Object Identification Based on Extended State Observer on Artificial Cat Whiskers

Abstract

The present work is focused on the implementation of a robot system that mimics cat whiskers to differentiate between different objects. The robotic system imitates the motion from whiskers in the same way a cat uses them to collide with objects. The states from the system are estimated with the use of an Extended State Observer to measure the perturbation applied over the motors responsible for the whisker collision. The estimated perturbation is analyzed on the frequency domain with the use of the Fast Fourier Transform to determine the fundamental frequencies. A pair of classifiers are used to determine the object that collided with the whiskers based on the frequencies of the estimated perturbation.

1. Introduction

The detection and classification of objects under low- or no-visibility conditions are among the main challenges during the exploration of uncontrolled environments [1]. There are several difficulties related to the evaluation of the surfaces under this class of environment when artificial vision algorithms are implemented, particularly regarding the quality of the images and the training data set used for some algorithms, such as Convolutional Neural Networks [2]. This problem is especially related to the identification of the materials that obstruct pipes, where it is important to differentiate between them to ensure that the cleaning is performed with the correct techniques to eliminate the residue [3,4].

Since the problem of detecting the environment has been widely studied, several techniques have been developed in the past, such as artificial vision reconstruction using SLAM algorithms [5,6] that utilize a Li-DAR camera to examine the surroundings, perform graphical evaluation and reconstruction, and determine the corresponding structure in space. The use of image processing techniques to determine the objects in the environment based on their shape employs techniques such as Histogram Equalization, Contrast Stretching, Smoothing Filters, Sharpening Filters, and the Canny Edge Detector [7,8]. Another widely used technique involves the use of ultrasonic sensors to perform mapping of the environment; this method is based on sending an ultrasonic wave to the desired area to be identified and computing the time required for the wave to return and be measured by a receptor to estimate the distance between the emitter and the surface [9,10]. The use of infrared sensor technology provides options to perform identification from the environment in cases where there are significant differences between areas of this light spectrum, usually related to temperature changes [11,12,13].

The techniques described previously are based on indirect identification from the surrounding area, where no direct contact is made between the device and the environment. This kind of technique is adequate when it is only necessary to identify the distribution in space or to recognize objects that possess a well-defined morphological structure and can be identified using pattern recognition techniques such as Convolutional Neural Networks [14], Semantic Clustering [15], the YOLO algorithm [16], and Deep Learning techniques [17]. However, there are cases where it is necessary to identify not only the shape or morphological structure of the object but also the physical properties that must be determined to evaluate the material from which it is composed. To perform the identification of the material, the most widely used methodology requires that a piece of the material be removed and retrieved from the explored environment to evaluate its properties with specialized equipment [18,19]. The mentioned techniques used for environmental sensing provide a wide range of data that allows for the navigation of the sensed environment. However, it is important to note that the data is susceptible to errors caused by environmental factors, such as illumination in the case of vision techniques and humidity and temperature in the case of ultrasonic sensors. Furthermore, the limitation of non-direct estimations is related to the lack of knowledge about the composition of the objects that are detected; this is fundamental to determining their properties and the way an exploration robot interacts with them or to determining the stability of a cavity when exploration is performed. For these reasons, an alternative way to identify objects based on cat whiskers is proposed in this work.

The cat’s whiskers are sensitive to changes in the environment based on vibrations; at the same time, they allow the cat to evaluate its position in space and detect objects to avoid collisions [20]. In some works, whiskers are used as inspiration to create sensors that allow for the evaluation of certain properties of the environment, such as collisions with objects in terrestrial and underwater environments, by measuring the forces applied to them [21,22,23,24], or for sensing the air or water flow, using whiskers to evaluate the environment and facilitate monitoring [25,26].

To analyze the effect of the collision on the whiskers, it is necessary to examine the disturbance in the mechanical system that generates the motion of the whiskers in order to differentiate between the objects that have collided. The disturbance can be estimated using several methods, such as the Nonlinear Disturbance Observer [27], which allows for estimating the nonlinear dynamics; the Generalized Momentum Observer [28], which provides the advantage of simplicity and does not require knowledge of the inertia matrix for the robotic system; the Disturbance Kalman Filters [29], which can be applied to systems that have nonlinear dynamic and avoid numerical problems in the estimation; and finally, the Extended State Observer (ESO) [30], which allows for disturbance estimation by generating a virtual state that represents the inner dynamics mixed with the external disturbance applied to the system. The main advantage of the ESO in relation to another class of techniques for disturbance estimation is related to the lack of requirements concerning the knowledge of the internal dynamics of the system. At the same time, the way the ESO can be implemented in combination with an Active Disturbance Rejection Controller allows it to perform the tracking task for the whisker motion.

