*2.1. AUV Nonlinear Model*

To study the motion of the AUV, the fixed coordinate system {E} and the motion coordinate system {O} established in this section are shown in Figure 1.

**Figure 1.** Coordinate system diagram, where *E* − *ξηζ* is the fixed coordinate system, *ξ* points due north, *η* points due east, O − xyz is the motion coordinate system, and O coincides with the center of gravity of the AUV, where the *x*-axis points to the bow of the vehicle.

A fixed point at sea level is usually chosen as the origin of the fixed coordinate system, where the *ξ* axis points to due north and the *η* axis points to due east. In order to simplify the nonlinear model of the AUV, the center of gravity of the AUV is chosen as the origin of the motion coordinate system {O}, where the *x* axis is located in the longitudinal midprofile and points to the bow of the AUV, and the *y* axis is perpendicular to the longitudinal mid-profile and points to the starboard side of the AUV.

In model building, it may be assumed that the AUV studied in this paper is a rigid body with a certain mass distribution, and the effect of its transverse rocking motion is not considered when the AUV is operating underwater, i.e., the transverse rocking attitude angle and angular velocity are kept as desired values. In the following, the nonlinear model of the AUV and the feedback linearization process are based on this assumption.

For the purpose of the following study, the following motion variables are defined:

The position vector in a fixed coordinate system is *η* = [*xyz θ ψ*] *T* ∈ *R*3 × *S*2. The position is *η*1 = [*xyz*] *T* ∈ *R*3, The attitude angle is *η*2 = [*θ ψ*] *T* ∈ *S*2. The velocity vector in the motion coordinate system is *v* = [*uvwqr*] *T* ∈ *R*5. The linear velocity in the motion coordinate system is *v*1 = [*uvw*] *T* ∈ *R*3. The angular velocity in the motion coordinate system is *v*2 = [*q r*] *T* ∈ *R*2. The forces and moments in the motion coordinate system are *T* = [*XYZMN*] *T* ∈ *R*6. The force in the motion coordinate system is *T*1 = [*XYZ*] *T* ∈ *R*3. The moment in the motion coordinate system is *T*2 = [*M N*] *T* ∈ *R*2.

Where *R*3 denotes the three-dimensional Euclidean space and *S*3 denotes the threedimensional torus, i.e., there exist three angles in the range [0, 2*π*].

Combining the AUV kinematic model and dynamics model, the AUV nonlinear mathematical model vector expression can be obtained as:

$$\begin{aligned} \dot{\eta} &= J(\eta)v\\ M\_R \dot{v} + M\_A \dot{v} + \mathbb{C}\_R(v)v + Y(v) + \mathbb{g}(\eta) &= T + \lambda \end{aligned} \tag{1}$$

The kinematic and kinetic mathematical model derivation process and model parameters of the AUV are shown in the literature [19] shown.

#### *2.2. AUV Feedback Linearization Model*

As can be seen from Equation (1), the nonlinear model of the AUV is still very complicated even if it is written in vector form. In this subsection, we simplify the AUV nonlinear model by using the transformation method to make the complex problem simple. By coordinate transformation, we can transform the nonlinear model of the AUV in the motion coordinate system to a specific coordinate system, in which the nonlinear model will realize the decoupling of each control channel and transform into a second-order integral model.

According to the literature [20], the AUV model is transformed appropriately:

$$\begin{cases} \dot{\eta} = J(\eta)v\\ \dot{v} = M^{-1}N(\eta, v) + M^{-1}T \end{cases} \tag{2}$$

where *M* = *MR* + *MA* is the sum of the inertia matrix and the additional inertia matrix. *T* denotes the control input forces and moments. Synthesizing the three terms of the model *CR*(*v*)*v*, *Y*(*v*), *g*(*η*) into a column vector *N*(*η*, *v*), then Equation (2) can be transformed into:

$$
\begin{bmatrix} \dot{\eta} \\ \dot{\upsilon} \end{bmatrix} = \begin{bmatrix} I & 0 \\ 0 & M^{-1} \end{bmatrix} \begin{bmatrix} J(\eta)\upsilon \\ N(\eta, \upsilon) \end{bmatrix} + \begin{bmatrix} 0 \\ M^{-1} \end{bmatrix} T \tag{3}
$$

In Equation (3), a mathematical model with three axial thrusters and two rudders is considered, replacing the controller input T in Equation (3) with the thrust of the axial thrusters *Xprop*, *Yprop*, *Zprop* and the rudder angles *δr*, *δs*. The vector *ξ* = [*ηT*, *vT*] *T* will be formed by *η* and *v*. The two matrices in Equation (3) are taken to be *M*1 = *I* 0 0 −*M*−1 ∈ 0

*R*10×10 and *M*2 = *M*−1 ∈ *R*10×5, respectively. The above Equation (3) is transformed into the following vector form for model linearization:

$$\dot{\tilde{\xi}} = f(\tilde{\xi}) + M\_2 \mathbf{g}'(\tilde{\xi}) \,\hat{\mathfrak{n}}\tag{4}$$

Among them *f*(*ξ*) = *M*1 *J*(*η*)*v N*(*η*, *v*) ∈ *R*10×1, *g* (*ξ*) =  *g ij*(*ξ*) ∈ *R*5×5, *u*ˆ = ' *Xprop*,*Yprop*, *Zprop*, *δs*, *δr* (*T* .

Vector field: the nonlinear first-order model is taken as the following equation:

$$\begin{array}{l} \dot{\mathbf{x}} = f(\mathbf{x}) + \mathbf{g}(\mathbf{x})u \\ \mathbf{y} = h(\mathbf{x}) \end{array} \tag{5}$$

where *f*(*x*), *g*(*x*), *h*(*x*) is smooth enough over the definition domain *D* ∈ *Rn*, the mapping *f* : *D* → *Rn* and *g* : *D* → *Rn* are vector fields over the domain of definition D.

Lie derivative: derivative of *y* in Equation (5).

$$\dot{y} = \frac{\partial h}{\partial \mathbf{x}}[f(\mathbf{x}) + \mathbf{g}(\mathbf{x})u] = L\_f h(\mathbf{x}) + L\_\mathcal{g} h(\mathbf{x})u \tag{6}$$

where *Lf h*(*x*) = *∂h ∂x f*(*x*), *Lgh*(*x*) = *∂h ∂x g*(*x*), is said to be the Lie derivative of *h* along the smooth vector field *f* .

Define the output function *ζ* = *h*(*ξ*), then the dynamics of the AUV are modeled as:

$$\begin{array}{l} \dot{\xi} = f(\xi) + M\_2 \xi'(\xi) \mathfrak{u} \\ \zeta = h(\xi) \end{array} \tag{7}$$

The basic idea of feedback linearization is to find an appropriate coordinate transformation and a control rate after the coordinate transformation.

Select the coordinate transformation *z* = *ϕ*(*x*).

$$\begin{aligned} z\_1 &= \left[ h\_1(\mathbf{x}), h\_2(\mathbf{x}), h\_3(\mathbf{x}), h\_4(\mathbf{x}), h\_5(\mathbf{x}) \right]^T \\ z\_2 &= \left[ L\_f h\_1(\mathbf{x}), L\_f h\_2(\mathbf{x}), L\_f h\_3(\mathbf{x}), L\_f h\_4(\mathbf{x}), L\_f h\_5(\mathbf{x}) \right]^T \end{aligned} \tag{8}$$

From transforming the coordinates, we have:

$$\begin{aligned} z\_1 &= h(\mathbf{x}) \\ z\_2 &= L\_f h(\mathbf{x}) \end{aligned} \tag{9}$$

The transformation gives:

$$\begin{array}{l}\dot{z}\_1 = z\_2\\\dot{z}\_2 = L\_f^2 h(\mathbf{x}) + L\_\mathcal{g} L\_f h(\mathbf{x})\hat{u}\end{array} \tag{10}$$

In a given coordinate system, to obtain a simpler form, we might as well allow *u* to equal *L*2 *f h*(*x*) + *LgLf h*(x)*u*ˆ. So, we can obtain the following equation:

$$u = B(\mathbf{x}) + \Gamma(\mathbf{x})\mathfrak{A} = L\_f^2 h(\mathbf{x}) + L\_\mathfrak{J} L\_f h(\mathbf{x})\mathfrak{A} \tag{11}$$

Then, the second-order integral model of the AUV in the new coordinate system after transformation can be obtained under the action of Equations (6) and (10).

$$\hat{u} = \Gamma^{-1}(\mathbf{x})(\mu - B(\mathbf{x})) \tag{12}$$

The AUV linearized mathematical model can be obtained as:

$$\begin{array}{l}\dot{z}\_1 = z\_2\\\dot{z}\_2 = \mu\end{array} \tag{13}$$

where, *z*1 is the position information of the AUV after the coordinate transformation, *z*2 is the speed information of the AUV after the coordinate transformation, and *u* is the control input of the AUV after the coordinate transformation.

#### **3. CNN-LSTM Prediction Model**

*3.1. Pre-Requisite Knowledge*

3.1.1. Convolutional Neural Network

In underwater formations of multiple AUVs, the transmitted track data from the leader to the follower may be subject to both delay and noise interference caused by various factors such as oceanic noise. To enable accurate trajectory prediction, the data must be filtered prior to analysis. In this study, a convolutional neural network is employed to filter the data and extract the relevant trajectory data features. The basic structure diagram of the network is illustrated in Figure 2.

