Tactile Resilience of Sensory Whisker by Adaptive Morphology

Nature is featured by the resiliency, which enables adaptivity to sudden change under many circumstances. Meanwhile, the resiliency in robotic systems is far from comparable to that of the nature. If a robot is partially damaged, often the whole system fails to operate properly. While some approaches have been proposed, the majority of them are focusing on updating the control policy. Such approach, while rather complex, is not always applicable to mechanical damage of the robot body, especially parts that continuously interact with the surrounding environment. In the previous works Nguyen and Ho, (2022) and Nguyen and Ho, (2021) we introduced an artificial whiskered sensor that exhibited resilience against physical damage by active change of its morphology around the placement of sensory elements (strain gauges), which allowed compensation of location sensing when the whisker was trimmed. In this paper, we extend the approach by using the whisker sensor for texture discrimination tasks. We demonstrate that changing the morphology of the whisker again helps to reduce mismatching between prior knowledge in the frequency/time domain of the sensory signal. This allows the sensory whisker to recover the tactile perception on texture discrimination after the whisker is partially damaged. Furthermore, we also observe that using adaptive sensor morphology would augment tactile perception without the need of computationally expensive recognition and re-classification. This work is expected to shed a light on a new generation of robots that automatically work in the open world where self-maintenance against uncertainties is needed.


C
One-hot vector used for categorizing a specific texture. WD Width×Distance index for a texture. H Height index for a texture. RTP Metrics for evaluating reliability of texture prediction.
Multi-output vector for texture classifier including C, WD and H . 20 The associate editor coordinating the review of this manuscript and approving it for publication was Tao Wang . S1, S2 Strain gauge 1 and Strain gauge 2.

SC
Spectrum centroid of a band-pass filtered signal.

TP
Total power of band-pass filtered signal.

PF
Predominant frequency of a band-pass filtered signal. Vector containing texture features.

PM , APM
Positive maximum peaks of a time-series signals and their averages. Q init , Q c , Q u Pressure value in the air chamber of the whisker's initial, compensated and unknown-predicting states.
, b Strain gauge responses of whisker's original and broken states. e , u Strain gauge responses perceived from existed and unknown texture. Trimmed length of the whisker body. a Ratio of contact position with respect to whisker body length. δ Deflection of the whisker body measured at the contact spot. E Young's modulus. κ, δ 1,2,3 Geometrical parameters derived from whisker structure.

23
There is a long standing history of artificial comput- 24 ing machines ranging from Antikythera mechanism of the tional material and recent emergence of soft robotics, MC has ple, Ho et al. [11] demonstrates a multi-modal tactile sensor 54 can be achieved by switching the morphology from one to 55 another. A similar attempt was done by Nurzaman et al. [12] 56 where different physical quantities (e.g., softness and temper- employed to amplify tactile response [13], [14]. Interest-62 ingly, the sensor morphology is not only the characteris-63 tics of the body alone but combined with other components.
64 FIGURE 1. Illustration of wrong tactile inference for discrimination tasks due to physical damages and our proposed solution for tactile resilience via adaptive morphology [1], [2].
The placement of sensing elements in the body layout is 65 similar to the interface between mechanoreceptors and the 66 environment in living creatures that drives what the sen-67 sor perceives [15], [16]. Authors in [17] attempted to alter 68 the layered rubber skin of a vision-based tactile sensor, 69 which contains a number of markers on it, in order to 70 vary the human-robot haptic interaction for control purposes. 71 Hughes et al. [18] proposed a changeable jamming-based fil-72 ter to enhance successful rate of the tactile discrimination 73 task. This work has proposed that, instead of trying to opti-74 mize the design in advance, the sensor body should be able 75 to adapt itself continuously and dependently on the sensing 76 task.