In this work, a novel way to sense and identify materials under low-visibility conditions is proposed based on the bio-mimetic method inspired by cat whiskers. The structure of the artificial whisker is based on biological whiskers, which possess two different sections and materials. At the same time, a set of experiments using image processing has been performed with a group of cats to determine how they manipulate their whiskers to sense their environment. Based on the obtained data, a bio-mimetic sensor has been constructed in which the whiskers possess a motion similar to that performed by cats to induce collisions with objects that must be identified. The actuation from the whiskers is performed using DC motors and a control law that ensures the required trajectory; this is combined with an ESO that identifies the perturbation related to the collision between the whiskers and the object. The data obtained from the disturbance allow for generating a frequency analysis in which the fundamental frequencies are used to differentiate between materials. The classification of the materials based on frequency was performed using a Support Vector Machine (SVM) classifier that allows for an effectiveness percentage over $70\%$.

The outline of this work is as follows: In Section 2, the analysis of cat whiskers and the construction of their duplication are described, while also providing information about the range of motion that the robotic system must emulate. The way the robotic system that generates the whiskers collides is described in Section 3. In Section 4, the methodology used to determine the objects that collide with the artificial whiskers, based on the Extended State Observer and frequency analysis, is described in this section. The results of the estimated perturbation, in combination with the classifiers, are given in Section 5. Finally, the conclusions of the work and future work are summarized in Section 6.

2. Design of the Bio-Mimetic Cat Whiskers

To evaluate how cats reliably identify their environment using their whiskers, an analysis is conducted to identify the mechanical properties required of the whiskers to enable the construction of an artificial version that emulates their behavior. This analysis is based on the identification of the parts of the biological whiskers to determine the polymeric materials that produce a mimetic equivalent based on their internal structure.

2.1. Internal Structure of the Cat Whisker

The evaluation of the mechanical morphology of the whisker requires identifying their sections through experimental tests. The experiments require that the whiskers be examined under a microscope; this implies that the ones used are isolated samples. These samples are not removed by force from the cats but are collected when the test subjects shed their whiskers as a natural process of their life cycle [31]. A total of five samples are obtained for this study and are examined using an optical digital microscope that allows an amplification of 100 times to explore the whisker structure.

The whiskers have been divided into three sections, as shown in Figure 1, which are the following: the tip, referring to the distal part of the whiskers; the middle part, corresponding to the major length of the whisker; and the base, which is the section of the whisker inserted into the cat’s skin to detect vibration information using the nerve terminals.

It is noted in Figure 1 that the base of the whisker has a conical structure designed to be inserted into the skin. At the same time, the middle part corresponds to a cylindrical structure with some imperfections on the surface, and the tip decreases the radius until the end structure forms a conical shape.

To evaluate the internal structure of the whisker and to generate a sensor that imitates the way vibrations are distributed on it, two sets of cuts are applied to the whisker. It is noted that the whisker possesses an internal circular structure made of a different material than that of the external part. Based on the light penetration during the sampling, it is expected that the internal structure will possess a lower density than that of the external section of the whisker. The difference in the damping coefficient of the materials is related to the way the vibrations are transmitted through the whisker. The second cut of the whisker is diagonal and allows for determining whether the structure noted in the previous cut is regular along the whisker shaft. The analysis from this cut allows us to notice that the internal structure observed in the transverse cut is uniform throughout the whisker. This implies that the proposed sensor, based on the whisker, must replicate it over its entire length. Considering the previous analysis of the whiskers, their structure is summarized in Figure 2. The sections of the whiskers exhibit differences between the internal and external structures and possess irregular shapes along the length of the whiskers. The problem related to these irregular structures on the whisker is not considered for the equivalent sensor, and only the differences in the materials for the internal and external structures are emulated in the proposed sensor.

2.2. Manufacture of the Bio-Mimetic Whiskers

The artificial whiskers emulate the structural components of biological whiskers to replicate their response when a collision with objects in the environment occurs. From the previously performed analysis, it is noted that the whiskers have an inner and an outer section that are composed of different materials, which modify the way they react to collisions.