**Figure 2.** CNN structure schematic.

Figure 2 shows the structure of a convolutional neural network (CNN), which consists of an input layer, a convolutional layer, a ReLU layer, a pooling layer, and a fully connected layer. CNNs differ from traditional neural networks in two main ways:

### 3.1.2. Long Short-Term Memory

For problems related to time series, such as AUV formation tracking, traditional neural network algorithms such as CNNs are not fully applicable. Long short-term memory (LSTM) networks are better suited for these problems due to their memory effect. LSTM networks use memory modules instead of traditional storage units, which are interconnected recursive subnetworks. The memory module contains gates that control the flow of information, allowing for memory information to affect neuronal nodes at longer time intervals. The three gates of an LSTM cell are the input gate, output gate, and forgetting gate, which control the storage and inflow of information as well as the core cell unit. The cell structure of LSTM is shown in Figure 3. The activation function plays an important role in the neural network by introducing nonlinear factors into the model, enabling it to perform well on problems where the linear model is not suitable.

**Figure 3.** LSTM cell structure diagram.

In Figure 3, the symbol " *ft*" represents the forgetting gate, "*it*" represents the input gate, and "*ot*" represents the output gate. "*xt*" denotes the input to the input layer at time "*t*", "*ht*" denotes the output at time "*t*", "*Ct*" denotes the state value of the memory cell at time "*t*", and "*σ*" represents the sigmoid function. The mathematical expressions for "*σ*" and "tanh" in the figure are as follows:

$$
\sigma(z) = \frac{1}{1 - e^{-z}} \tag{14}
$$

$$\tanh(\mathfrak{x}) = \frac{e^{\mathfrak{x}} - e^{-\mathfrak{x}}}{e^{\mathfrak{x}} + e^{-\mathfrak{x}}} \tag{15}$$

The LSTM processes the data internally as follows:

$$f\_t = \sigma \left( \mathcal{W}\_{xf} \mathbf{x}\_t + \mathcal{W}\_{hj} h\_{t-1} + b\_f \right) \tag{16}$$

$$\dot{\mathbf{u}}\_t = \sigma(\mathbf{W}\_{ri}\mathbf{x}\_t + \mathbf{W}\_{hi}h\_{t-1} + b\_i) \tag{17}$$

$$o\_f = \sigma(\mathcal{W}\_{\text{x}\text{v}}\mathfrak{x}\_t + \mathcal{W}\_{\text{hu}}h\_{t-1} + b\_o) \tag{18}$$

$$\mathcal{L}\_t = f\_t \cdot \mathcal{L}\_{t-1} + i\_t \cdot \tanh(\mathcal{W}\_{\mathbf{x}\mathbf{c}} \mathbf{x}\_t + \mathcal{W}\_{\mathbf{h}\mathbf{c}} h\_{t-1} + b\_{\mathbf{c}}) \tag{19}$$

$$h\_l = o\_l \cdot \tanh(c\_l) \tag{20}$$

where, *W* is the weight matrix, · is the product of point pairs, and *b* is the deviation.

From Equations (14)–(18), it can be seen that the LSTM is computed by first calculating the values of the forgetting gate, input gate, output gate, and candidate state *ht*−1 and the input at the current moment based on the external state. Next, the internal state *ct*−1 is used to compute the values of the forgetting gate, the input gate and the candidate state in order to update the internal state *ct*. Finally, the information is passed to the external state *ht* via the current internal state and output gates.

#### *3.2. CNN-LSTM Prediction Model Building*

This paper proposes a neural network prediction model that combines the advantages of CNN feature extraction and noise filtering with LSTM temporal memory. The model is designed by connecting the CNN and LSTM layers in series, and its structure is depicted in Figure 4.

**Figure 4.** CNN-LSTM prediction model diagram.

The proposed structure is composed of two main modules: the data processing module and the model prediction module. Upon receiving the navigator state information, the data are first preprocessed and then fed into the prediction model. As illustrated in Figure 4, the CNN module is composed of three convolutional layers: a BatchNorm layer, a dropout layer, an expansion layer, and a fully connected layer, which is responsible for receiving the preprocessed data and extracting data features. The LSTM module, on the other hand, consists of two LSTM layers, which analyze the features extracted by the CNN, explore the time series relationships in the data, and predict multiple future points.

The overall prediction process is as follows: the navigator state information is preprocessed by the data processing module, and the processed data are passed to the CNN module for filtering and spatial feature learning. The CNN generates a sequence of highlevel features representing the capture and passes it to the tensor processing module. The tensor processing layer then reshapes the output of the CNN so that it can be accepted by the LSTM sub-module. Finally, the LSTM module learns the time-series dependencies of the delayed data and outputs the predicted values for the current moment.

#### **4. Predictive Control of Multi-AUV Formations Based on CNN-LSTM Models**

*4.1. Multi-AUV Formation Controller Design under Ideal Communication Conditions*

It may be assumed that there are five AUVs in the formation: one leader and four followers. The formation that the formation wants to form and maintain is an isosceles triangle (the specific formation is shown in Figure 5 below), and the AUVs are required to maintain the formation even when making a spiral dive.

**Figure 5.** Formation diagram.

As shown in Figure 5, L denotes the leader, and *F*1, *F*2, *F*3 and *F*4 are all follower AUVs. According to the formation that we want to achieve, we introduce the variables *R* and *β* to constrain the formation, where the distance from the leader to the followers *F*1 and *F*2 line is *R*, the distance from the follower *F*1 and *F*2 line to the follower *F*3 and *F*4 line is also *R*, and the attitude angle of the formation hold is *β*. The formation constraints proposed in this paper are:

$$\begin{cases} \begin{aligned} \eta\_{F1} + d\_1 &= \eta\_L \\ \eta\_{F2} + d\_2 &= \eta\_L \\ \eta\_{F3} + d\_3 &= \eta\_L \\ \eta\_{F4} + d\_4 &= \eta\_L \end{aligned} \end{cases} \tag{21}$$

$$\begin{cases} \begin{aligned} \dot{\eta}\_{F1} + d\upsilon\_1 &= \dot{\eta}\_L \\ \dot{\eta}\_{F2} + d\upsilon\_2 &= \dot{\eta}\_L \\ \dot{\eta}\_{F3} + d\upsilon\_3 &= \dot{\eta}\_L \\ \dot{\eta}\_{F4} + d\upsilon\_4 &= \dot{\eta}\_L \end{aligned} \end{cases} \tag{21}$$

where *d*1, *d*2, *d*3, *d*4, *dv*1, *dv*2, *dv*3 and *dv*4 are denoted as:

$$\begin{cases} \begin{aligned} &d\_{1} = \left(-(\cos\beta)^{-1}R\cos(\psi\_{L}-\beta-\frac{\pi}{2}), (\cos\beta)^{-1}R\cos(\psi\_{L}+\beta-\frac{\pi}{2}), 0, 0, 0\right)^{T} \\ &d\_{2} = \left(-(\cos\beta)^{-1}R\cos(\psi\_{L}+\beta-\frac{\pi}{2}), -(\cos\beta)^{-1}R\cos(\psi\_{L}-\beta-\frac{\pi}{2}), 0, 0, 0\right)^{T} \\ &d\_{3} = \left(-(\cos\beta)^{-1}2R\cos(\psi\_{L}-\beta-\frac{\pi}{2}), (\cos\beta)^{-1}2R\cos(\psi\_{L}+\beta-\frac{\pi}{2}), 0, 0, 0\right)^{T} \\ &d\_{4} = \left(-(\cos\beta)^{-1}2R\cos(\psi\_{L}+\beta-\frac{\pi}{2}), -(\cos\beta)^{-1}2R\cos(\psi\_{L}-\beta-\frac{\pi}{2}), 0, 0, 0\right)^{T} \\ &\left\{ \begin{aligned} &dv\_{1} = l\_{\eta}(r\_{L}\tan(-\beta)\times R, 0, 0, 0, 0)^{T} \\ &dv\_{2} = l\_{\eta}(r\_{L}\tan(\beta)\times R, 0, 0, 0, 0)^{T} \\ &dv\_{3} = l\_{\eta}(r\_{L}\tan(-\beta)\times 2R, 0, 0, 0, 0)^{T} \\ &dv\_{4} = l\_{\eta}(r\_{L}\tan(\beta)\times 2R, 0, 0, 0, 0)^{T} \end{aligned} \right. \end{cases} \end{cases} \tag{22}$$

In a leader-follower formation control with five AUVs, the motion state vector of the *i* th follower AUV at the moment of *t* is *εi*(*t*) = *ηi*(*t*) and the motion state vector of the leader is *εL*(*t*) = *ηL*(*t*). If the formation satisfies Equation (23), it is said that the formation can achieve formation maintenance and stability convergence.

$$\begin{vmatrix} \lim\_{t \to \infty} \left| \varepsilon\_i(t) - \varepsilon\_L(t) + d\_i \right| = 0\\ \lim\_{t \to \infty} \left| \dot{\varepsilon}\_i(t) - \dot{\varepsilon}\_L(t) + d\upsilon\_i \right| = 0 \end{vmatrix} = 1, 2, 3, 4 \tag{23}$$

Let the attitude vector of the *i* th follower AUV at the time of *t* and the attitude vector of the leader AUV at the time of *z*1*d* in the lead follower formation control of the AUV be *z*1*i*.

Define the trajectory tracking error of the *i* th follower AUV as *zi*1*e* = *zi*1 − *z*1*d* + *di*, then . *zi*1*e* = *zi*2 − . *z*1*d*.

