3.1. Neuromorphic dynamic vision sensors

Recently developed neuromorphic event-based dynamic vision sensors (DVS) use event cameras with patented technology that mimics the human retinal response. First, light is reflected from surrounding objects and enters through the cornea (i.e., the aperture), pupil, and lens, ultimately hitting the retina. The photoreceptor cells in the retina respond to light, converting its energy into an electrical signal. Furthermore, this signal travels through the human optic nerve to the brain, where it is finally converted to portray the images of objects [Reference Levin, Kaufman and Hartnett26, Reference del Río and Betancourt27].

Neuromorphic DVS integration of the recently developed cameras enables them to capture detailed visual information about objects’ spatial properties, dynamics, and environmental interactions. Both frame and event cameras are used in designing state-of-the-art neuromorphic DVS for robotic grasping applications [Reference Shimonomura28, Reference Atkeson and Yamaguchi29].

Neuromorphic event-based cameras generate asynchronous events triggered by significant changes in brightness intensity at individual pixels. This on-demand operation offers advantages in the design of robotics tactile sensors over frame-based cameras, such as high temporal resolution, low energy consumption, fast response, and a broad dynamic range [Reference Gallego, Delbrück, Orchard, Bartolozzi, Taba, Censi, Leutenegger, Davison, Conradt, Daniilidis and Scaramuzza30].

3.2. A novel-designed neuromorphic dynamic vision sensor

Figure 3 illustrates our in-house, bio-inspired, neuromorphic vision-based sensor that uses event-based vision technology to rapidly detect tactile interactions. This novel neuromorphic sensor is designed to emulate the high tactile sensitivity of human fingerprint ridges, featuring protruding markers that detect the slightest touch or minimal contact. These markers, alongside the sensor’s backbone skin, are printed using Ninjaflex material. The sensor’s entire assembly is encased in a PLA-based 3D-printed housing, and internally, a DVXplorer Mini neuromorphic event camera is secured to capture real-time, dynamic deformations of the sensor’s markers and strips under various contact scenarios. The sensor’s actual dimensions are 40 × 50 × 40 mm. The complete design and fabrication of this sensor are described in ref. [Reference Gallego, Delbrück, Orchard, Bartolozzi, Taba, Censi, Leutenegger, Davison, Conradt, Daniilidis and Scaramuzza30].

Figure 3. Novel neuromorphic dynamic vision sensor.

This sensor is designed to detect early slips in robotic grasping applications. Embedding this sensor within a robotic manipulator’s end-effector will measure data on pressing and slipping with rigid and moderately soft objects. During initial grasping, the sensor’s markers will be partially axially pushed, causing changes in brightness through the aperture holes and giving data about the pressing operation. If the grasped object starts to slip, causing relative displacement, the sensors’ marker strips will bend proportionally, altering the aperture area and brightness (i.e., marker strips). The red arrow in Figure 3 illustrates the optical path for the tactile sensor, starting from the external light source, being reflected through the aperture area of the marker strips, and ending at the event camera as a change in intensity.

Figure 4 illustrates the generated light diffractions through the aperture and the detection by the DVXplorer Mini event camera [Reference Faris, Awad, Awad, Zweiri and Khalaf31]. The used event camera reports time-stamped relative logarithmic changes in the light intensity on the pixel level in the form of occurring events $\{+1, -1\}$ based on predefined ON/OFF thresholds. Positive indicates an increase, while negative suggests a decrease in logarithmic intensity, and no changes in logarithmic intensity will be reported.

(2) \begin{equation}\textit{Event}=sgn\left(log \!\left(\frac{I(x,y,t+{\unicode[Arial]{x0394}} t)}{I(x,y,t)}\right)\right)\end{equation}

where $\textit{Event}\in \{+1, -1\}$ are the reported events of a pixel that is located at $(x,y)$ , $I(x,y)$ is the pixel’s intensity states, which occurred at a time $t$ and at the time $t+{\unicode[Arial]{x0394}} t$ , respectively.