The mechanical design of the artificial whiskers in Figure 3 shows a perspective of the proposed bio-mimetic devices. The length of the artificial whiskers corresponds to $21.5$ cm from the base to the tip, and the base radius of 1 cm decreases until it reaches the tip.

To emulate the physical properties of cat whiskers, the analogous whisker is composed of two different materials during construction:

• Outer section: The main structure of the artificial whisker is constructed from 3D printing resin with an F69 from Resione, the company Dongguan Godsaid Technology Co., Ltd., Dongguan, Guangdong, China. This material possesses a Shore Hardness of 60–75 A that corresponds to a semi-flexible nature, allowing the whisker shape to remain intact even when collisions with the environment occur. A tensile strength of 7.9 MPa and a temperature range from 5 °C to 120 °C provide suitable characteristics for the application. These mechanical properties are the ones closest to the Keratin that composes cat whiskers in comparison to other commercial resins that can be used with 3D printing technology, particularly for the Shore Hardness coefficient, which provides a similar stiffness. The outer section is printed on a Phrozen Sonic Mighty 4K resin printer using a $0.05$ mm layer height, $1.2$ s exposure time per layer, and a post-printing process that includes washing with isopropyl alcohol and an additional curing process using a Wash and Cure station from Creality.
• Inner section: The material used in this section corresponds to Ecoflex 00-30 silicon from the Smooth-On Company, Macungie, PA, USA. This material provides a Shore Hardness of 00–30 that corresponds to soft and flexible materials, a tensile strength of 200 psi, and a useful temperature range from −53 °C to 232 °C that is suitable for the desired application. This material is selected based on its Shore Hardness, which provides flexibility similar to the inner material of cat whiskers. Other types of silicon, if their value is lower, dampen the transmission of vibrations, while a higher value reduces the flexibility of artificial cat whiskers. This material typically must be poured into a mold that allows the form to remain in it once it has cured. However, for this application, the material is poured directly onto the inner section from the artificial whiskers to fill it.

3. Robotic System for Object Identification

To emulate the motion of the whiskers, the researchers conduct a behavioral analysis of a group of cats subjected to non-harmful stimuli. Their corresponding reactions of the whiskers are captured using video recording, which is subsequently combined with image processing software to determine the Degrees of Freedom (DoF) and the corresponding range, necessitating a mechanism that emulates the behavior of the whiskers’. Once it is completed and the motion range is defined, a robotic system is implemented to emulate this process.

3.1. Motion Range of the Cat Whisker

To determine the degrees of freedom (DoF) from the whisker motion in cats, a set of experiments is performed on domestic cats under several stimuli to evaluate the motion of the whiskers using artificial vision techniques, ensuring that the legal requirements and guidelines in the country and/or state or province for the care and use of animals are followed. The process of experimentation does not imply any harm to the subjects, since no invasive tests have been performed on them; the legal guidelines specify that approval from an ethics committee is not required. The owners of the domestic cats supervised the entire experimental process and signed the consent forms that allowed the testing to proceed. All hygienic protocols were fully implemented to avoid contamination between experimental subjects. A total of ten domestic cats have been used in this study, which was performed in the Advanced Robotics Laboratory at UPIITA-IPN. All the experiments have been performed on different days to avoid any modifications in the behavior of the cats related to their interactions with one another. Each one of the cats is exposed to a set of stimuli that are described below:

• Auditory stimulus: A recording of meowing cat kittens is played at frequencies between 100 and 400 Hz to induce an alert in the experimental subjects as they try to identify the source of the noise. This process includes reorienting from the whiskers to sense the environment, as shown in Figure 4a.
• Olfactory stimulus: Two sets of olfactory stimuli are applied. The first one corresponds to wet food that is placed in a bowl to be consumed by the cat, and the orientation of the whiskers is noted when they interact with a food source, as shown in Figure 4b. The second stimulus corresponds to catnip in spray form, which is dispersed over the experimental area, allowing for the identification of motion from the cat whiskers during a relaxation stage.
• Contact stimulus: A set of objects is placed in the experimental area to identify how the whiskers are used to explore the environment. The first element corresponds to a box with a 20 cm diameter hole that the subjects use to exit. It is expected that this part allows for the study of the motion of the whiskers on cats in closed environments, as shown in Figure 4c. The second element corresponds to a scratching post and a remote-controlled mouse to analyze how the cats interact with them using their whiskers.