Define the following Lyapunov function:

$$V\_{i1} = \frac{1}{2} z\_{i1\mathfrak{e}} \,\,^2\,\tag{24}$$

Define *zi*2 = *zi*2*e* + . *z*1*d* − *ci*1*zi*1*e*, where *ci*1 is the positive constant and *zi*2*e* is the intermediate virtual control item. We can get *zi*2*e* = *zi*2 − . *z*1*d* + *ci*1*zi*1*e*, and the derivation gives . *zi*1*e* = *zi*2 − . *zi*1*d* = *zi*2*e* − *ci*1*zi*1*e*.

The derivative of *Vi*1 gives:

$$
\dot{V}\_{i1} = z\_{i1\varepsilon} \dot{z}\_{i1\varepsilon} = z\_{i1\varepsilon} z\_{i2\varepsilon} - c\_{i1} z\_{i1} \,\,^2 \tag{25}
$$

Define the switching function as:

$$
\sigma\_i = k\_{i1} z\_{i1c} + z\_{i2c} \tag{26}
$$

Among them, *ki*1 > 0. Because of . *zi*1*e* = *zi*2*e* − *ci*1*zi*1*e*, we can derive:

$$
\sigma\_i = k\_{i1} z\_{i1c} + z\_{i2c} = k\_{i1} z\_{i1c} + \dot{z}\_{i1c} + c\_{i1} z\_{i1c} = (k\_{i1} + c\_{i1}) z\_{i1c} + \dot{z}\_{i1c} \tag{27}
$$

Because of *ki*1 + *ci*1 > 0, there is *σi* = 0 only when *zi*1*e* = 0, *zi*2*e* = 0 and . *Vi*1 ≤ 0. For this, the next design step is needed.

Define the following Lyapunov function.

$$V\_{i2} = V\_{i1} + \frac{1}{2}\sigma\_i^2\tag{28}$$

The derivative of *Vi*2 gives:

$$\begin{array}{l} \dot{V}\_{2} &= \dot{V}\_{i1} + \sigma\_{i}\dot{r}\_{i} \\ &= z\_{i1\epsilon}z\_{i2\epsilon} - c\_{i1}z\_{i1\epsilon}^{2} + \sigma\_{i}\dot{r}\_{i} \\ &= z\_{i1\epsilon}z\_{i2\epsilon} - c\_{i1}z\_{i1\epsilon}^{2} + \sigma\_{i}(k\_{i1}\dot{z}\_{i1\epsilon} + \dot{z}\_{i2\epsilon}) \\ &= z\_{i1\epsilon}z\_{i2\epsilon} - c\_{i1}z\_{i1\epsilon}^{2} + \sigma\_{i}(k\_{i1}(z\_{i2\epsilon} - c\_{i1}z\_{i1\epsilon}) + \dot{z}\_{i2} - \ddot{z}\_{1d} + c\_{i1}\dot{z}\_{i1\epsilon}) \\ &= z\_{i1\epsilon}z\_{i2\epsilon} - c\_{i1}z\_{i1\epsilon}^{2} + \sigma\_{i}(k\_{i1}(z\_{i2\epsilon} - c\_{i1}z\_{i1\epsilon}) + \mathcal{U}\_{i} + F - \ddot{z}\_{1d} + c\_{i1}\dot{z}\_{i1\epsilon}) \end{array} \tag{29}$$

where *Ui* is the expression of the controller to be designed. *F* is the total uncertainty of the system.

The design of the *i* follower controller is shown below.

$$\mathcal{L}I\_{\bar{i}} = -k\_{\bar{i}1}(z\_{\bar{i}2\varepsilon} - c\_{\bar{i}1}z\_{\bar{i}1\varepsilon}) - \overline{F}\tanh(\sigma\_{\bar{i}}) + \ddot{z}\_{1d} - c\_{i1}\dot{z}\_{i1\varepsilon} - k\_{\bar{i}}(\sigma\_{\bar{i}} + \mathcal{J}\_{\bar{i}}\tanh(\sigma\_{\bar{i}})) \tag{30}$$

where *hi* and *βi* are positive constants.

Substituting Equation (30) into . *Vi*2 yields:

$$\begin{array}{rl} \dot{V}\_{i2} &= z\_{i1\varepsilon}z\_{i2\varepsilon} - c\_{i1}z\_{i1\varepsilon}{}^2 - h\_{i}\sigma\_{i}^{2} - h\_{i}\beta\_{i}|\sigma\_{i}| + F\sigma\_{i} - \sf{F}\sigma\_{i} \\ &\leq -c\_{i1}z\_{i1\varepsilon}{}^2 + z\_{i1\varepsilon}z\_{i2\varepsilon} - h\_{i}\sigma\_{i}^{2} - h\_{i}\beta\_{i}|\sigma\_{i}| \end{array} \tag{31}$$

Let *Qi* be equal to the following matrix.

$$Q\_i = \begin{bmatrix} c\_{i1} + h\_i k\_{i1}^2 & h\_i k\_{i1} - \frac{1}{2} \\ h\_i k\_{i1} - \frac{1}{2} & h\_i \end{bmatrix} \tag{32}$$

Due to

$$\begin{array}{rcl}z\_{i\varepsilon}{}^{\mathrm{T}}Q\_{i}z\_{i\varepsilon}&=& \left[\begin{array}{cc}z\_{i1\varepsilon}&z\_{i2\varepsilon}\end{array}\right]\left[\begin{array}{c}c\_{i1}+h\_{i}k\_{i1}^{2}&h\_{i}k\_{i1}-\frac{1}{2}\\h\_{i}k\_{i1}-\frac{1}{2}&h\_{i}\end{array}\right]\left[\begin{array}{c}z\_{i1\varepsilon}&z\_{i2\varepsilon}\end{array}\right]^{\mathrm{T}}\\&=\prescript{}{{}\_{i1}}z\_{i1\varepsilon}^{2}-z\_{i1\varepsilon}z\_{i2\varepsilon}+h\_{i}k\_{i1}^{2}z\_{i1\varepsilon}^{2}+2h\_{i}k\_{i1}z\_{i1\varepsilon}z\_{i2\varepsilon}+h\_{i}z\_{i2\varepsilon}^{2}\\&=\prescript{}{{}\_{i1}}z\_{i1\varepsilon}^{2}-z\_{i1\varepsilon}z\_{i2\varepsilon}+h\_{i}\sigma\_{i}^{2}\end{array}\tag{33}$$

Among them, *zieT* = ' *zi*1*e zi*2*e* ( . If you want to guarantee that *Qi* is a positive definite matrix, then

$$\dot{V}\_{i2} = -z\_{i\mathfrak{e}}{}^{\mathsf{T}}Q\_{i}z\_{i\mathfrak{e}} - h\_{i}\beta\_{i} \left| \mathfrak{e}\_{i} \right| \lessapprox 0\tag{34}$$

Due to

$$\left| Q\_i \right| = h\_i \left( c\_{i1} + h\_i k\_{i1}^2 \right) - \left( h\_i k\_{i1} - \frac{1}{2} \right)^2 = h\_i (c\_{i1} + k\_{i1}) - \frac{1}{4} \tag{35}$$

Therefore, it is possible to guarantee . *Vi*2 ≤ 0 by taking the values of *hi*, c*i*1 and *ki*1 such that |*Qi*|> 0, i.e., *Qi* is a positive definite matrix.

By taking the values of *h*, c1 and *k*1, you can make |*Q*|> 0. Thus, it can be deduced that *Q* is a positive definite matrix and that . *V*2 ≤ 0 is guaranteed.

According to LaSalle's invariance principle, when . *Vi*2 ≡ 0 is taken, it can be deduced that *zie* ≡ 0, *σi* ≡ 0. When *t* → ∞, since *zi*1*e* → 0, *zi*2*e* → 0, it can be deduced that *zi*2*e* → 0, . *zi*1 → . *z*1*d* .

In summary, it can be seen that the Lyapunov functions *Vi*1 and *Vi*2 are positive definite, and the values of *Vi*1, c*i*1 and *ki*1 can be reasonably chosen to ensure that . *Vi*1 and . *Vi*2 are negative definite, so the designed AUV formation controller (30) is stable and convergent.

#### *4.2. Sliding Window-Based Predictive Control of Multi-AUV Formations under Communication Constraints*

In the previous section, the backstepping sliding mode control method was used and the formation controller was designed according to the formation constraint relationship. The controller for the follower AUV in the formation with time-lag state is presented below due to the communication delay between the leader and the follower and the limitations of the hydroacoustic sonar in transmitting high-frequency signals, resulting in a longer communication interval between them. As a consequence, the follower may not receive the real-time status information of the leader.

$$\mathcal{U}I\_{\bar{i}} = -k\_{\bar{i}1}(z\_{\bar{i}2\varepsilon} - c\_1 z\_{\bar{i}1\varepsilon}) - \overline{F} \tanh(\sigma\_{\bar{i}}) + \bar{z}\_{1d} - c\_1 \dot{z}\_{\bar{i}1\varepsilon} - h(\sigma\_{\bar{i}} + \beta \tanh(\sigma\_{\bar{i}})) \tag{36}$$

where, *zi*1*e* = *zi*1 − *z*1*d*(*t* − *τ*) + *di*, *zi*2*e* = *zi*2 − *z*2*d*(*t* − *τ*) + *c*1*zi*1*e* + *dvi*, *σi* = *k*1*zi*1*e* + *zi*2*e*, and *τ* are the communication delay times between the navigator and the follower.