Figure 4. Event camera change in intensity.

Event cameras do not send their captured high-definition images at a fixed frame rate, unlike conventional frame-based cameras. Instead, only events that occur when movement or change happens in the scene are produced, significantly reducing power consumption, data rate, and computational requirements. Even ultrafast cameras are designed for demanding applications in robotics, motion analysis, aerospace, AR/VR, and autonomous vehicles [32].

A DVS-generated event is documented using the address event representation (AER) format: E = [x, y, t, p], which records the pixel address (x, y), the time at which the address was reported, t, and the polarity of the brightness change (i.e., increase or decrease).

For the proposed model-based approach, we must establish a mathematical relationship between the event camera parameters and the sensor used in this work. In optometry, the viewable area that the camera lens can capture is referred to as the field of view (FOV), while the strength of the lens’s focus (i.e., convergence) or the divergence of light is referred to as the focal length (f). The FOV determines the portion of the object that is cast onto the camera’s sensor. This enables correlating the object’s physical area, which can be imaged and modeled as a horizontal or vertical FOV in millimeters, or as an angular FOV specified in degrees. Referring to Figure 5 and using mathematical geometry, the following equation relates the sensor’s marker strips aperture area to the camera sensor array’s vertical size [32]:

(3) \begin{equation}H=\frac{f}{\delta }FOV\end{equation}

(4) \begin{equation}A_{p}=l_{2}^{\,2}\theta\end{equation}

where H is the camera sensor vertical size, f is the used camera focal length, and 3.6 mm lens, $\delta$ is the strip object setup distance that is the distance from the strip object to the camera after calibration, FOV is the strip object’s FOV, $A_{p}$ is the marker strip opening area, $l_{2}$ is the sensor dome radius, and $\theta$ is the marker strip angular displacement. Figure 5 illustrates the overall light optical path, the event camera parameters, and the relationship between FOV, sensor size H, and $\delta$ for a given angular FOV (AFOV).

Figure 5. Object and captured image correlation.

3.3. The proposed neuromorphic DVS sensor modeling

The sensor’s markers and strips are made of Ninjaflex, a material that is rubber-like in it's flexibility and damping. To simplify the model without compromising accuracy, the strips will be modeled using spring and damper elements, as shown in Figure 6. The markers pressing action will be physically modeled using linear stiffness and damping, represented by K1 and B1, respectively. In contrast, the fixed-end marker strips will undergo rotational motion during the slip action, which will be physically modeled using linear and rotational stiffness and damping coefficients, K2 and B2, respectively. Finally, the inertial effects of the markers and strips will be neglected due to their small masses and low slipping rates.

Figure 6. Tactile sensor markers strip sensor physical modeling.

In robotic applications, objects are first secured in a stable grip but may suffer undesired slips due to dynamic effects during motion, which can propagate to a complete object slip. The initial gripping action will push the sensor’s markers axially, causing a small angular displacement $\theta _{0}$ of the markers’ strips. However, a slip will cause the markers to bend and cause further angular displacement of the markers’ strips that is proportional to the object’s slipping displacement.

As mentioned earlier, the mathematical modeling of the sensor’s actions, pressing and slipping, will be treated in two steps. Referring to Figures 6 and 7, first consider a robotic action that requires an external force $P $ , which may be decomposed into two force components $P_{1}\ \text{and}\ P_{2}$ . Consequently, the dynamical equilibrium is given by

Figure 7. Single-marker detailed model.

(5) \begin{equation}\sum F_{i}(t)=m_{s}\ddot{x}(t)=0\end{equation}

(6) \begin{equation}P_{1}(t)=B_{1}\dot{x}(t)+K_{1}x(t)\end{equation}

Now, for the slipping action, the analysis from the pressing initial position is performed, and the following equations model the object’s slip.