During each test, a recording was performed using a CANON EOS 6D MARK II (Canon Mexicana, Mexico City, Mexico), which allows the acquisition of images with a quality of 26.2 megapixels and 60 frames per second. The video is processed and divided into frames to facilitate the analysis; this involves the conversion from RGB to grayscale images to assist in the identification of the whiskers, which are enhanced with an automatic contrast adjustment to sharpen their silhouette. The stages from the tests are summarized in Figure 5, which consists of the following steps:

1.

Cleaning and sterilization are necessary to eliminate all odors that could modify the behavior of the test subjects.

2.

A closed environment using the box with a circular exit to visualize the whisker behavior in narrow spaces.

3.

Food combines dry and wet foods to enhance olfactory stimuli.

4.

Audio activation occurs when the auditory stimulus is presented to verify how the test subject reacts.

5.

Interaction test: This combines the contact stimulus from toys and scratches with the olfactory stimulus from the catnip to analyze the motion of the whiskers.

Once the video has been processed, the Kinovea software (Version 2024.1.1) is used to analyze the motion of the whiskers in the videos. The sampled videos allow us to notice that the motion of the whiskers can be described as the combination of two rigid joints: the first corresponds to a rotational joint, and the second is equivalent to a translational joint, as shown in Figure 6. It is noted that the whiskers allow the sensing of objects and surfaces that are near the cat’s head, enabling the cat to navigate their environment by reorienting itself based on their needs.

The computed data provide information about how cats use their whiskers to interact with the environment. The provided data show the variability in the testing based on the subjects who modify the motion of their whiskers according to their particular behavior in response to the stimulus. The fact that several subjects are used to evaluate this characteristic allows us to observe a set of limits as follows:

• Rotational motion lower bound: $14.{19}^{°}$;
• Rotational motion upper bound: $68.6^{°}$;
• Translational motion lower bound: $0.2$ cm;
• Translational motion upper bound: $2.24$ cm.

This data allows us to notice the range of motion required from the proposed artificial whiskers to bio-mimic the natural behavior of cat whiskers used to identify objects in space.

3.2. Manufacture of the Robotic System

Once the analysis is performed, it is determined that the whiskers require both linear and rotational motion. The equivalent robotic system has been implemented using an endless screw and a linear rail acted upon by a 380:1 Pololu Micro Metal Gearmotor with an encoder (Pololu Corporation, Las Vegas, NV, USA) that emulates the translational motion that cats execute to detect their environment. The rotational motion is executed with a gear system that allows for the synchronized turning of the shaft to which the whiskers are attached, based on a 250:1 Pololu Micro Metal Gearmotor with an encoder (Pololu Corporation, Las Vegas, NV, USA). These mechanisms are presented in Figure 7, which shows how the whiskers are positioned to produce collisions with the objects with an accuracy of 0.078 that is based on the pulses from the encoder; it is noted that both whiskers are actuated by a single motor, such that any disturbance produced by a collision on either of them is transmitted to the motor axis via the gear mechanism.

The required electronics to implement the robotic system are shown in Figure 8; It is noted that the information is visualized and stored on a personal computer. This communication is realized with the STM32F407DISCOVERY micro-controller via a USB protocol; this board is programmed using the Waijung environment in MATLAB 2021b, which configures the acquisition of the position of the motor axis using the Encoder information with a sampling time of $0.001$ s and the activation of the motors through the use of PWM signals that are applied to an H-Bridge L298N (STMicroelectronics, Plan-les-Ouates, Switzerland) with a $0.01$ s period, which supplies energy to the DC Motors. The current required by the robotic mechanism is around 350 mA from the two DC motors during the motion process, combined with the requirements from the H-Bridge and the micro-controller, which corresponds to an 500 mA during the sensing process.

To ensure that the robotic system generates the required trajectories from the whiskers, the implementation of a closed-loop strategy is needed, which generates the control signal u, which is converted to a PWM signal. The selected controller is defined as follows:

$$u=K_p(q_d-q)+K_d({\dot{q}}_d-\dot{q})+K_i\int (q_d-q)$$

(1)

where q is the position of the motor, and $q_d$ is the desired signal for the tracking process. This desired signal is generated using the Bézier polynomial [32]; in this case, it is assumed that the selected polynomials are of fifth order and are defined as follows:

$$q_d\left(t\right)=a_0+a_{1}t+a_2{t}^2+a_3{t}^3+a_4{t}^4+a_5{t}^5$$

(2)

where the coefficients $a_i\in {\mathbb{R}}^{+}$ are computed as the solution to a system of linear equations in which the position, velocity, and acceleration from the initial and final positions are defined previously.