To illustrate the effect of communication delay on formation control while preparing for a new predictive control strategy, the following assumptions are made about the communication delay between the leader and the follower and the hydroacoustic sonar occurrence interval:

**Assumption 1.** *The distance between the navigator and the follower is close, and the speed of acoustic wave transmission in the water is 1500 m/s, so the communication time delay caused by the communication transmission is small, where it is assumed that the delay time between the broadcast of the navigator sending the status information and the follower receiving the information and measuring the settlement is 1 s.*

**Assumption 2.** *Due to the limitation of communication bandwidth, the navigator cannot send too many beats of historical status data to the follower at one time; so, suppose the navigator can send five beats of status data to the follower at one time.*

**Assumption 3.** *The hydroacoustic sonar is unable to sound at high frequencies and the sounding time is affected by the size of the data sent, assuming that the communication interval of the hydroacoustic sonar is 6–9 s.*

To solve the communication delay and communication interval problem between the leader and the follower, this section proposes a formation control strategy based on a sliding window to achieve multi-step prediction, which iterates the historical state information of the leader to predict the current state information of the leader step by step, which saves computational efficiency and has better adaptability compared with the observer-based iterative prediction method. The specific principle of the strategy is described below.

At the *M* time, the navigator sends its own status data {*Z*1, *Z*2, ······ *ZM*−1, *ZM*} from the previous *M* time to the follower in the formation. Due to the communication transmission delay *τtran* and the hydroacoustic sonar sounding time consuming *τ*int*er*, a fixed time delay *τonce*\_*tal* = *τtran* + *τ*int*er* is defined, and the follower receives the status information of the navigator at the *M* + *τonce*\_*tal* time, and the status information of the navigator received by the follower at this time is the status information of the navigator at the *M* time. So, the follower needs to predict the state information of the leader at the *M* + *τonce*\_*tal* time as the tracking target based on the state information of the leader at the *M* time.

The second sounding of the sonar starts immediately after the first sounding. Since the transmission delay after the first sounding is included in the second sonar sounding elapsed time, the follower needs time *τ*int*er* to receive the information of the navigator for the second time. Therefore, after the follower receives the status information of the navigator at the *M* + *τonce*\_*tal* time, the follower firstly has to predict the status information of the navigator at the *M* time as the tracking target; secondly, since the follower cannot receive the status information of the navigator at the *τ*int*er* time in the future, the follower needs to then predict the status information of the navigator at the *τ*int*er* time in the future. A schematic diagram of the information transfer process is shown in Figure 6.

**Figure 6.** Information transmission diagram.

This paper focuses on predicting the real-time state of the leader in AUV formation by using delayed state data received by the followers as input to the prediction model. The delayed data are in the form of a time series, and to achieve continuous prediction, a sliding window approach is designed where the delay information is fed into the window as input and the real information as output, as illustrated in Figure 7. To evaluate the model's performance, a delay time of 10 s is set, and the size of the sliding window, which corresponds to the time step of the input data, is set to 5. The prediction equation is given as follows:

$$z(t) = f(\{z(t-14), \cdot, \cdot, z(t-11), z(t-10)\})\tag{37}$$

where *z* = [*z*1, *z*2] denotes the position vector of the navigator in time. *z*1 = [*x*, *y*, *depth*, *θ*, *ψ*] *T*, where *x*, *y* and *depth* represent the displacement in three coordinate directions; *θ* and *ψ* represent the pitch and heading angles. *z*2 = [*u*, *v*, *w*, *q*,*r*] *T*, where *u*, *v* and *w* are the longitudinal, lateral and vertical velocities respectively; *q* and *r* are the longitudinal and bow angular velocities.

**Figure 7.** Schematic diagram of the sliding window.

The prediction strategy designed in this paper has two main phases: fixed delay prediction and communication interval prediction. In the fixed delay prediction stage, the follower puts the state information sent by the navigator into the designed sliding window and uses the prediction model to predict the state quantity *Z*ˆ *M*+1 at the *M* + 1 th time based on the data in the first *M* times of the sliding window. Put *Z*ˆ *M*+1 into the sliding window, and then the sliding window moves forward to obtain *Z*ˆ *M*+2 using *Z*ˆ *M*+1 and the historical state quantity prediction, and finally obtain the state prediction *Z*ˆ *M*+*τonce*\_*tal* at *M* + *τonce*\_*tal* moments through continuous iterative prediction.

At the same time, due to the effect of hydroacoustic sonar sounding time consumption, the follower will only receive the next status data from the navigator at the moment of *M* + *τonce*\_*tal* + *τ*int*er*, so the follower will continue to make iterative predictions based on the status quantity *Z*ˆ *M*+*τonce*\_*tal* obtained from the prediction compensation during this period, obtain *Z*ˆ *M*+*τ once*\_*tal*+1+1, *Z*ˆ *M*+*τonce*\_*tal* +2······ *Z*ˆ *M*+*τonce*\_*tal* +*τ*int*er*, and output in turn until it receives the time delay status data from the navigator again. Based on the above strategy, the follower will get the predicted value of the current moment of the leader; the controller of the follower in the AUV formation at this time is shown below.

$$\mathcal{L}I\_{\hat{i}} = -k\_{\hat{i}1}(\hat{z}\_{i2\epsilon} - c\_1 \hat{z}\_{i1\epsilon}) - \overline{F} \tanh(\hat{\sigma}\_{\hat{i}}) + \ddot{z}\_{1d} - c\_1 \dot{\hat{z}}\_{i1\epsilon} - h(\hat{\sigma}\_{\hat{i}} + \beta \tanh(\hat{\sigma}\_{\hat{i}})) \tag{38}$$

where, *z*ˆ*i*1*e* = *zi*1 − *z*ˆ1*d*(*t*) + *di*, *z*ˆ*i*2*e* = *zi*2 − *z*ˆ2*d*(*t*) + *c*1*z*ˆ*i*1*e* + *dv*2, *σ*ˆ*i* = *k*1*z*ˆ*i*1*e* + *z*ˆ*i*2*e*, *z*ˆ1*d*(*t*) and *z*ˆ1*d*(*t*) are the predicted values of CNN-LSTM model.

The block diagram of CNN-LSTN-based multi-AUV formation prediction control under communication constraints is shown in Figure 8. Based on the pilot-follower formation control strategy, there is a communication delay when the follower AUV receives the position and speed information from the pilot due to the influence of hydroacoustic communication. In this paper, a CNN-LSTM prediction model is established to make predictions based on the historical information of the pilot, which can well offset the effects of noise and communication delay on formation control. The prediction information and feedback information are used as the input of the AUV formation controller to finally realize the AUV formation prediction control.

**Figure 8.** AUV formation prediction control block diagram.

#### **5. Simulation Verification and Analysis**

#### *5.1. Simulation Results and Analysis of CNN-LSTM Model*

The trajectory data of a small AUV, consisting of longitude and latitude measurements from multiple positioning systems, as well as values from GPS, bathymetry, and Doppler measurements with a maximum depth of 20 m, were selected as the training set for this study. The relevant information of the training set is shown in Table 1.

**Table 1.** AUV status information.

These training data were obtained from the trajectory data of an AUV on-lake experiment, and some of its trajectories are shown in Figure 9. The raw data were preprocessed and used for the training of the CNN-LSTM model.

**Figure 9.** AUV partial trajectory data.

The CNN model designed in this paper contains three convolutional layers with filter sizes of (2, 1), (3, 1) and (3, 1) for each layer, and a dropout layer is added to prevent overfitting. The processed features were passed to the two-layer LSTM model, and the predicted data were output by the last LSTM layer. Through continuous debugging, it was found that the network with 125 and 128 neurons in each layer was trained well. Additionally, to prevent the overfitting of the network, a discard layer with probability 0.3 is built after the hidden layer. The Adam algorithm is used for optimization, and the design learning rate decline period is 100, the learning rate is 0.012, the learning rate decline coefficient is 0.8, and finally, the gradient threshold is set to 1 in order to prevent gradient explosion.

After processing the delayed data according to the aforementioned data processing steps, they are fed into the CNN-LSTM model using the sliding window format. The performance of the model is then evaluated by computing the mean square error (*MSE*) and maximum absolute error (MAXERR) between the predicted values and the actual trajectory data. The evaluation metrics can be formulated as follows:

$$MSE = \frac{1}{N} \sum\_{t=1}^{N} (\text{observed}\_t - \text{predicted}\_i)^2 \tag{39}$$

where *N* indicates the number of samples.

$$\text{Maxerr} = \max \left| \frac{\text{observed}\_l - \text{predicted}\_t}{\text{observed}} \right| \tag{40}$$

According to Assumption 2, the leader broadcasts the data of the past five beats to each follower at a time, so the size of the sliding window is set to 5, and the prediction effect of the prediction model is verified under the fixed delay of 2 s and the communication interval of 7 s. The selected navigator trajectory is a spiral dive trajectory, and Gaussian white noise with an amplitude of 0.003 is superimposed on the trajectory data, and the LSTM prediction model is selected for simulation comparison. The parameters of the two model designs are shown in Table 2.

**Table 2.** AUV status information.

Since the velocity quantities in the selected trajectories are kept constant, in order to objectively compare the advantages and disadvantages of the two prediction models, only the navigator state quantities *z* = [*x*, *y*, *depth*, *θ*, *ψ*] are compared for prediction, and the simulation results are shown in Figure 10.

**Figure 10.** AUV trajectory prediction error: (**a**) northward trajectory prediction error, (**b**) eastward trajectory prediction error, (**c**) vertical trajectory prediction error, (**d**) longitudinal inclination angle prediction error and (**e**) bow angle prediction error.