(7) \begin{equation}\sum T_{j}(t)=J_{s}\ddot{\theta }(t)=0\end{equation}

(8) \begin{equation}T(t)=B_{2}\ \dot{\theta }(t)+K_{2}\ \theta (t)\end{equation}

For a rectangular beam in torsion, the maximum stress occurs at the center of the fixed ends of the beam, and the angle of twist of the beam is given as [32]:

(9) \begin{equation}\theta (t)=\frac{2T\!(t)w_{2}}{\beta bt_{2}^{3}G}=\alpha T(t)\end{equation}

where $\beta$ is a constant that depends on $b/t_{2}$ ratio, b, and t ₂ are the marker’s strip width, respectively; G is the material rigidity; T(t) is an induced torque: T(t) = $P_{2}(l_{1}+l_{2}+l_{3})$ , and $ \alpha =\frac{2w_{2}}{\beta bt^{3}G}$ is a constant.

The adopted physical model mathematically demonstrates that the marker’s strip angle behaves as a first-order system (FOS) with the applied force and the time constant $\tau$ . Consequently, the corresponding transfer functions for the press and slip actions are given as follows:

(10) \begin{equation}\text{Press}\colon X(S)=\frac{1}{B_{1}S+K_{1}}F(S)=\frac{\alpha _{1}}{S+1/\tau _{1}}F(S)\end{equation}

(11) \begin{equation}\text{Slips}\colon \theta (S)=\frac{\frac{1}{t_{1}}}{B_{2}S+K_{2}}F(S)=\frac{\alpha _{2}}{S+1/\tau _{2}}F(S)\end{equation}

The sensor’s markers undergo two types of force-generated displacements: axial and bending of the marker strips. Figure 7 illustrates the displacements of bending marker strips (i.e., those on the light optical path) modeled as cantilevered beams. Using basic beam theory, the beam’s bending profile (i.e., elastica curve) may be correlated to the aperture area, A.

The length of the deflected part of the beam $l_{b}$ varies depending on the degree of pressing axial force $P_{1}$ on the grasped object. On the other hand, the lateral force $P_{2}$ causes the marker to bend, and the maximum deflection $y_{max}$ is given from the cantilevered beam theory as

(12) \begin{align}y_{max}=\frac{P_{2}l_{b}^{\,3}}{3EI}=\frac{P_{2}\left(l-x_{c}\right)^{3}}{3EI} \\[-25pt] \nonumber \end{align}

(13) \begin{align}\quad P_{1}=K_{1}x_{c} \\[2pt] \nonumber \end{align}

where $x_{c}$ is the beam end point ‘C’ displacement, $l_{b}$ is the beam’s cantilevered length, l is the beam’s total length, E is the material modulus of elasticity of the marker, and I is the moment of inertia for the marker’s rectangular cross-section. Consequently, the marker object slipping force $P_{2}$ will cause the marker strip to bend and vary the aperture area in front of the event camera.

(14) \begin{equation}{\unicode[Arial]{x0394}} A_{p}=l_{2}^{\,2} {\unicode[Arial]{x0394}} \theta =\frac{l_{2}^{\,2}}{l_{b}} y_{max}\end{equation}

(15) \begin{equation}{\unicode[Arial]{x0394}} A_{s}=w_{s}{\unicode[Arial]{x0394}} H=w_{s}\frac{\hspace{1pt}f\hspace{1pt}}{\delta } {\unicode[Arial]{x0394}} FOV=w_{s}\frac{2f}{\delta } {\unicode[Arial]{x0394}} y_{max}\end{equation}

where ${\unicode[Arial]{x0394}} A_{p}$ is the marker strip, a small change in the aperture area, $\Delta H$ is the corresponding affected vertical pixel array in the camera sensor, and $w_{s}$ is the fixed sensor marker strip aperture window width. The pixel array has a resolution of 640 × 480 and measures 640 pixels × 9 μm/pixel = 5.76 mm wide and 480 pixels × 9 μm/pixel = 4.32 mm high. Figure 8 illustrates the integration of all previous equations in block diagram form, where an input pressing force results in a change in aperture area on the sensor, which is recorded by the event camera.