The implementation of this system is shown in Figure 9, which provides the linear and angular motion of the artificial whiskers. The motion process of the whiskers ensures that a controlled collision occurs between them and the objects. It must be noted that each part is constructed from 3D-printed materials, and the artificial whiskers are attached to the gear system.

4. Methodology of Object Identification Using Extended State Observer

The identification of the objects is based on the use of an Extended State Observer (ESO) that allows us to estimate the disturbance in a system, as shown in Figure 10. This consists of the collision between the artificial whiskers and the object to be identified; this collision produces a perturbation in the actuator that generates the estimated motion. The characteristics of the perturbation are estimated to classify the collided objects based on it. The identification process has two stages: The first is an online process in which the robotic system generates the collision while the ESO is running for the estimation of the disturbance that occurs over the elapsed time of 7 s; the second is offline, corresponding to the data processing of the disturbance and the implementation of the classifier.

Since it is used on a mechanical system where the whiskers collide with an object, the estimated disturbance is modified based on the class of material of the object. Once the disturbance is estimated, a frequency analysis is performed to determine the minimum and maximum component frequencies of the signal. Based on the different frequency components, a set of classifiers is used to differentiate between the objects that collide with the whiskers.

4.1. Extended State Observer for Disturbance Estimation

The artificial whiskers require motion to execute detection by causing a collision between themselves and their environment. As with cats, the whiskers require their insertion sites to contain a set of nerve receptors that determine whether a collision occurs and its characteristics. In this bio-mimicry, the detection of collisions and their evaluation are executed using an ESO [33], considering that there exists a mechanical system that modifies the orientation of the whiskers and estimates the perturbation on the actuator performing a tracking task. The ESO emulates the nerve endings connected to the hair sacs of the vibrissae that measure the perturbations applied to the whiskers. The ESO estimates the perturbation based on the force required by the actuator to perform the tracking task; this implies that the measurement of the vibration is performed using an indirect method that considers the effects produced at the insertion point of the whiskers, rather than through direct detection by them. The dynamical model of the actuator, considering a DC servomechanism, is as follows:

$$\begin{array}{ccc}\hfill {\dot{x}}_1& =& x_2\hfill \\ \hfill {\dot{x}}_2& =& -\alpha x_2+\beta u+\eta \left(t\right)\hfill \end{array}$$

(3)

where the terms $x_1$ and $x_2$ correspond to the angular position and the angular velocity, respectively. The viscous coefficient of friction corresponds to $\alpha \in {\mathbb{R}}^{+}$, and the gain from the servomechanism is $\beta \in {\mathbb{R}}^{+}$. The external perturbation is represented by the term $\eta \left(t\right)$ and varies over time due to the different stimuli that are applied to the artificial whisker attached to the motor shaft.

The implementation from the ESO simplifies the dynamical model to the following structure:

$$\begin{array}{ccc}\hfill {\dot{x}}_1& =& x_2\hfill \\ \hfill {\dot{x}}_2& =& u+\xi \left(t\right)\hfill \end{array}$$

(4)

where $\xi \left(t\right)$ corresponds to the disturbance in the system produced by the internal dynamics and external perturbations acting on it. Since the model is rewritten in this form, the following ESO can be proposed to estimate the term $\xi$ based on the observation error $e=x_1-{\widehat{x}}_1$ as follows:

$$\begin{array}{ccc}\hfill {\widehat{\dot{x}}}_1& =& {\widehat{x}}_2+{\lambda }_{2}e\hfill \\ \hfill {\widehat{\dot{x}}}_2& =& {\lambda }_{1}e+u+\widehat{z}\hfill \\ \hfill \dot{\widehat{z}}& =& {\lambda }_{0}e\hfill \end{array}$$

(5)

The term z corresponds to the extended state that is considered equivalent to the disturbance $\xi$ computed by the observer. The terms ${\lambda }_0$, ${\lambda }_1$, and ${\lambda }_2$ are the observer gains that are related to the error dynamics, such as the following:

$$e^{\left(3\right)}+{\lambda }_2\ddot{e}+{\lambda }_1\dot{e}+{\lambda }_{0}e=\ddot{\xi }\left(t\right)$$

(6)

