Intelligent Dynamic Trajectory Planning of UAVs: Addressing Unknown Environments and Intermittent Target Loss

Abstract

Precise trajectory planning is crucial in terms of enabling unmanned aerial vehicles (UAVs) to execute interference avoidance and target capture actions in unknown environments and when facing intermittent target loss. To address the trajectory planning problem of UAVs in such conditions, this paper proposes a UAV trajectory planning system that includes a predictor and a planner. Specifically, the system employs a bidirectional Temporal Convolutional Network (TCN) and Gated Recurrent Unit (GRU) network algorithm with an adaptive attention mechanism (BITCN-BIGRU-AAM) to train a model that incorporates the historical motion trajectory features of the target and motion intention the inferred by a Dynamic Bayesian Network (DBN). The resulting predictions of the maneuvering target are used as terminal inputs for the planner. An improved Radial Basis Function (RBF) network is utilized in combination with an offline–online trajectory planning method for real-time obstacle avoidance trajectory planning. Additionally, considering future practical applications, the predictor and planner adopt a parallel optimization and correction algorithm structure to ensure planning accuracy and computational efficiency. Simulation results indicate that the proposed method can accurately avoid dynamic interference and precisely capture the target during tasks involving dynamic interference in unknown environments and when facing intermittent target loss, while also meeting system computational capacity requirements.

1. Introduction

Unmanned aerial vehicles (UAVs) have demonstrated significant strategic importance in both military and civilian applications as aerospace technology continues to advance [1,2]. However, these systems face unprecedented challenges in complex electromagnetic environments. When UAVs encounter enemy-established dynamic interference zones, their navigation systems may fail or lose target-tracking capabilities, severely compromising both mission success and flight stability. Consequently, the development of methods for precise target recapture while avoiding dynamic interference zones has become both theoretically significant and practically urgent [3].

To enable UAVs to avoid interference and blind areas during flight, most of the research adopts flight trajectory planning methods [4]. This planning can be conceptualized as a control optimization problem that seeks to achieve optimal performance under various constraints. Trajectory planning can be regarded as a control problem related to achieving an optimal performance under various index constraints. Traditional flight trajectory planning methods mainly fall into analytical and numerical approaches [5,6]. Analytical methods dominated early research, but as system complexity increased, their computational time and accuracy struggled to meet requirements. Consequently, numerical methods have gradually become research focuses [7]. Among them, three widely used numerical methods are Goal Distance-based Rapidly Random-Exploring Tree Star (GDRRT*) [8], the direct targeting method [9], and the pseudospectral method [10]. The GDRRT* algorithm excels in handling motion planning problems involving obstacles, non-holonomic constraints, or inverse kinematics constraints, and has been successfully applied to UAV trajectory planning [11] and autonomous vehicle path planning [12]. However, GDRRT* has limitations in finding global optimal solutions and may not sufficiently able to meet the complex constraints of highly dynamic UAVs. The direct targeting method is suitable for relatively simple optimal control problems, such as precise lunar landings [13] and trajectory optimization in aircraft gliding phases [14]. However, in dealing with trajectory planning in complex dynamic environments for UAVs, its iterative numerical integration burden can be excessively heavy, and it may sometimes fail to converge on a feasible solution.