Figure 8. Sensor block diagram equations summary.

4.1. Experiment description

The following laboratory experiment demonstrates the operation and testing of a novel model-based neuromorphic dynamic vision sensor. Figure 9 illustrates the integration of the sensor with an end-effector on a UR10 Robotic Manipulator. The robot’s end-effector and sensor will press against a dummy target plate to simulate a gripped object. The selected target plate is rigid, flat, and has a smooth surface finish, fabricated from PLA material using 3D printing techniques. The robot’s end-effector will move at a constant speed to simulate a wide range of tactile interactions with its slips. The interaction starts by moving the robot from a start home position and placing the sensor at an arbitrary reference position close to the target plate (i.e., approaching). Then, the robot manipulator is instructed to perform the pressing by advancing the robot manipulator’s prespecified displacement amounts. Finally, the robot will move vertically, mimicking a slip for a predefined displacement, then release the press and return to the home position. Performing all experiments from a home position with constant robot speed and selecting prespecified displacements guarantees repeatability of the pressing force experiments, which is given as $P=B\frac{dx}{dt}+K{\unicode[Arial]{x0394}} x$ , function of speed and displacement.

Figure 9. Experimental tactile sensor setup.

The experiment design is engineered to provide different levels of applied pressing forces against the target plate. The selected force levels are labeled as light, small, small medium, medium, small, big, and big pressing levels. Four experimental trial groups were carried out, and each trial consisted of twelve different extents of applied pressing forces on the sensor markers.

Finally, the robot operating system establishes as accurate and synchronized experimental datasets as possible. It enabled the control of the UR10 robot to precisely execute robotic actions such as approaching, pressing, sliding, and releasing while simultaneously managing data acquisition from the DVXplorer event-based camera. This ensures seamless synchronization between the robot’s movements and sensor data, providing accurate and repeatable experimental conditions.

4.2. Experimental results modeling

Three sets of raw data generated by neuromorphic tactile sensors are captured and depicted at the top of Figure 10. The three curves represent three degrees of applied force: small, medium, and big. A 20 ms of accumulated raw events are used to identify four distinct regions corresponding to the robotic manipulator’s actions. The first region represents the robotic manipulator as it approaches the target plate. The second region represents a pressing action against the target object, while the third region shows the object slipping action. Finally, the last region represents the object’s release action. The bottom graph in Figure 10 illustrates the same data in a filtered form, where moving averages are used to filter and smooth the data, allowing the four action regions to be clearly identified.

Figure 10. Three datasets of event tactile sensor raw data visualization.

The regions of pressing and slipping behavior portrayed in Figure 10 clearly validate the first-order system (FOS) derived mathematically in Eqs. (10) and (11). Figure 11 depicts two grasping axial pressing force contact levels applied on the sensor, “low” and big” contacts. The left graph shows the low-contact pulse-pressing axial force response, which represents a typical FOS behavior for the pressing action. In contrast, due to the nonlinear behavior of the Ninja flex material, the right-hand graph’s “big” contact force response exhibits a higher level of nonlinear, unmodeled dynamics. Considering only the linear FOS behavior and using an exponential unit pulse input, the FOS curve fitting may be given as follows:

(16) \begin{equation}x(t)=\left\{\begin{array}{cc} \alpha _{1}(1-e^{-t/{\tau _{1}}}) & 0\leq t\lt T\\[5pt] \alpha _{1}(e^{-(t-T)/{\tau _{1}}}-e^{-t/{\tau _{1}}}) & t\geq T \end{array}\right\}\end{equation}

where $\alpha _{1}\in [1365, 2280]$ and $\tau _{1}\approx 300 $ ms. The red curves in Figure 11 represent the fitted FOS linear model with a Pearson correlation coefficient of R = 0.983138, which was used as training data for the AI classifier.

Figure 11. Unit step input force model fitting for the pressing FOS.