The dynamic of the system are represented by a characteristic polynomial as follows:

$$p\left(s\right)=s^3+{\lambda }_2{s}^2+{\lambda }_{1}s+{\lambda }_0$$

(7)

To assure that the error has a stable dynamic, it is required that the roots of the polynomial $p\left(s\right)$ have a negative real part. To simplify the implementation of this, the polynomial is rewritten as follows:

$$p\left(s\right)={(s+{\omega }_n)}^3$$

(8)

where ${\omega }_n$ corresponds to the natural frequency of the observer. On the implementation of this work, the value is proposed as ${\omega }_n=100$ such that the observer is capable of reproducing each of the changes in the states of the system, and the resulting disturbance provides an accurate estimation of the effect produced by the collision. The implementation of this observer is realized in Matlab 2017b in the Simulink environment, utilizing the fixed-step Euler integration method with a sampling time of $0.001$ s. The resulting data is exported to the workspace to facilitate the following steps of the methodology.

4.2. Frequency Analysis of the Disturbance and Classification for Object Identification

To perform classification to determine the material sensed by the collision from the whiskers, a pair of algorithms is proposed to be compared to identify the one that provides better accuracy based on the frequency response from the state z. To estimate the frequency, the Fast Fourier Transform (FFT) [34] is applied to the perturbation estimation z computed by the ESO. Once the FFT is computed, the frequencies with the maximum ($f_{max}$) and minimum ($f_{min}$) amplitudes are selected as inputs to the classification algorithm. This is shown in Figure 11, which exemplifies the estimation of the frequency components of a signal using the FFT; it can be noticed that the frequency with the maximum amplitude can be easily identified with the use of standard algorithms.

A pair of classifiers is tested for the identification of the objects that collide with the whiskers. The first classification algorithm corresponds to a Support Vector Machine (SVM), and the second one is a Random Forest (RF); both algorithms are widely used in the literature to solve classification problems [35] with the type of data provided by the ESO.

The SVM is a machine learning algorithm based on statistical learning frameworks [36]. The main idea behind this technique is the generation of a hyperplane that separates two different classes from a set of data points; this separation is computed so that the hyperplane has the widest margin between the two classes. This process requires a subset of data to train the SVM to generate the hyperplane used to perform the classification process described on [37]. The RF classifier [38] employs a supervised learning method consisting of a collection of classifiers structured in the form of decision trees $h(x,k)$ for $k=1,2,\cdots$, where k are independent and uniformly distributed random vectors. Each decision tree evaluates the data and determines its own decision regarding the class to which the data belongs; then, a consensus is computed based on a voting system to reach a classification. The training process of the RF is based on determining the number of trees that execute their own classifications. For each of the trees, the updates and splits from the nodes, as well as the observation weights, are updated as described in [39]. The total number of trees proposed to execute the classification is equal to 500; this quantity has been obtained using heuristic methods that demonstrate high performance effectiveness. The selection of the number of trees has been performed using a heuristic method that tests several configurations; the total of 500 is selected as the one that provides the highest accuracy from the classifier without increasing computational complexity.

The proposed classifiers are selected to exemplify the capability of the data obtained with this methodology to be used for the identification of the objects that collide with the whiskers. A wide range of classifiers can be used to solve this problem since the information provided consists only of data points related to the frequencies.

5. Results

To evaluate the performance of the sensor, a set of tests has been executed to ensure that the disturbances produced by the collisions yield results that can be classified using the proposed algorithms. To ensure that no other class of perturbations is applied to the whiskers, the tests are performed in a closed space where the sensor and the object that needs to be identified are placed, as shown in Figure 12.

The classifiers are trained to identify two classes of materials:

• Class 1, Soft material: The testing of this kind of material is composed of 180 samples performed on foam rubber and 180 samples performed on sponge.
• Class 2, Hard Material: The testing of this kind of material is composed of 180 samples conducted on aluminum and 180 samples conducted on wood.

The performance from the ESO is shown in Figure 13, which allows us to notice that the performance from the observer enables us to estimate the state $x_1$ with an average error of $0.{45}^{°}$ during the task. This performance is reached with the gains ${\lambda }_2=30$, ${\lambda }_1=300$, and ${\lambda }_0=1000$, corresponding to an error dynamic with three poles $s=-10$ that provide a stable dynamic. If the velocity of the whiskers’ motion is increased, then it is necessary to modify the error dynamic to accommodate the observer velocity capable of performing the task.