In contrast, the pseudospectral method has emerged as a particularly effective approach, distinguishing itself through the superior handling of complex constraints and enhanced computational efficiency. These advantages have led to its widespread adoption in flight trajectory planning applications [15,16,17]. Liu et al. [18] successfully used Gaussian pseudospectral methods to plan the entire trajectory of booster rockets while considering no-fly zones. Tian et al. [19] employed the adaptive Radau pseudospectral method to minimize heat flux as an optimization objective, addressing the trajectory planning problem for supersonic vehicles during re-entry, but this method still struggles to effectively handle high dynamic complex constraints in optimal conditions. Wang et al. [20] further improved the pseudospectral method by combining it with a particle swarm optimization algorithm to enhance solution accuracy, but this approach can lead to local optima. A fundamental limitation of both numerical and analytical methods is their offline nature, which makes them inadequate for handling trajectory deviations caused by uncertain factors such as dynamic disturbances or engine failure. This limitation has led to increased interest in online trajectory planning methods based on neural networks [21,22,23,24]. When applying pseudospectral methods for trajectory optimization, incorporating advanced neural networks for sample database training can significantly enhance the precision of trajectory planning. The backpropagation (BP) neural network, valued for its simplicity and straightforward implementation, has found widespread application in aircraft trajectory optimization. However, it exhibits significant limitations including susceptibility to local optima, slow convergence rates, and inadequate response speeds for UAV applications [25]. While Radial Basis Function (RBF) networks demonstrate superior performance in terms of avoiding local optima, their application in dynamic threat environments remains under-explored [26].

To address the aforementioned limitations, we propose a novel method for terminal target trajectory prediction. Trajectory prediction methods can be mainly categorized into traditional prediction methods and machine learning methods [27]. Statistical analysis is the best method for trajectory prediction using machine learning. Its principle involves analyzing the historical information of maneuvering targets to derive the distribution characteristics of flight trajectories, enabling future trajectory predictions based on the distribution features obtained [28]. The prediction of maneuvering target trajectories can be framed as a time series prediction problem within statistical analysis. Through comprehensive experimental studies, Bai [29] demonstrated that Temporal Convolutional Networks (TCNs) consistently outperform Recurrent Neural Network (RNN) models across diverse sequence modeling tasks. While researchers have proposed bidirectional TCN models, incorporating multiple gating mechanisms, to address migration difficulties and information loss, these enhancements have introduced new challenges, specifically increased model complexity and overfitting tendencies. Li [30] proposed a multi-classification model based on spatiotemporal feature fusion to tackle network traffic classification issues. The modeling S [31] utilized a lattice network with a general weight matrix to absorb structural and algorithmic elements from recurrent and convolutional network models, demonstrating the progress of TCN in lattice networks. Ref. [32] established PSO and GRU models for accurate buoy trajectory prediction. Ref. [33] employed attention mechanisms to predict the intelligent trajectory of hypersonic vehicles. Li [34] optimized the CNN-LSTM algorithm based on adaptive attention mechanisms to achieve the accurate prediction of aerial combat target maneuvering trajectories. Wang [35] proposed a UAV tracking algorithm that integrates attention mechanisms for UAVs in low-altitude complex backgrounds. Time Convolutional Networks (TCNs) are favored for their excellent performance in sequence modeling tasks. However, traditional TCNs still face issues like information loss and migration difficulties when handling long sequence data. To further optimize the model, some scholars have proposed improved methods that incorporate attention mechanisms, but these methods still have limitations when dealing with highly nonlinear hypersonic flight trajectories [36,37,38]. None of these methods incorporate target motion’s future state features in their predictive training models, which limits their ability to fully demonstrate the statistical analysis approach’s trajectory prediction capabilities.

In summary, when performing flight obstacle avoidance trajectory planning in dynamic interference environments, the pseudospectral method is preferred due to its high adaptability to dynamic environments and ability to resolve local optima, though it requires optimization through improved RBF networks. Additionally, thanks to the BITCN and BIGRU networks’ ability to simultaneously consider both forward and backward information in feature sequences, effectively extract rich local features, and reduce gradient vanishing during the prediction process, they have become the preferred methods for predicting the terminal target state in order to address the issue of UAV original trajectory failure caused by intermittent target loss.