77
Most of the attention to this research area aims to enrich 78 information gain, it is lacking elaboration on how variable 79 morphology can be utilized to remain sensing ability against 80 unexpected damage to the original sensor body (e.g., being 81 broken, eroded). Our previous work [1] tackled this issue 82 on a whiskered tactile sensor. By actively changing the sen-83 sor's morphology thanks to air regulation of the embedded 84 air chamber, the tactile information (mechanical strain) per-85 ceived by the broken one was compensated to get close to 86 that of the same stimuli before being damaged [2]. In this 87 work, we highlighted the efficiency of such tactile resilience 88 strategy for the contact localization task which is actually 89 an analysis of quasi-static deformation between equilibrium 90 states of the whisker-object contact. The performance drop of 91 the broken sensor remains unclear in more complex dynamic 92 sensing problems as simply illustrated in Fig. 1. From this 93 perspective, two following research questions will be clari-94 fied in this paper: 95 1) Could adaptive morphology help to recover sensing 96 ability of a broken sensor for texture discrimination 97 task? which is actually sensible to strain and vibration. In detail, 141 it is speculated that the shape of Lyriform organs changed 142 so that resulted feedback of the broken leg facilitates the 143 neural system (i.e., the brain) to justify the performance in 144 comparison to the original leg. Rodent's vibrissae system 145 exposes a similar phenomenon. A region in the brain called 146 Barrel cortex allocated to the damaged whisker will be shrunk 147 in shape to reduce its sensitivity, while the contrary (i.e., sen-148 sitivity increase) will happen to neighbor whiskers to allow 149 them to take over the sensing task temporarily [22]. angle. Two inextensible fibers are wound helically around the chamber's middle wall to allow only axial length exten-158 sion (i.e., in x-direction) of the chamber region under inner 159 compressed air Q of the chamber. Two strain gauges (S1 160 and S2) are bonded onto the chamber region so that their 161 principal sensing planes are perpendicular one to another. 162 By increasing the air pressure Q, the chamber wall will be 163 stiffened. As a consequence, mechanical responses measured 164 by strain gauge are expected to be tuned appropriately to aid 165 sensing capabilities (classification in particular) even with a 166 damaged structure.

168
A comprehensive understanding of the correlation between 169 sensor morphology (both geometrical and material aspects) 170 and the robotic device outcome is crucial to establishing a 171 proper tactic for damage compensation. In this regard, we pre-172 viously introduced an analytical model that estimates the 173 strain gauge output for a wide range of contact conditions and 174 morphology states [1]. Based on this, an optimized whisker's 175 layout (upon pressure Q) equivalent to the desired sensitivity 176 is chosen to perform the tactile compensation task. A physics 177 engine based on FE was used to prove that job could be 178 accomplished with high accuracy [2]. A brief derivation of the 179 model is introduced below. For the detail, please refer to [2] 180 The model leverages two classical beam theories: Hooke's 181 laws and Castigliano's theorem, for the derivation of mechan-182 ical strain ε generated due to a certain applied stress σ : where σ is applied stress generated in whisker body due to 185 pure bending moment M (x), y is the radius of the outermost 186 layer of the chamber's wall where the strain gauge is attached. 187 The final expression is: where U is the total strain energy within the body, a is the

210
and when the chamber is under a certain air pressurization: are expected to be sufficient to reveal 3-dimensional (3-D) 234 geometry characteristics of the scanned surface. The sensor 235 fabrication is done through a four-step molding process (ini-236 tially detailed in [1]) using silicon-rubber Dragon Skin 30 237 (Smooth-On, USA). The strain gauge KFGS-2-120-C1-11 238 L1M2R (Kyowa, Japan) was used.

239
Here, our whisker sensor explored 3 sets of textures. Each 240 set represents a specific type of surface pattern (see Fig. 3B): 241 Dimple bumps (DB), Honeycomb (HC) and Pyramid bump 242 (PB). These textures are parameterized by three measures: 243 width (W ), distance (D) from a pattern to the adjacent one 244 and height (H ). For simplification, W and D are set equal to 245 each other in all samples (hereafter, WD is used to present 246 both metrics). Each texture collection has 6 different textured 247 plates (numbered from 1 to 6) whose geometrical parameters 248 are listed in Table 1. In summary, a total of 18 samples were 249 designed and 3D printed using ABS-based filament in such a 250 way those pattern elements are centered along the plate.