Based on Figures 10 and 11, it can be observed that the CNN-LSTM model predicts a trajectory that is closer to the actual value, with a smoother prediction curve and lower error fluctuations. These results demonstrate that the CNN-LSTM model provides higher accuracy and stability. The *MSE* values for the predicted states by the LSTM model are 1.7911, 1.7947, 1.1921, 1.6871, and 0.2564, while the CNN-LSTM model predicts the state with lower *MSE* values of 0.6868, 0.6315, 0.0664, 1.3078, and 0.1139. These *MSE* values are smaller compared to those of the pure LSTM model, indicating that the CNN-LSTM model provides better prediction results.

**Figure 11.** AUV trajectory prediction: (**a**) horizontal plane trajectory prediction and (**b**) 3D trajectory prediction.

#### *5.2. Formatting of Mathematical Components*

To verify the prediction effectiveness of the CNN-LSTM prediction model in the formation and formation holding phases of the multi-AUV formation, the communication transmission delay *τtran* is set to 1 s and the hydroacoustic sonar sounding delay *τ*int*er* is set to 4 s, i.e., the fixed time delay *τonce*\_*tal* is defined to be 5 s and the maximum total time delay is 9 s. The formation design is consistent with Figure 5.

The navigational track of the navigator is

$$\begin{cases} \begin{array}{l} \chi\_p = 60 \cos(2\pi t/1000) \\ y\_p = 60 \sin(2\pi t/1000) \\ z\_p = -0.3t \end{array} \end{cases} \begin{array}{l} \begin{array}{l} \chi\_p = 0 \\ \end{array} \end{array} \tag{41}$$

The initial state of the AUV is as follows: initial position *x*(0) is randomly taken in the range of [55, 65] m, *y*(0) is randomly taken in the range of [−10, 10] m, *x*(0) is 65 m, depth is 0 m, initial attitude *θ*(0) is 0 rad, bow angle *ψ*(0) is 4π/3 rad, longitudinal velocity *u*(0) is 0.5 m/s, all other velocities are initialized to 0 m/s, and controller parameters are *h* = 1, *k*1 = 0.3, *c*1 = 0.3, *F* = 0.02, *β* = 0.5.

The simulation results are shown in Figures 12 and 13.

In Figure 12, (a) to (e) are the simulation plots of AUV formation position information, from which it can be seen that the leader and the follower always keep the same position, pitch angle and bow angle during the spiral dive under the action of the formation controller; (f) to (j) are the simulation plots of AUV formation speed information, from which it can be seen that the bow speed, lateral speed and vertical speed of the follower in the formation have some fluctuations, but the overall velocity remains stable. Figure 13 shows the 3D trajectory of the AUV formation and its projection on the horizontal plane, from which it can be seen that the followers can follow the leader more accurately and can realize

the multi-AUV formation control in a 3D environment. The simulation results illustrate that the formation control method combining CNN-LSTM prediction and backstepping sliding mode control designed in this paper can better realize the three-dimensional predictive control of multi-AUV formation under the communication constraints.

**Figure 12.** *Cont*.

**Figure 12.** Simulation diagrams of formation position and velocity information: (**a**) AUV northward trajectory, (**b**) AUV eastward trajectory, (**c**) AUV vertical trajectory, (**d**) AUV longitudinal inclination angle state, (**e**) AUV bow angle state, (**f**) AUV longitudinal velocity, (**g**) AUV lateral velocity, (**h**) AUV vertical velocity, (**i**) AUV longitudinal inclination angle velocity and (**j**) AUV bow angle velocity.

**Figure 13.** AUV formation 3D trajectory diagram and its horizontal projection: (**a**) 3D trajectory diagram and (**b**) horizontal projection diagram.

Figure 14 shows the position and attitude errors of the AUV formation under CNN-LSTM prediction. Figure 15 shows the position and attitude error of AUV formation under communication delay. From Figures 14a,b and 15a,b, it can be seen that the northward and eastward errors of the AUV formation under predictive control are much smaller than the control errors under delay, indicating that the CNN-LSTM prediction-based AUV formation control method can better overcome the effect of communication delay on formation control.

**Figure 14.** Errors of follower AUV under CNN-LSTM model prediction: (**a**) northward error, (**b**) eastward error, (**c**) vertical error, (**d**) longitudinal inclination angle error and (**e**) bow angle error.

#### **6. Conclusions**

This paper focuses on the multi-AUV formation control problem under communication constraints. Firstly, a five-degree-of-freedom nonlinear model of the AUV is established and processed by using feedback linearization to obtain a second-order integral model of the AUV. A sliding-window-based formation prediction control strategy is designed to iteratively predict the current state information of the leader by the historical state information of the leader step by step. The method saves computational efficiency and has better adaptability. The CNN-LSTM prediction model is chosen to predict the trajectory state of the navigator for the characteristics of AUV motion trajectory with certain temporality, which compensates for the influence of communication delay on the formation control; and the backstepping method and sliding mode control are combined to design the formation controller, which improves the robustness of the controller. The stability of the control is proved based on Lyapunov stability theory. The effectiveness of the CNN-LSTM prediction model and the designed controller are verified by simulation.

**Author Contributions:** Conceptualization, J.L. and Z.T.; methodology, J.L.; software, J.L.; validation, J.L. and Z.T.; formal analysis, J.L.; investigation, J.L. and Z.T.; resources, J.L.; data curation, G.Z.; writing—original draft preparation, J.L.; writing—review and editing, W.L. and Z.T.; visualization, G.Z. and Z.T.; supervision, J.L.; project administration, J.L.; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No.<PHONE_NUMBER>), the Research Fund from Science and Technology on Underwater Vehicle Technology (Grant No. JCKYS2021SXJQR-09) and the Natural Science Foundation of Shandong Province (Grant No. ZR202103070036).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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## **Numerical Computation, Data Analysis and Software in Mathematics and Engineering**

Edited by Yumin Cheng Printed Edition of the Special Issue Published in *Mathematics*

www.mdpi.com/journal/mathematics


Citizen X: Exploring Connectedness and Engagement: Among Engaged Youth - An Existential Analysis

*Diann Cameron Kelly*

#### **Abstract**

What value do we place on *being* engaged? Civic engagement connects us to social institutions that enhance well-being, self-worth and quality of life satisfaction. Yet, for youth (ages 18–22), there exists the phenomena of civic engagement in spite of isolation, lack of skills or discrimination. This article explores the explicit and implicit meanings of civic engagement among our youth, and the elements needed to achieve meaning in their lives – even through civic engagement. This analysis explores the interpretation of civic engagement among youth, and the individuals who present as connected and engaged. Forty individuals were surveyed with 18 comprising the youth group (ages 20–22). The results show the types of civic duties they participated in and the relationship to their satisfaction with their quality of life. It is believed that the respondents who presented as most connected and engaged were those who were saturated with strong civic messages pre-adolescence. These individuals presented a strong sense of hope, a conscious choice in serving others and a strong sense of community that are central to existential theory.

**Keywords:** civic engagement, existential meaning, connectedness, efficacy, civic commitment, political affiliation, volunteerism, voting, philanthropy, minority, minorities

#### **1. Introduction**

Civic engagement is an indicator of one's connection to society [1–6]. More than one's level of volunteerism and voting practices, civic engagement is social, emotional and financial participation in civic life to positively influence the future of the community through shared governance [1, 5, 7, 8]. Civic engagement constitutes a range of activities, such as voting, volunteerism, association membership or political and community activism, that strengthen participatory democracy [1, 7–10]. However, civic engagement also involves an individual's commitment to the common good as well as a sensitivity or empathy to positive social change [2–4, 9, 11].

Through the explicit practices of voting, volunteerism, and association membership, civic engagement enhances one's feelings and perceptions of citizenship [2, 7, 8, 11–15]. Engagement allows individuals to develop a greater sense of

#### *Interpersonal Relationships*

community as extensions of their diverse civic identities [4, 16, 17], and emphasizes an individual's social connectedness, social integration and influence in self-governance as depicted by their civic commitment, political affiliations, and external efficacy, or belief that one can make a difference in society [2, 3, 9, 11, 12, 15, 18].

This article explores both the explicit and implicit meanings of civic engagement among young minorities. A qualitative analysis, the article presents findings that are theoretically driven by an existential perspective of freedom, choice and self-discovery through *being*. This exploration concludes with a discussion on the meaning of civic engagement and the process of being engaged as it may be interpreted by young minorities.

#### **2. Literature review**

Civic engagement connects minorities to social institutions that enhance wellbeing and feelings of self-worth in society [1, 2, 7, 8, 19]. Yet, for minorities, there exists the phenomena of civic engagement and the will to be engaged in spite of racism, discrimination or marginalization [1, 3, 4, 18, 19].

Alienation, suffering, feelings of aloneness and estrangement from various aspects of society can diminish connectedness, hopefulness and one's self-discovery as an engaged citizen, especially among young minorities [3, 4, 18–21]. Individuals who may be likely to experience disengagement, social exclusion or alienation due to race, ethnicity or cultural background, may be less likely to experience social connectedness and civic engagement, be involved in civic activities, or able to positively evaluate the worth of their engagement [1, 3, 11, 20, 22].

For minorities in communities plagued by poverty, crime and sustained estrangement from mainstream society, aspects of disengagement abound [3, 10, 12, 20]. There is less voter turnout often in these communities, fewer member associations to promote volunteerism, and minimal political involvement to promote external efficacy, for instance [10, 11, 14, 15, 17]. In essence, these individuals, who have a great potential to being engaged in society, are more likely to believe themselves as and feel alienated from civic and political institutions [3, 10, 18, 20, 22].