The estimation from the perturbation state z is shown in Figure 14; this allows us to observe the differences that exist in the perturbation based on the material that collides with the whiskers. It is noted that the collision with the metal material produces a set of oscillations that are delayed with respect to those generated with the wood and foam rubber.

To implement a classification algorithm, it is necessary to evaluate the maximum amplitude frequency response from the perturbation produced by the collision using the FFT, which is computed with the Matlab software. This utilizes a discrete version that estimates the amplitudes of energy from each of the frequency components. This is shown in Figure 15, which displays the frequency analysis from the state z to identify their maximum and minimum amplitudes to be used in the classification problem. These values are presented in

Table 1. Data of the frequency response of the state z when the whiskers collide with different materials.

Material	Frequency with Maximum Amplitude	Frequency with Minimum Amplitude
Metal	4978.50	71.767
Wood	3689.23	69.660
Sponge	4171.71	69.560
Foam rubber	4482.92	41.153
Lettuce leaves	3825.90	52.781
Polypropylene	4645.25	65.284

, which shows the average value for the 180 samples of each material.

The classification algorithms are trained with a total of 100 samples. The remaining 80 samples are used to evaluate the trained algorithms and make a comparison between the classification algorithms, providing the following results based on the class and the algorithm applied:

• Support Vector Machine

  –

  Class 1: 25 correct classifications out of 40 tests.

  –

  Class 2: 32 classifications out of 40 tests.

  –

  Out of the total 80 tests conducted, there were 57 correct classifications.

  –

  Classifier effectiveness percentage: 71.25%

• Random Forest

  –

  Class 1: 28 correct classifications out of 40 tests.

  –

  Class 2: 24 correct classifications out of 40 tests.

  –

  Out of the total 80 tests conducted, there were 52 correct classifications.

  –

  Classifier effectiveness percentage: 65%

6. Conclusions

This study allows for the evaluation of the creation and testing of a touch sensor based on cat whiskers to identify different materials based on the perturbations applied to the motion mechanism. The conclusions can be summarized as follows:

• To emulate cat whiskers requires implementing the two sections that compose them using two materials with different mechanical properties. The use of flexible polymers ensures that the whiskers are not damaged by collisions with objects.
• The motion of cat whiskers can be replicated by the combination of a linear and a rotational mechanism that allows for the emulation of the range of movement that cats perform under different stimuli.
• The physical implementation of the mechanism requires the application of a controller that allows for the performance of a tracking process that emulates the motion of cat whiskers with a soft trajectory, which can be implemented using Bezier polynomials.
• The energy consumption of the robotic system during the sensing process needs to be estimated, considering the time lapse generated by the collision, to ensure that the application in real-world scenarios is feasible without exhausting the energy from the power source.
• The implementation of an ESO allows for the estimation of the perturbation on the servomechanism to identify the effect applied to the gear mechanism of the DC motor when a collision with an object in respect to the whiskers occurs.
• The computation of the gains from the ESO requires assurance that the designated poles allow for a sufficiently fast speed response to reach the observation from the desired state. However, it is required to avoid increasing their values without a bound because the peaking phenomenon could be observed, especially during the collision of the whiskers.
• The evaluation of the frequency response on the perturbation estimation shows different behavior based on the type of material that collides with the whiskers. This can be especially noted in the amplitude of the frequencies of the disturbance computed with the FFT.
• The implementation of an RF algorithm and an SVM provides a feasible way to classify the frequency data generated by the collision to identify the material; the latter provides better performance in this task. However, the implementations from other classes of classifiers must be evaluated in future work to improve performance.

Future Work

Based on the results and conclusions of this study, the different aspects that must be considered for the future development of the work are summarized as follows:

• The analysis of the motion of the cat whiskers requires an increase in the sample population to enhance accuracy and feasibility, taking into account the difficulties faced by the cats in completing the study. The increase in the accuracy of the motion range estimation that the robotic system must achieve ensures an emulation of the biological process of cat whiskers.
• The evaluation of other materials to implement the artificial cat whiskers must be conducted to enhance the similarity of their mechanical properties to those of biological whiskers.
• The mechanism can be improved by modifying it to ensure that the range of motion corresponds to the one generated by the cats. The speed of the system can be increased to reduce the time required for the identification process while simultaneously decreasing the energy consumed by the robotic system.
• The evaluation of other classification algorithms must be conducted to increase the accuracy of material identification and the classifier effectiveness percentage.