252
A series of sweeping experiments were implemented using 253 the setup shown in Fig. 3A. Two motorized linear stages 254 (Suruga Seiki, Japan) were set up orthogonally to carry the 255 whisker sensor (X-axis stage) and the texture plates (Y-axis 256 stage). While the X stage is responsible to ensure the rela-257 tive position of the whisker tip and the textured plate, the 258 Y stage drives texture plates back and forth with constant 259 velocity v = 20 mm/s for surface exploration. Both stages 260 are controlled by a motor controller DS102 (Suruga Seiki, 261 Japan). During the surface exploring process of the whisker, 262 the strain output was recorded at a sampling rate of 100 Hz by 263 EDX-15A connected with a bridge box UI-54A-120, Kyowa, 264 Japan, in synchronization with the movement of stages. Strain 265 output in µm/m from the measuring device is converted by 266 the equation: ε = ε read GF × 10 −3 , where: ε read is read from the 267 software and GF stands for the gauge factor provided by the 268 vendor (GF = 2.21±1%). Additionally, the air chamber was 269 pressurized to the desired value of Q by a pneumatic actuation 270 system comprising a solenoid valve VQO1211 (SMC Co., 271 Japan) and a pressure control valve AS2211FE-01 within 272 the mainstream. Thanks to this combination, desired levels 273 of inner pressure Q were always ensured. This system is 274 controlled by a microprocessor (Arduino MEGA 2560) with 275 feedback from a digital pressure sensor ISE20A-R-M (SMC 276 Co., Japan).

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The following identical procedure was performed for every 278 texture. Firstly, the chamber was given an initial condition 279 equivalent to the inner pressure Q init = 100 kPa as previously 280 VOLUME 10, 2022 suggested in [1] and [2]. The test did not begin until the 281 whisker tip reached the base of the texture plate. Then, a com-282 plete cycle of texture exploration is carried out as followed: 283 a) sliding the texture plate forward for 160 mm (the plate 284 length) at a preset speed of 20 mm/s. In the meantime, the 285 response of S1 and S2 will be recorded within a time window  been exploited for many purposes such as radial distance 296 estimation [13], measuring geometrical attributes [23] and 297 also texture discrimination [24]. Although up to date, the data 298 processing method of rodent brains to extract the nature of 299 a texture has not been fully understood, many approaches 300 to biomimetic or artificial whiskers have shown that spec-301 tral analysis could prove significant texture-related informa-302 tion [25]. However, since we address a classification problem 303 for variable textures (see Table 1), the spectral analysis may 304 infer a wrong conclusion when there were differences in 305 spectral phase [26]. Thus, texture discrimination based solely 306 on frequency-amplitude spectrum is considered insufficient, 307 resulting in the necessity of time-series data.  To fulfill the purpose of this study, we attempted to solve a 360 multi-output classification problem, in which, outputs char-361 acterize separately texture types and geometrical dimensions 362 of texture (WD and H ). In terms of labeling for texture types, 363 we apply One-Hot encoding approach [28] to categorize a 364 texture by a 3 × 1 vector (notated as C) of binary variables 365 where a texture is ascribed to a specific element and set to 366 ''1'', while the rest are dummy variables (i.e., ''0''). Vector C 367 is equivalent to the probability of which texture category an 368 arbitrary input data could belong to. Vector C combines with 369 numerical values of WD and H to form the final observation 370 vector for training and testing: 5×1 = C 3×1 WD H T .

371
We employed supervised Linear Regression (LR) learning 372 algorithms. It should be noticed that the reference model 373 was only trained with a subset of the database (80% of 374 it) acquired from the intact whisker at initial pressure (i.e., 375 Q init = 100 kPa). Consequently, performance assessment 376 for any sensor configuration was compared against results 377 of the remaining 20% testing data. Model training and 378 data pre-processing were implemented with scikit-learn [29]. 379 Database splitting for training and testing data was repeat-380 edly conducted 10 times to demonstrate the independence of 381 tactile sensing ability on random data selection. Therefore, 382 experimental results (shown in the next section) are averaged 383 over 10 trials.