However, social connectedness and civic engagement enhance hope and increase the likelihood that an individual feels included, understood and valued by society [4, 16], as well as feel a sense of confidence about their contributions to society [8, 11, 19]. From an existential perspective, being engaged decreases the level of inertia and feelings of aloneness and helplessness especially among our young minorities [19–21, 23–26].

*Being* connected and engaged has, in itself, a myriad of meanings for each individual [19, 21]. This will to *being* socially connected and civically engaged provides an individual with the ability to make civic choices, feel a sense of freedom, and evaluate those choices and feelings as they relate to a loss or gain of one's civic value to society [19, 21, 22]. An individual demonstrates external efficacy by acting on securing his or her future to shape its outcome through civic activities, association memberships, political activism and voting practice [12, 19, 21]. But when an individual struggles to find meaning or purpose in their lives, when he or she experiences worthlessness or even nothingness, this individual is thrust into an "existential vacuum," an existence Frankl [24] notes as a "state of boredom," or apathy and cynicism that can lead to distress, depression and aggression (p. 111).

There are, however, several elements that help us achieve meaning overall in our lives (**Figure 1**). Persons achieve meaning when they 1) achieve valued goals; 2) engage in inspiring activities; 3) perceive the world as fair (i.e. general social trust); 4) understand their own abilities and limitations (self-efficacy); 5) exhibit a level of

*Citizen X: Exploring Connectedness and Engagement: Among Engaged Youth - An Existential… DOI: http://dx.doi.org/10.5772/intechopen.96062*

**Figure 1.** *Existential elements to achieving meaning.*

social desirability and openness among others; 6) demonstrate some level of spirituality and exhibit a relationship with a higher power; and, 7) exhibit positive emotionality and a level of agreeableness [19, 21]. When presented in the form of civic meaning in the life of an individual, several civic indictors can be applied to this model to assist in informing whether an individual has achieved civic meaning.

Specific civic indicators serve as the focus of this article. These indicators are 1) *Commitment* – one's level of commitment to their civic activities and contributions to the common good [2, 3, 12]; 2) *External Efficacy* – one's level of external efficacy, or the belief that one's actions have a positive influence on others and society [12]; 3) *Service Satisfaction* – one's level of satisfaction with helping others and contributions to the common good [7, 12]; 4) *Political Affiliation Satisfaction* – one's level of satisfaction with a political party of choice and/or one's political activism [14, 15, 27]; 5) *Volunteerism* – one's volunteer activities [4, 11]; 6) *Philanthropy* – one's level of philanthropy and how one directs their resources toward the common good [8, 28]; and, 7) *Voting* – one's voting routines [22, 27].

While voting, philanthropy and volunteerism appear to illustrate explicit meanings of the individual's actual civic experience; commitment, efficacy, and satisfaction appear to describe implicit meanings of an individual's connectedness and engagement [19]. It is the relationship between explicit and implicit meaning that helps to capture the depth and breadth of an individual's connectedness to and engagement with society [19]. Thus, *being* connected to society and engaged as *citizen* is defined by the individual's own existence.

#### **3. Methodology**

The purpose of the qualitative study was to explore social connectedness and civic engagement as interpreted and evaluated by minority young adults. According to Strauss & Corbin [29], grounded theory allows us to study subjects or areas we know little about. Grounded theory allows conceptual models to emerge from immersion in the field of study and data collection. This allows themes to become known that can clarify the area under study [29, 30]. While research exists that defines and measures minority civic and political participation [7, 12, 17, 22], grounded theory helps us further explore reasons for civic participation in specific activities and how these elements intersect among young minorities.

#### **3.1 Research background, the study sample & focus group**

This qualitative exploration emerged from a descriptive study on how participation in youth mentoring programs influenced educational outcomes and community service involvement [28]. The study consisted of economically disadvantaged minorities between the ages of 20 through 27 years, from communities throughout the U.S. – New York, California, Massachusetts, Texas, Louisiana, Ohio, New Jersey, Illinois, and Maryland to explore civic involvement and civic beliefs from adolescent through young adulthood.

The principal investigator returned to the original respondents requesting participation in an asynchronous, web-based focus group. The qualitative study consisted of a detailed, online survey that allowed respondents to present a reflective journal on their civic experiences from adolescence to young adulthood. These questions included "In looking back on your years of voting since turning 18 years of age, are you now more likely or less likely to believe your vote counts? *Please explain*?" Or, it included questions such as "How would you characterize your level of satisfaction with the service you performed? (Describe your satisfaction with what you do or have done in serving others?)"

Out of three initial mailings, only 29 respondents expressed an interest in being involved in the self-directed, intensive web-based focus group. Much of the contact between the principal investigator and the respondents occurred via internet-based interaction. Regular follow-up through additional mailings (a total of three) were required to ensure respondents' reflective journals were completed. With attrition, the focus group consisted of 13 respondents.

#### **3.2 Data analysis**

Each journal entry was downloaded from the server and converted to a text file (ASCII format; .txt). The text files were transferred to Atlasti, a qualitative data management program. Coding of data occurred by coding each reflection according to questions posed. The reflections were reviewed for emerging themes such as degree of external/political efficacy; types of service performed by respondents; voting practices; and, satisfaction with political affiliations.

#### **4. Limitations**

There are several limitations within this qualitative study. First, the length and duration of the journal reflections were much longer than the principal investigator initially considered. The journal took, on average, two to three weeks to complete,

*Citizen X: Exploring Connectedness and Engagement: Among Engaged Youth - An Existential… DOI: http://dx.doi.org/10.5772/intechopen.96062*

rather than the three days presumed by the investigator. Thus, the time factor was more of an investment for the respondents than initially intended. Also, the requests to participate in this study came within six months of the completion of the previous study. Potential respondents may have experienced fatigue, as the second survey was less direct (open-ended) and much longer than the first.

In addition to the length of the survey, technology may have also encroached on the strengths of this exploration. The qualitative study was particularly reliant on technology and web-based interaction between the respondents and the principal investigator. This required more than minimal technological skill of respondents to properly engage in the study. As such, it is unknown the degree to which an emphasis on technology prevented potential respondents from participating.

#### **5. Results**

There were thirteen respondents in the focus group. Four of the respondents were males and nine of the respondents were females (**Table 1**). The average age is 23.85 years. The median salary range is \$25 K to 30 K. Respondents were given pseudonyms.

**Table 1.** *Current demographics (N = 13).*

#### **5.1 The group**

"Ella" is a 23 year old African American female from Ohio, and received an associate's degree in business. She credits her religious faith with influencing her civic activities. "Meris" is a 22 year old Hispanic female from Illinois. She serves on the board of a public cultural institution designed to promote and serve the Hispanic community within the state. Finally, she is the first in her family to attend and graduate from college. "Lynda" is a 26 year old African American female from Ohio, who already attained an advanced degree and is seeking another. "Archie" is a 22 year old African American male from Louisiana, and is a graduate of a selective university. He credits his parents with influencing his commitment to civic activities. "Olivia" is a 25 year old bi-racial female from Ohio. In addition to her advanced degrees, Olivia has association memberships that have sustained since her early adolescence.

"Colin" is a 23 year old African American male from Maryland, a college graduate and currently involved in the field of engineering. "Jack" is a 23 year old African American male from New York and is a graduate of a selective university. "Charlotte" is a 23 year old bi-racial female from Louisiana and expressed strong community attachment. "Ana Lee" is a 25 year old immigrant female from the Caribbean who identifies herself as African American. She took over six years to complete her college degree because, as she indicates, of limited finances and family support. She is from New York.

"Ben" is a 24 year old immigrant male from the Caribbean and also identifies himself as African American. He also resides in New York, and acknowledges irregular involvement in civic activities. "Gia" is a 26 year old African American female from Maryland who has a strong belief in the public good and general welfare, but does not involve herself in the activities that would benefit the public good. "Harmony" is a 23 year old African American from Ohio who expressed feelings of alienation and disengagement from the school community. Finally, "Gemma" is a 25 year old African American female from New York. She is an officer with the United States military where she is also studying to be a physician. Gemma always wanted to join the armed forces and completed college in order to fulfill her dream of becoming an officer.

While this summary provides an overview of the respondents' general characteristics, how is connectedness and engagement explicitly and implicitly represented among the group? Respondents' reflections are coded into groupings of explicit meaning and implicit meaning of civic indicators (**Table 2**).

#### **5.2 Explicit meaning of civic indicators of connectedness and engagement**

Civic indicators that illustrate explicit meaning of connectedness and engagement are volunteerism, level of philanthropy and voting practices. Responses indicating volunteerism were coded and expressed through the respondents' hours of volunteer service as well as the types of service performed. Philanthropy is represented as "high contributions" (i.e. more than \$200 per year), "moderate contributions" (i.e. \$1 to \$200 per year), and "no contributions" (i.e. \$0 per year). Voting responses were grouped into three categories – 1) respondents who voted regularly; 2) respondents who voted sometimes; and, 3) respondents who had not voted.

**Volunteerism:** Archie completed more than 50 hours the year prior to the study. The bulk of his service was directed to after school tutoring for elementary children, serving as an adult mentor, and participating mostly through his worship center. Ella completed over 50 hours of service. Ella's service included volunteering at nursing homes as well as cultural organizations. In addition, she is very active in

*Citizen X: Exploring Connectedness and Engagement: Among Engaged Youth - An Existential… DOI: http://dx.doi.org/10.5772/intechopen.96062*

*†= high levels of civic participation.*

**Table 2.** *Categories of groupings.* her religious community visiting the sick. Meris completed more than 20 hours of service in the year prior to the study. Her volunteerism is filled with various activities from working with "soup kitchens" to board leadership. As a board member, Meris creates programs designed to address and improve quality of life issues for the state's Hispanic community. In addition to her community leadership, Meris mentors a young girl who had been involved with the state's juvenile court system. These three individuals exhibited the highest levels of volunteerism among the focus group.