Based on the conclusions above, this study proposes a novel UAV trajectory planning structure. When designing the predictor, in order to enhance the algorithm’s understanding of complex dynamic patterns and improve the stability of the prediction model, we employ a bidirectional information-capturing Temporal Convolutional Network (TCN) and Gated Recurrent Unit (GRU) method, incorporating an adaptive attention mechanism (AAM) into the algorithm. Additionally, we incorporate motion intention inference features into the predictive training samples to enhance prediction accuracy and reliability. Regarding planner design, when facing unknown environments and intermittent target loss, we use the predicted target state as a terminal virtual guidance point. This approach combines an improved RBF network and pseudospectral method with the offline–online method to achieve rapid online trajectory planning. The main contributions and innovations of this paper are as follows:

(ⅰ) The development of a mathematical model for target maneuvering intention based on a DBN network, and the proposal of a prediction algorithm using bidirectional Temporal Convolutional Network and Gated Recurrent Unit network with an adaptive attention mechanism (BITCN-BIGRU-AAM).

(ⅱ) The proposal of an online dynamic obstacle avoidance trajectory planning method based on an RBF network combined with terminal prediction, addressing the trajectory failure issues faced by traditional planning methods, i.e., the failure to predict the target motion state and quickly avoid dynamic interference, leading to capture failure.

(ⅲ) The establishment of a parallel processing structure, integrating a predictor and trajectory planner to ensure system solution timeliness and real-time communication performance.

The rest of this paper is arranged as follows: The second part describes the problem, expands the motion intention model of the target, and establishes the relevant UAV flight constraint and scene threat model. Section 3 introduces the prediction algorithm proposed in this paper and an offline–online trajectory planning algorithm based on an RBF network and the pseudospectral method. It also introduces the network structure of the system. Section 4 describes the experimental content. Finally, Section 5 gives the conclusion.

2. Preliminaries

2.1. Problem Formulation

The UAV encounters the challenge of the intermittent loss of targets, caused by it crossing unpredictable obstacle areas during the mission. The uncertain factors that may lead to UAV trajectory failure mainly include the following situations:

(ⅰ) The dynamic interference zones: in the mission to capture the target, the UAV may encounter the change position of the threats.

(ⅱ) The target kinematic variability: the tracked target has a certain degree of maneuverability, which may cause it to change trajectory during capture.

(ⅲ) The sensor’s occlusion effects: when the detection device of the UAV is occluded, the incomplete motion information of the target greatly affects the encounter position between the drone and the target.

The situational awareness of the UAV is sustained through onboard systems or ground-based radar, which provide critical kinematic data including two-dimensional positional coordinates, velocity vectors, and line-of-sight angles in the horizontal plane. When the UAV is faced with the above uncertainties, there will be a situation where the flight direction of the UAV cannot be determined, which will lead to the failure of the mission to capture the flying target. To simulate real-world conditions and ensure that the experimental results approximate the operational scenarios, the simulation environment incorporates stochastic interference and fixed-state update intervals. Throughout the whole capture mission, the UAV continuously refines the flight trajectory to avoid the risk of flight in an unknown environment. The definition of mission success is the ability of a UAV to maintain a safe distance from obstacle zones before entering the designated target capture area, and the failure to meet these criteria results in mission invalidation. Figure 1 presents a schematic diagram illustrating the avoidance maneuvers executed by UAV during flight operations.

2.2. Aircraft Motion Model

To simplify the flight process of the UAV while ensuring that generality is not lost, the pitching motion equation considered in this paper is expressed as follows:

$$\{\begin{array}{l}\dot{v}={\displaystyle \frac{Pcos\alpha -D-mgsin\theta }{m}}\\ \dot{\theta }={\displaystyle \frac{Psin\alpha +L-mgcos\theta }{mv}}\\ \dot{x}=vcos\theta \\ \dot{h}=vsin\theta \\ \dot{m}=-m_c\\ \dot{\vartheta }=q_y\\ {\dot{q}}_y={\displaystyle \frac{M_{yy}}{I_{yy}}}\end{array}$$

(1)

where v and D are the UAV velocity and position, m and $m_c$ are the mass and the fuel mass flow, $\theta$ and $\vartheta$ are the trajectory inclination and pitch angle, $\alpha =\vartheta -\theta$ is the angle of attack, g is the gravitational acceleration, P is the thrust, L and D are the lift and drag, $M_{yy}$ is the pitching moment, $I_{yy}$ is the moment of inertia, and $q_y$ is the pitch angular velocity. The remaining UAV parameters, such as lift, drag, pitch moment and flight constraints, are derived from Ref. [39]. The motion model is schematically illustrated in Figure 2.