384
The reliability of the above model will be challenged with 385 two critical problems: (1) partially damaged whisker body 386 and (2) encountering novel textures. Whilst most previous 387 research focused on developing an often computationally 388 expensive correction algorithm and manually adding new 389 tactile data into the database, we rely on the interplay between 390 the mechanics of the whisker morphology and external stim-391 uli to form desired afferent sensory feedback to the central 392 system. This interdependency is used to form a correction for 393 strain data to maintain the sensing ability. Tactile information is inferred from the consequences of 397 physical interaction between soft bodies and the environ-398 ment. Therefore, physical damages occurring to the sensor 399 body lead to erroneous tactile information (e.g., mechanical 400 strain) transmitted to the controller. Assuming the whisker 401 sensor used for data collection is trimmed off by a certain 402 length (mm). The corresponding whisker's sensitivity to 403 bending is increased proportionally to the fourth power of 404 the outer diameter, making the strain output larger with the 405 same stimuli (texture). Figure 4 pictures the signal magnitude 406 in time domain and spectral power of three example cases: 407 = 0 mm (intact), = 1 mm, and = 5 mm for 408 texture HC1. One may observe the amplification of strain 409 magnitude and power spectrum as increases. This was 410 also observed for the other texture features. In detail, except 411 for the predominant frequency, other attributes (e.g., when 412 VOLUME 10, 2022   Notice that this searching process was implemented 436 for only S1 since its contribution to texture detection 437 outperforms its counterpart (S2). Short expression for 438 above method is as follows: (10) 440 2) The second approach is inspired by searching adap-441 tive behaviors of natural creatures throughout a ''trial-442 and-error'' process [30], [31]. Similarly, a trial-and-443 error could allow the whisker sensor to creatively 444 discover compensatory solutions without an model. 445 More specifically, the whisker sensors will gradually 446 decrease inner pressure Q to maximize their sensing 447 performance in spite of being damaged. Compensa-448 tion results produced by these two methods will be 449 compared for further clarification on pros and cons of 450 resilient function based on an analytical approach. Supervised learning techniques strongly depend on the qual-454 ity and quantity of training data. Once an outlier appears, 455 it is often necessary to collect related information and man-456 ually assign new labels to the training database for restarting 457 the learning process (either online or offline). Otherwise, 458 a degrading trend in classifier performance is unavoidable. 459 However, the experimental data acquisition process is often 460 burdensome in terms of time and cost. Not to mention the 461 failure in control based on unfamiliar feedback from the envi-462 ronment will cause the failure of the robotic system. In this 463 section, we tackle the problem when the classifier encounters 464 a novel texture patterned similarly to DB, HC or PB, but with 465 differences in geometrical dimensions.

466
To significantly improve the real-time roughness (i.e., 467 parameter H ) recognition for unknown texture properties, 468 our proposition is to actively change the sensor morphology 469 (i.e., changing from Q to Q u ) to enforce tactile information 470 perceived from an unknown texture close to the one already 471 included in the prior database. This variation in morphology 472 could be referred equivalently to differences in geometry 473 between them. Therefore, once the contribution of each state 474 of sensor morphology to its perception is well-understood, 475 we might be able to get knowledge about new textures with 476 the help of solely morphological computation instead of any 477 expensive-computational data analysis. 478 Let us assume that the strain signal reaches PM peaks (i.e., 479 whisker deflection δ is maximum) only when the whisker 480 tip is sweeping over the highest points of the texture. In this 481 scenario, the similarity in tactile data acquired from existed 482 and unknown texture after calibration at these PM points (i.e., 483 ε e APM = ε u APM ) yields following expression based on Eq. 6: 484 .
We argue that the ratio of whisker deflection in Eq. 10 (the 486 left-hand side) is intuitively proportional to difference in 487 height of the unknown texture and its counterpart. Moreover, 488 logical computation (the right-hand side of Eq. 11). The evaluation session mainly focuses on two following crite-  to robot operation no matter how easy the task is. Corre-541 sponding actions to change the whisker's morphology (i.e., 542 lowering initial pressure Q init down to compensation value 543 Q c ) were activated to overcome the degrading in classifica-544 tion results. To identify proper values for Q c , we first rely on 545 the analytical model (method 1). Similar effort done in [1] 546 suggested a reduction of the inner pressure down to 94 kPa 547 and 48 kPa to achieve compensated states for the whisker with 548 = [1, 5] mm, respectively. The compensation results are 549 summarized in Fig. 7. Only a slight improvement is observed 550 for the case of 1 mm cut-off length, while a relatively substan-551 tial enhancement in texture classifying with the 5 mm cut-off 552 whisker sensor is recognized. However, their performances 553 are still far from what the intact whisker could achieve with 554 a perfect body. The above results demonstrate the feasibility 555 of tactile compensation ability against critical damages in 556 structure based on morphological change. Since the overall 557 sensing performance was not 100 percent recovered to the 558 original state, it suggests that morphological transformation 559 strategies tailored from the analytical model might not be 560 optimal.