Respondents with moderate levels of volunteerism had an irregular continuum of service since early adolescence, and were less likely to have volunteered in the year prior to the study. In particular, Lynda completed over 100 hours of service in high school and college, in the year prior to this study, she did not perform service. Ben performed about 10 hours of service during college where he helped out at neighborhood pantries, and assisted with home building through an affiliate of Habitat for Humanity. Yet, in the year prior to this study, Ben did not participate in service. Jack completed only 5 hours of service raising money for Lupus, breast cancer or HIV/AIDS awareness through the running of marathons. Olivia completed less than 20 hours of service with a women's crisis shelter and sometimes with her local library.

Respondents with the lowest levels of volunteerism either did not perform service at all during their youth or performed service on an irregular basis. This may signify little attachment to volunteerism. These individuals were Harmony, Gia, Colin, Gemma, Ana Lee and Charlotte.

**Philanthropy:** Only three respondents contributed more than \$300 per year to a charity. Ella donated \$2000 to her church community in the year preceding the study. Much of her donations were attributed to "tithing" or special offerings to her church community, in addition to in-kind gifts of clothes, food and other non-financial gifts. Gemma contributed \$350 to charity, and Meris contributed \$300 to charitable causes. While Gemma did not elaborate on the recipients of her donations, Meris elaborated that she gives back to the youth programs that helped her. The consensus in this sub-group was that they were financially giving back to meaningful institutions that influenced their engagement – religious community and youth programs.

Moderate contributions were provided by Gia, Lynda and Olivia. In the year preceding the study, Gia gave a total of \$110. The recipient of her gift was a mentoring program that guided her through high school and college. In addition, she noted that all of her current and future "monetary donations go to programs that support children and/or education." Lynda gave a total of \$50 to charity in the year preceding the study. Finally, Olivia gave a total of \$30. The recipients of her gifts are the Sierra Club, the Arbor Day Foundation, or her alma maters (high school, college, and graduate school). Olivia expressed that she never considered donating significant financial contributions until this survey arrived.

The remaining respondents did not give any financial contributions to charitable causes in the year preceding the study. This sub-group includes all of the males, Archie, Ben, Jack and Colin, as well as Ana Lee, Harmony and Charlotte. Some of the reasons presented were lack of funds, no time to contribute, or contributing was not an immediate focus.

**Voting:** Respondents discussed their beliefs about voting, but also their voting history or likelihood of voting. Interestingly, for some of the respondents, they had not considered voting as a civic behavior until the receipt of the surveys. Five respondents identified themselves as regular voters. Gemma noted that she votes regularly to "affect change," and Lynda noted that she goes out of her way to vote with others, as a group, to make an impact. Ella votes in all of the elections, no

*Citizen X: Exploring Connectedness and Engagement: Among Engaged Youth - An Existential… DOI: http://dx.doi.org/10.5772/intechopen.96062*

matter the type of election, and Harmony votes regularly because of her faith and belief in the power of voting. Charlotte indicated that by regularly voting she's "participating in the community [and] its decisions."

Moderate voters included Ben, Ana Lee, Olivia, Meris, and Archie. Their voting practices were irregular. However, the strong consensus of this sub-group was that their votes counted for less in national elections than in local elections. The non-voters are Jack, Colin and Gia. Gia expressed her cynicism about voting. Yet she indicated she was more likely to vote in local elections rather than in national elections.

#### **5.3 Implicit meaning of civic indicators of connectedness and engagement**

Civic indicators that illustrate implicit meaning of connectedness and engagement are commitment to service, external/political efficacy, and satisfaction with service along with satisfaction with political party affiliation. Responses indicating level of commitment to service were coded and expressed through the following areas – extremely committed, committed, somewhat committed, not very committed, not committed. Responses indicating external/political efficacy – or the belief that one's actions, particularly one's vote, has a positive influence on society – were coded and expressed through the following areas – a *strong* external efficacy, or belief that one's actions, particularly one's vote, have a positive influence on society; *moderate* external efficacy, or the belief that one's actions, particularly one's vote, have some positive influence on society; and, *weak* external efficacy, or the belief that one's actions, particularly one's vote, have little or no positive influence on society.

Responses indicating satisfaction with civic activities, particularly civic service, were coded and expressed through the following areas – "extremely satisfied," "satisfied," "somewhat satisfied," "neither satisfied or dissatisfied," "somewhat dissatisfied," "dissatisfied," "extremely dissatisfied." Responses indicating satisfaction with political party affiliation were coded and expressed through the following areas –strong democrat, weak democrat, independent, weak republican, strong republican, and then grouped by level of satisfaction.

**Level of Commitment:** When looking at the study group, only five respondents (all female) appeared more committed to service in adulthood than the other respondents. Meris expressed she was extremely committed to her service in community leadership as well as her mentoring of at-risk youths. She cited that "[c]ommitment is shown through time and resources dedicated." Charlotte also expressed extreme commitment to service through voting and her service to others through her in-kind gifts. Lynda, Olivia and Ella presented as "committed" to service. Lynda expressed a strong attachment to her community and its improvement, while Olivia expressed being committed to service but also trying to balance this commitment with her responsibilities to her family. Ella cited her commitment as a result of her religious beliefs.

Ana Lee, Jack, Archie and Colin presented as "somewhat committed" to service. However, the consensus among this sub-group was the many other obligations or commitments obstructed or diminished their level of commitment to civic issues or activities. Finally, Harmony presented as "not committed" to service. Both Gemma and Harmony see their vocations as their contributions to society and do not have an interest or level of commitment to volunteerism or other civic activities beyond the parameters and requirements of their vocations.

**External/Political Efficacy:** Lynda, Ella, Harmony and Charlotte exhibited strong external/political efficacy in their responses and strongly believed their voting practices counted. In particular, Harmony expressed that she knew her vote counted because of her faith, and Charlotte believed her vote affects outcomes in her community. Olivia, Meris, Archie and Gia exhibited moderate external efficacy in their responses. Olivia believed her voting practices, in particular, counted, but not in races where candidates were "pre-selected by party brokers." Meris indicated that she was more inclined to participate more in local races and school board elections rather than participate in national elections. Archie concurs with Meris and is more inclined to vote in local elections because "there are no electoral colleges at these levels of governments." Finally, Gia believes in voting but admits she is still too cynical.

Colin, Jack, Gemma, and Ben and Ana Lee exhibited weak external efficacy. This sub-group presented a significant level of cynicism post-2000 Presidential elections. In particular, the 2000 Presidential election decreased Jack's desire to vote again – even in local elections. Gemma does not believe her vote counts or that she has any power in the governance of her community or nation. The two respondents who immigrated to the United States while they were children also exhibited a weak level of external efficacy. Ben strongly believed that votes count more in suburban areas that are less likely to be populated by "persons of color," and Ana Lee expressed that she did not believe her vote counted.

**Satisfaction with Service:** When looking at the responses, most respondents expressed they were either "extremely satisfied" or "satisfied" with their civic service. Respondents who feel less than satisfied with their service were Ana Lee, Archie, and Colin. Ana Lee indicated that she feels guilty about her current level of service. Archie was somewhat dissatisfied because of his level of participation is not comparable to his past performance of service in his youth. Colin, however, is significantly dissatisfied with his performance of service and expressed a lot of concern regarding his lack of service. "I don't have the time to involve myself in community activities."

**Satisfaction with Political Party Affiliation:** A majority of the group identified themselves politically as "independent" while the remaining respondents identified themselves as strong or weak democrats, or strong republicans. Jack, Ella, and Gia identified themselves as strong democrats. However, Jack is not satisfied with the Democratic Party, and asserts that "I don't think [my needs] have been met." Ella, on the other hand, expressed satisfaction with the Democratic Party and noted that the "democrats have lived up to my expectations." Gia, finally, is neutral in her satisfaction, as she faults Democrats and Republicans for having "both hurt the Black community."

Archie and Lynda identified themselves as weak democrats. Archie, in particular, leans more toward the Democratic Party as he said he found that "democrats tend to do what is best for the community, especially economically." Archie indicated that while a person can never expect candidates to do everything that they promised in their campaigning, he feels more satisfied with the Democratic Party. Lynda, on the other hand, did not have a strong affinity for the Democrats. Charlotte was the only respondent who identified herself as a strong republican. She expressed that she is "very pleased so far with my decision to be republican." Charlotte noted that while she votes consistently for the party's candidates, she votes for the person and on character rather than the candidate's affiliation with the Republican Party.

Given the results, who are the independents within the group? Ben, Ana Lee, Gemma, Olivia, Harmony, Meris, and Colin all identified themselves as independents. Ben and Ana Lee are the only immigrants within the group. Ben cited he had no specific affinity for either party – Democrat or Republican, or any other political group, and indicated that he did not "feel like I am mainstream with democratic or republican…." Ana Lee identifies with the Green Party, but is not active with the

#### *Citizen X: Exploring Connectedness and Engagement: Among Engaged Youth - An Existential… DOI: http://dx.doi.org/10.5772/intechopen.96062*

Green Party. Gemma does not "trust the wisdom or motivations of [any] political party…" and prefers to retain her objectivity, while Harmony just identifies herself as an independent and purposely desires not to belong to *any* political party. Olivia leans more toward the liberal party. She expressed that she grew up with republican parents but always felt her views were more liberal. She's satisfied with her political choices as she identifies them as "well-balanced." Meris identifies herself as independent and votes based on a person's character and their public service history. Finally, Colin identifies himself as independent and indicates that while he leans toward the Democratic Party he is less than satisfied with the Democrats and the extent of their liberalism.