2.3. Target Motion Intention Model

Given the inherent uncertainty in inferring target motion intent, we express the inference results probabilistically. This approach quantifies the probability of each potential outcome representing the true motion direction and the resulting probability sequence serves as the input that enables subsequent trajectory prediction algorithms to enhance the model’s overall predictive performance. To facilitate the establishment of the motion intent model for targets, we assume the following:

Assumptions a. The target is constrained by maneuverability in the pitch plane, meaning it cannot perform right-angle or 180-degree turns, and it cannot make rapid directional changes.

Assumptions b. The target is considered an intelligent agent, demonstrating Boltzmann rationality in its decision-making processes.

Assumptions c. The influence of earth rotation, Coriolis acceleration, and object centrifugal force on the target can be neglected.

Grounded in these assumptions, we formulated a mathematical model representing the target’s motion intent and employed the Dynamic Bayesian Network (DBN) algorithm to derive the model. The derivation process is as follows:

The UAV can continuously update the observation state when it is not occluded, and we represent the observation state information as ${\theta }_t=\left\{p_T^t,\eta \right\}$, and construct the mathematical model of the target motion intention as $F\left({\epsilon }_i,\theta \right)$, which can be represented by $P$. $P$ is the probability that the possible motion direction ${\epsilon }_i$ of the target calculated by the observation state ${\theta }_t=\left\{p_T^t,\eta \right\}$ is the real motion direction. Therefore, the target motion intention model $F\left({\epsilon }_i,\theta \right)$ is transformed as follows:

$$F\left({\epsilon }_i,\theta \right)\to P\left({\epsilon }_i|\theta \right)$$

(2)

According to the Bayesian theorem, we can derive the following: $P\left({\epsilon }_i|\theta \right)={\displaystyle \frac{P\left({\epsilon }_i,\theta \right)}{P(\theta )}}$. Furthermore, in the reasoning process, the likelihood probability model $P\left(\theta |{\epsilon }_i\right)$ is used to calculate the probability distribution $P\left({\epsilon }_i,\theta \right)$ as follows:

$$P\left({\epsilon }_i,\theta \right)=P\left(\theta |{\epsilon }_i\right)P\left({\epsilon }_i\right)$$

(3)

where $P\left({\epsilon }_i\right)$ is the prior probability that the direction of motion is the true direction of the target. Then, the result of calculating the conditional probability distribution $P\left({\epsilon }_i|\theta \right)$ is expressed as follows:

$$P\left({\epsilon }_i|\theta \right)={\displaystyle \frac{P\left({\epsilon }_i,\theta \right)}{P(\theta )}}={\displaystyle \frac{P\left(\theta |{\epsilon }_i\right)P\left({\epsilon }_i\right)}{P(\theta )}}\to P\left(\theta |{\epsilon }_i\right)P\left({\epsilon }_i\right)$$

(4)

Therefore, the $F\left({\epsilon }_i,\theta \right)$ is transformed into the calculation of the likelihood probability $P\left(\theta |{\epsilon }_i\right)$, and the DBN algorithm is used for the next step.