561
The trial-and-error processes (method 2) for searching for 562 better morphology states were also executed. In detail, the 563 broken whisker sensor will be tested its sensing ability within 564 a decreasing range of pressure Q, with a step of 10 kPa until 565 the sensing performance converges. Figure 8 illustrates the 566 outcome of this approach. At first glance, the compensation 567 performances for both damage cases apparently started to 568 converge within the pressure range 90 − 80 kPa and 40 − 569 30 kPa when = 1 and 5 mm, respectively. This fact is 570 reflected in RMSE of all interested indicators (see Fig. 7). 571 Interestingly, these observations also narrow down the region 572 VOLUME 10, 2022  where the optimal sensor morphology can be found to recover 573 malfunction in tactile sensing due to physical damages. 2) allow successful sensitivity calibration within the trans-594 formability limit of the body and sensitive range of the 595 strain gauge.

596
As a result, for this experiment, the closest pairs for DB7 597 are DB3 or DB4 textures. Then, in order to predict the 598 roughness of DB7, we adjust the whisker's sensitivity so as to 599 receive similar strain gauge's outputs ( u APM ) with that of DB3 600 and DB4 ( e APM ) when the whisker reaches the texture's high-601 est points. The ratio of max deflection between two contesters 602 (δ e max (a) and δ u max (a)) can be attributed to the difference 603 in height among them and mathematically calculated using 604 Eq. 11. Table 2 reports the results of roughness estimation 605 based on the above hypothesis in comparison with real values 606 acquired from experiments.

607
The ratio 1.215 and 0.789 indicates that, due to the dif-608 ference in H , interaction with DB7 would most likely deflect 609 the whisker sensor 1.215 times larger and 0.789 times smaller 610 than that of DB3 and DB4, respectively. Furthermore, these 611 ratios are not too far off from the real values (1.1875 and 612 0.869, respectively). They do not necessarily represent the 613 ratio of unforeseen texture roughness but a measure to give us 614 a rough estimate of it in general. If the correlation between 615 maximum deflection of the whisker and texture peaks is given 616 we could more precisely quantify the estimated value of H. 617

618
Firstly, this paper extends our previous works to deal with 619 structural damages in the soft whiskered tactile sensor in 620 a more challenging sensing task (texture discrimination). 621 Despite being trimmed, the tactile perception of the sensory 622 whisker still remains unaffected, thanks to the tactile com-623 pensation method via adaptive sensor morphology. In detail, 624 we demonstrated changing properly the whisker body by 625 air regulation in the chamber would ''pre-processing'' the 626 incorrect sensor response (mechanical strain) toward the right 627 classification of the texture in sensor space. This hypothesis 628 was tested with two: broken body length = 1 mm and 629 = 5 mm. Two approaches are applied to discover the cor-630 rect compensatory morphology, one is based on an analytical 631 model first introduced in [1] and the other is inspired by a 632 trial-and-error process that is widely used in natural creatures. 633 Evaluation results shown in Fig. 7 have proved the feasibility 634 of both approaches in enhancing the feature-based identifica-635 tion of texture plates for the broken whisker prototypes. 636 mance based on the analytical model showed a gap to those 638 attained by the trial-and-error method (see Fig. 7). This variable morphology [33]. In addition to providing tactile 692 sensation which is a commonly known drawback of MIS, 693 variable morphology allows controlling with adaptive sen-694 sory feedback toward more safe interaction with different 695 types of organs. This direction is expected to push the role of 696 sensor morphology beyond being a crucial part of constituting 697 the sensory-actuator network. 698 spectives,'' IEEE Access, vol. 8, pp. 7682-7708, 2020.