#### **6. Discussion: an existential analysis**

When looking at all of the results and how connected and engaged respondents appear, we see the seven elements highlighted by Mascaro and Rosen [19]. The minority respondents who presented as most connected and engaged were those who were saturated with strong civic messages and modeling since pre-adolescence. These individuals presented a strong sense of hope and conscious choice in serving others [19, 23]. Also, they presented a strong sense of community – or community attachment [4, 10, 16] that is central to existential theory [23–25].

Ella presents as the most engaged and connected of the respondents and appears to possess a purpose to her civic involvement and engages in inspiring activities that appear attributed to her religiosity. In addition, Ella appears to perceive the world as fair and exhibits both self and external efficacy. Further, she presents a good level of social desirability through her various civic activities, and exhibits some level of spirituality. Finally, she exhibits positive emotionality.

Likewise, Meris is also significantly engaged and connected, and maintains an influential role throughout her state in the Hispanic community. Not only does she involve herself on an individual level by shaping the future of a young teen she mentors, Meris also shapes the future of her community and her state through her community leadership role. She, too, presents a purpose to her civic activities, which are in themselves inspiring. In addition, she exhibits a strong degree of self and external efficacy as well as a level of social desirability. While it was unclear her level of spirituality, she did exhibit a level of positive emotionality in her responses.

Archie is the only male in the group who demonstrated a significant level of connectedness and engagement. Archie's parents were strong role models for him and how one "gives back" to the community. Being a contributor to society is a part of his emotionality and how he may see himself in society. In addition to his level of spirituality, Archie also engages in inspirational activities, and demonstrates some levels of efficacy.

When looking at the respondents who exhibited less than strong social connectedness and engagement, it is very important to look at their outcomes in view of the elements by Mascaro & Rosen [19]. Gemma presents that her vocation in the armed forces is her service to society. In addition, Gemma gives larges amounts to charity and votes regularly. However, she does not volunteer or link herself with any group that serves the public good, nor does she articulate a satisfaction with her political affiliations. Finally, while she is a member of the armed forces, she does not see herself making a difference in society nor is she committed to serving others except through her role in the armed forces. It is possible that Gemma prefers the impersonal aspects of philanthropy and voting and that she may find civic involvement through volunteerism outside her role in the armed forces and, thus, *meaningless* [19, 23, 25].

Harmony is another interesting respondent who exhibited less than strong social connectedness and civic engagement. From high school, Harmony did not feel as if she "belonged" in the school community because it was predominantly White and she was African American. She felt alienated at school, and did not feel as though her concerns had an audience in her home community. Although she may vote regularly, Harmony is less likely to volunteer, less likely to contribute to charitable causes, and is less likely to feel committed to service. Harmony is a good example of one who existed in an existential vacuum. Hopelessness, according to Mascaro and Rosen [19], is the loss of existential meaning and the will to *being*. It is this lack of meaning and hope that results in an existential neurosis leaving an individual experiencing the world as alone, estranged, and excluded.

This analysis helps us understand that exploring civic engagement is more than measuring explicit indicators such as voting or implicit indicators such as external efficacy or satisfaction. What value do we place on *being* engaged? According to existential theorists, we thrive in society when we have an *experience* not just an explanation of our existence [19, 23–26].

Overall, respondents with moderate to high external efficacy and regular voting practices and service behaviors are able to self-categorize their civic and political development [3, 14, 17, 22, 27]. Respondents who exhibited higher levels of disengagement were young persons who had a history with immigration as a child, or young adults who had strained relations with their parents or their educational settings. However, those individuals who embody the process of achieving civic meaning – Ella, Meris and Archie – consciously chose to be connected and involved in society [19, 23] based on their experiences, role models and meaningful connections in their early years [3, 4, 7, 9, 12, 17].

Ella, Meris and Archie appear to have been guided toward discovering their civic identities either through their parents, mentors or positive peer groups [12]. They remind us that spirituality combined with feeling supported and having an inspiring purpose keeps an individual from experiencing an existential vacuum. Spirituality, faith or religiosity cannot be overlooked when discussing connectedness and engagement. One's religious experiences contribute to one's civic values and sense of *being* connected and engaged.

#### **7. Conclusion**

Participation in service alone is not enough to sustain service and promote social connectedness and civic engagement. Young minorities must feel a sense of purpose and be inspired to participate in the activities while exhibiting social trust and efficacy. While being engaged in civic society may be an ideal goal for many citizens, civic engagement is not something that automatically occurs upon one's transition to adulthood. Too many young minorities have little or no background in civic or political participation. In order to alter this disparaging fact, we must ensure that minority youth and their families are intrinsically and regularly involved in aspects of society from volunteering to voter mobilization to association and community memberships and charitable giving. Such processes diminish alienation and feeling dehumanized and ensures a person has a say in determining the worth of their *civic existence.*

#### **Acknowledgements**

Diann Kelly, PhD, is an Associate Provost for Student Success at Adelphi University. She is also a board member of the Child Care Council of Westchester in *Citizen X: Exploring Connectedness and Engagement: Among Engaged Youth - An Existential… DOI: http://dx.doi.org/10.5772/intechopen.96062*

New York. The author wishes to acknowledge CIRCLE – Center for Information and Research on Civic Learning and Engagement (www.civicyouth.org).

#### **Note**

This article stems from a research report titled "Civic Views of Young Adult Minorities: Exploring the Influences of Kinship Communities and Youth Mentoring Communities on Prosocial Civic Behaviors" for the Center for Research and Information on Civic Learning and Engagement (CIRCLE), CIRCLE Working Paper 25, December, 2004.

#### **Author details**

Diann Cameron Kelly Adelphi University, New York, United States

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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## Section 3


**Author details**

A. Raquel Esteves1,2, Diana F. Silva1,2, Daniel Santos1,2, Emanuel Candeias1,2, Filipa Filipe1,2 and Sandra M. Cardoso1,2,3\*

\*Address all correspondence to<EMAIL_ADDRESS>
1 CNC–Center for Neuroscience and Cell Biology, University of Coimbra, Coimbra, Portugal

2 CNC-IBILI, University of Coimbra, Coimbra, Portugal

3 Institute of Cellular and Molecular Biology, Faculty of Medicine, University of Coimbra, Coimbra, Portugal


**5. 3D bioprinting for developing in vitro tissue/organoid models for drug discovery**

The invention of 3D bioprinting has revolutionized biomedical research and significant development in translational research closing the gap from bench to bedside. In the pharmaceutical industry, the value of 3D bioprinting is expected in lowering the attrition rate of a new drug since 3D bioprinting has the potential to precisely position multiple cell types as needed according to the tissue of interest (**Figure 5**). Thus, 3D bioprinting enables a more robust design of drug screening, drug delivery, high-throughput drug testing, and ADME assays. The application of 3D bioprinting in the development of in vitro tissue or organoid models for drug discovery is discussed in this section.


# **Online and Distance Learning during Lockdown Times COVID-19 Stories (Volume 2)**

Edited by Palitha Edirisingha

Printed Edition of the Special Issue Published in *Education Sciences*

www.mdpi.com/journal/education


**2.1 EVs derived from the ovary**

The ovarian follicle is the basic unit of female ovary, which contains an oocyte that is surrounded by two-layer granulosa cells (GCs, including membrane/mural granulosa and cumulus granulosa), stromal cells (theca cells), and a liquid called follicular fluid (FF). FF offers a suitable micro-environment for follicle growth and oocyte development (oogenesis) in the ovary, so their relative stability of composition is indispensable. Similar to gap junctions between oocytes and somatic cells which mediated cell-to-cell communication, EVs in GCs, somatic cells, and FF mediate signal transmission and cell communication [7, 8], suggesting that EVs are carriers for molecular transfer in the ovary.

The first EVs in FF was reported in equine, which contains microRNAs (miRNAs) and proteins, and they could be taken by surrounding GCs *in vitro* and *in vivo* [9]. MiRNAs are involved in RNA silence as post-transcriptional regulators [10]. There are numerous miRNAs indirectly regulating follicular growth and oocyte maturation in human FF [7]: (1) miR-10b, miR-21-5p, miR-31, miR-95, miR-99b-3p, miR-134, miR-135b, miR-140-3p, and miR-190b participate in WNT signaling through glycoprotein signaling molecular WNTs potentially regulate follicle formation, growth, and ovulation/luteinization [11]. (2) miR-203, miR-218 regulate MAPK (ERK1/2) pathway which activation is crucial for oocyte meiotic resumption, GCs proliferation and cumulus expansion [12]. (3) miR-489, miR-493, miR-503, miR-542-5p, miR-654-3p, miR-874, miR-886-5p, miR-887 as mediators of TGFβ. (4) miR-337-5p, miR-339-3p, miR-370, miR-449a, miR-455-5p, miR-483-5p as mediators of ErbB, etc. In addition, as we know, the expansion of cumulus-oocyte complex (COC) is a key process of ovulation. A study showed that bovine FF EVs taken in cumulus could increase gene expression of cumulus expansion (PTGS2, PTX3, and TNFAIP6) and support the expansion process *in vitro* [13].