Figure 12 shows the slip action of the experimental and fitted models for a unit-ramp input. The FOS response may be captured using the following equation:

(17) \begin{equation}\theta (t)=\alpha _{2}\Big(\frac{1}{\tau _{2}}t-1+e^{-t/{\tau _{2}}}\Big)\end{equation}

where $\propto _{2}\approx 1615$ and $\tau _{2}\approx 325$ ms. The FOS model is fitted with a correlation coefficient of R = 0.999762.

Figure 12. Unit ramp input force model fitting for the slipping FOS.

4.3. Experimental results visualization

The sensor actions' experimental data may be visualized as an image. Spatially visual-mapped camera frames are constructed by mapping event coordinates onto a 2D grid corresponding to the sensor’s camera resolution of 480 by 640. The frames are segmented by dividing the event stream into frames based on an accumulation time delta. Furthermore, noise suppression and reduction in accumulated frames (i.e., salt-and-pepper noise) were achieved using a median filter.

Figure 13 shows the picture frame, which displays the sensor’s markers and strip displacement during a slip action. These highlighted rectangular areas are used as a ROI in subsequent analysis.

Figure 13. Slip frame picture visualization, deformed markers.

4.4. Experimental pressing raw results

The raw data events comprise positive and negative polarities; positive marks increase in event intensity, while negative marks represent a decrease in event intensity. Consider a medium-pressure force action, as shown in Figure 14, which exhibits this dual behavior. During the pressing action, two interrelated changes in intensity occur. The sensor markers block ambient light and lower their intensity as they are pressed. On the other hand, the pressing action opens the marker strips further, resulting in increased intensities in the camera’s vicinity. To decouple these interrelated effects, one can find the difference between these events, shown in the blue curve.

Figure 14. Pressing events polarity issues example.

Furthermore, quantifying the amount of pressing force (i.e., “light,” “small,” “small medium,” “medium,” “small big,” and “big”) is characterized by the increased number of sensor-reported events. One way to quantify the pressing amount is to use the area under the designated pressing region as portrayed in Figure 10. Consequently, Figure 15 depicts the strong correlation between the degree of pressing and the computed area in the selected region.

Figure 15. Pressing force qualitative extent.

5.1. Temporal LSTM classification

Model-based LSTM classification can be utilized to leverage the previously identified FOS behavior. This work generated four experimental trials based on the derived model, which were used to train the LSTM neural networks. Each trial consisted of twelve applied pressing forces with different grasping force severities or extents. The experimentally identified FOS dynamical model is used to generate experimentally trained data for the spatial–temporal dynamical LSTM neural nets. The identified model is used to generate numerous FOS training trajectories for neural network training, using a diverse set of random robotic actions and their corresponding initial conditions.

Referring to Figure 16, the data analysis process diagram, the first step is to qualitatively classify the robot’s action type using a temporal LSTM network. The second step estimates the extent of the pressing force qualitatively using a fuzzy logic (FL) classifier. The LSTM results are shown in Table I, and the corresponding confusion matrix is shown in Figure 17.

Table I. Temporal LSTM classifications results.

Figure 17. Temporal LSTM confusion matrix.

5.2. Spatial–temporal LSTM classification

A model-based LSTM classification approach using the weighted centroid feature is applied similarly to the temporal LSTM training, with four model-based experimental trials generated to train the spatial–temporal LSTM neural nets. Each experimental trial consisted of twelve applied pressing forces with different grasping force severities or extents.

Referring to the Figure 16 data analysis process diagram, the first step is to qualitatively classify the robot’s action type using the spatial–temporal LSTM based on the weighted centroid estimations of the ROI. The second step estimates the extent of the pressing force qualitatively using a FL classifier.

Finally, the weighted centroid dynamics is used to calculate the slip rate and compute the traveled displacement in $\Delta t$ time. The spatial–temporal LSTM classification results are shown in Table II, and the corresponding confusion matrix is shown in Figure 18.

