distance a from one of the supports is

In the current case, the inset a is small compared to L so a purely multiplicative model containing the factors w, h, a, and BR would probably be a good fit for estimating the compliance. Therefore, we take the logarithm of all the explanatory variables, but not of the predicted variable. The final model becomes

For the sake of completeness, both models were considered in the results. The same model structures were also used for the sum of electrodes 7–10.

Linear discriminant analysis (LDA)

Linear discriminant analysis (LDA) is a supervised dimensionality reduction method that seeks to find the linear subspace of the original feature space that maximizes the difference between classes. In contrast to principal component analysis (PCA), a related unsupervised method for dimensionality reduction, LDA will only retain variance that is meaningful, i. e. has predictive power (Hastie et al. 2001).

In this case, we used LDA to determine which electrodes are informative in distinguishing between packages made from board of varying bending stiffness. While we have already provided hypotheses for this and shown the correlation with bending stiffness, we wanted to verify that these are in fact the electrodes with the most explanatory power. We first applied a scaling transformation to the dataset, bringing the mean to zero and all variances to 1. We then applied LDA, defining each combination of package and grammage as one class, ignoring differences in inset a. This will make sure that the extracted combined features are robust to slight differences in a, which will be useful since the alignment of this dimension is difficult to get accurate.

LDA makes the important assumption that the covariance matrix is identical for all classes. Considering that we have relatively few samples of each class, we do not have enough data to be able to reliable estimate the differences between classes so this assumption should be sensible.

Figure 4

DC pressure at 4 N versus the logarithm of the bending resistance of the board. PDC at a given force is essentially a measure of contact area. Increasing bending stiffness decreases contact are and thus gives lower PDC.

Figure 5

Sum of the electrodes E7-E10 at 4 N versus the logarithm of the bending resistance of the board. Increasing bending stiffness leads to smaller contact area and hence more liquid displaced around the contact. Displacement of liquid translates into higher impedance, which is digitized by the BioTac as a lower binary value.

Linear discriminant analysis

Figure 7 shows a visualization of coefficients of the first discriminant function, which explains 85 % of the variance. LDA confirms that the most important sensors are the pressure and the tip electrodes 7–10. However, the tip electrodes should have alternating signs, effectively computing a second spatial derivative in the distal direction. This analysis gives a rigorous motivation for the sensors we choose to study in detail.

Figure 7

Visulization of the first discriminant function. The color intensity shows how much the sensor influences the discriminant function. The hue (pink or green) shows the sign. Electrode number included in the middle of the dot.

This fits well with the idea that similar to the presumed sensory function of the apical tuft during precision grip in humans, these electrodes have a strong sensitivity to the angle that they are making to the surface (Su et al. 2016).

The difference in magnitude of the coefficients for electrodes 8 and 9 is likely due to asymmetries in the structure of the packages tested. In general, there is no reason to believe that there would be a preferred direction of asymmetry, so it could be argued that when designing a general method one should constrain the coefficient for these electrodes to be equal.

Figure 8 shows the samples projected to the space spanned by the first two discriminant functions. The LDA algorithm has ordered the samples by board stiffness. Comparing the bottle packages, the large bottle package comes out as less stiff than the small bottle package with the same material. For example, the smaller package (Package II) made from Material F is ranked similar in the first discriminant to the larger package (Package III) made from Material G, despite Material F having only 65 % of the bending resistance of Material G. Note that the labeling of the training data does not contain an explicit ordering of the classes by stiffness or other measure. Thus, the fact that the algorithm has ordered the classes according to stiffness suggests that this information has been inferred from the tactile sensor data.

Figure 8

Samples plotted in the space spanned by the first two discriminant functions. The first discriminant function has ordered packages in order of board bending resistance.

Further work

Further work is needed in order to make the method more reliable and to correlate its results with human perception and preferences. An automated method to press the finger at a known, constant velocity or gradually increasing force would enable interpretation of the PAC signal that might reveal sudden events such as crumpling within the paperboard. It should also make the other signals more reliable because paperboard is a rate-dependent material rather than purely elastic.

If the method described here were combined with a measurement of the overall displacement and force of the finger, it might be possible to combine cutaneous and kinaesthetic information in a manner more similar to human perception (Bergmann Tiest and Kappers 2009).

It would also be interesting to investigate the data over time as the force ramps up to maintain stable grip of heavier packages. This analysis may present more information than earlier methods have given. For example, it could be possible to track the influence of factors such as crease quality, as well as transient events such as localized yielding.