Table II. Spatial–temporal LSTM classifications results.

Figure 18. Spatial–temporal LSTM confusion matrix.

5.3. Fuzzy logic pressing force estimation

The estimation of the extent of the pressing force is achieved using a FL-based classifier. The proposed FL classifier comprises four key steps: fuzzification of all crisp inputs, a rule base for classification rules, inference for decision-making, and defuzzification for the outputs. Figure 19 illustrates the structure of the proposed FL classifier [Reference Houdt, Montero and Nápoles34].

Figure 19. Fuzzy logic pressing force estimation.

The fuzzification and defuzzification of the input and output linguistic variables and their corresponding interval ranges are captured using the fuzzy membership functions illustrated in Figures 20 and 21, respectively. The overlaps between the membership functions are embedded to account for boundary values and induce continuous, smoother transitions, allowing for multiple rules to fire [Reference Abdalla, Musa and Jafar35].

Figure 20. FL input fuzzification.

Figure 21. FL output fuzzification.

The pressing force classifier rule base is simple in structure yet effective. Table III summarizes the simple rules used in the classifier. Each rule is evaluated using the If–Then statement. To illustrate the operation of the FL classifier, Figure 22 is used for illustration. Considering a pressing force action classification, where two adjacent rules are fired simultaneously (i.e., due to input overlap), the corresponding output areas are aggregated to produce their centroid.

Table III. FL rule base.

Figure 22. FL rules firing and inference example.

Ultimately, a thorough analysis reveals that the weighted centroid feature effectively represents events and regional concentrations. The weighted centroid of the ROI correlates with the object’s slip action. Hence, by continuously evaluating the centroid feature over time, we can estimate the slip velocity profile, enabling us to calculate the slip displacement at any instant. Spatial–temporal tracking of the centroids over time is used to analyze movement patterns within each ROI.

(18) \begin{equation}RoI=\left\{\left(x_{i} ,y_{j}\right) \colon i, j\in \textit{corners}\ of\ RoI\right\}\end{equation}

Using the events intensities as weights, we shall use a weighted centroid to account for the varying intensities within the ROI.

(19) \begin{equation}\overline{x}=\frac{\sum x \ I(x,y)}{\sum I(x,y)} , \overline{y}=\frac{\sum y\ I(x,y)}{\sum I(x,y)}\end{equation}

where $I(x,y) $ is the intensity at the pixel $(x,y)\in RoI $ after performing data filtering.

Finally, the object’s slip displacement may be estimated from the centroid’s rate of change by implementing numerical integration. The integration acts as a low-pass filter, reducing the effects of high-frequency noise.

(20) \begin{equation}\vec {v}(t)=\frac{1}{{\unicode[Arial]{x0394}} t}\left(\overline{x}(t) \ \hat{\! i}+\overline{y}(t)\ \hat{\!j}\right)\end{equation}

(21) \begin{equation}\vec {d}(t)=\int _{t_{1}}^{t_{2}}\vec {v}(t)\, dt\end{equation}

The change in the centroid coordinates in the ROI $(\overline{x}, \overline{y})$ provides information about the object’s slipping trajectory at its contact point. In this work, only translational information is reported by the tactile sensor. Consequently, only the $\overline{y}\_ \textit{coord}$ is used to estimate the object’s slip displacement. Figure 23 illustrates the linear behavior of the $\overline{y}\_ \textit{coord}$ as the object is slipping for a medium grasping force extent, and the negative slope is from the orientation of the pixel grid (i.e., during the slip, the object falls while markers move up) as shown in Figure 13. The slope of the linear regression line should represent the speed of the slip, which reflects the robotic manipulator end-effector speed. The estimated average slope for the experimental trials is approximately 0.005 m/s, while the robotic manipulator end-effector speed is 0.004 m/s. This demonstrates the sensor’s ability to estimate the object’s slipping speed and displacement.

Figure 23. Centroid vertical trajectory.