Based on the derivation process above, the inference of the target’s motion intent is iterated from the observation starting point to time $t$.

$$P\left({\epsilon }_i|{\theta }_{0:t}\right)\to P\left({\theta }_t|{\theta }_{t-1},{\epsilon }_i\right)P\left({\epsilon }_i|{\theta }_{0:t-1}\right)$$

(5)

In the above formula, the likelihood probability model $P\left({\theta }_t|{\theta }_{t-1},{\epsilon }_i\right)$ is used to describe the mapping relationship between the target motion intention and the motion state, as shown below:

$$P\left({\theta }_t|{\theta }_{t-1},{\epsilon }_i\right)=P\left(p_T^t,\eta |p_T^{t-1},\eta ,{\epsilon }_i\right)=P\left(p_T^t|p_T^{t-1},{\epsilon }_i,\eta \right)$$

(6)

The model $P\left(p_T^t|p_T^{t-1},{\epsilon }_i,\eta \right)$ is the probability of the target at the next moment $p_T^t$ when the position of the target in the flight environment $\eta$ is $p_T^{t-1}$ and the direction of motion is ${\epsilon }_i$. Therefore, the target motion intention model is further transformed into $P\left(p_T^t|p_T^{t-1},{\epsilon }_i,\eta \right)$.

Remark 1.

Considering the rationality of model simplification and reasoning, we make a Markov assumption based on the likelihood probability model, which posits that the current state only depends on the state of the previous moment and has nothing to do with the previous historical observation state. At the same time, the conditional probability model is further be simplified under the assumption of conditional independence.

From the previous Assumption a, the motion intention of the target can be modeled as follows:

$$\begin{array}{l}P\left(p_T^t\mid p_T^{t-1},{\epsilon }_i,\eta \right)={\displaystyle \frac{1}{K}}\exp \left(-\beta \cdot Q\left(p_T^t,p_T^{t-1},{\epsilon }_i,\eta \right)\right)\\ K={\displaystyle \sum _{p_T^{\prime }\in \aleph \left(p_T^{t-1}\right)}\exp }\left(-\beta \cdot Q\left(p_T^t,p_T^{t-1},{\epsilon }_i,\eta \right)\right)\end{array}$$

(7)

where $K$ is the probability normalization coefficient; $\beta$ is the rational index of the target motion with a value greater than zero; and $Q\left(p_T^t,p_T^{t-1},{\epsilon }_i,\eta \right)$ is the cost function of the target from $p_T^{t-1}$ to $p_T^t$ in the flight environment when the moving direction of the target is $\epsilon$. Its value is used to correct the difference between the inference and the reality. $\aleph (p_T^{t-1})$ is the set of all possible motion directions of the target, and $p_T^{\prime }$ is the next point that the target may reach from position $p_T^{t-1}$. The model establishment of the cost function $Q$ can be expressed as shown below:

$$Q\left(p_T^t,p_T^{t-1},{\epsilon }_i,\eta \right)=\arccos \left({\displaystyle \frac{v_{t-1}(p_T^t)\cdot v_{t-1}^{+}({\epsilon }_i)}{\Vert v_{t-1}(p_T^t)\Vert \Vert v_{t-1}^{+}({\epsilon }_i)\Vert }}\right)$$

(8)

where $v_{t-1}(p_T^t)$ is the motion direction of the target from position $p_T^{t-1}$ to position $p_T^t$, and $v_{t-1}^{+}({\epsilon }_i)$ is the optimal motion direction at position $p_T^{t-1}$.

Remark 2.

The cost function $Q$ considers the relationship between it and the gap between the actual motion direction and the optimal motion direction of the target and the influence of the outside world on the target motion intention. Therefore, the cost function $Q$ is expressed as the angle relationship between the target motion direction and the optimal motion direction in the derivation process. When the deviation angle is larger, the value of $Q$ is larger, and vice versa.

In summary, we derived the parameter values that describe the relationship between the target’s motion intent at the previous time step and the current time step. Therefore, the expression of the target motion intent inference model is as follows: the probability set $P\left({\epsilon }_i|{\theta }_{0:t}\right)$ of the target motion intention in the iterative process is derived, which is used as part of the input of the prediction algorithm.

$$\begin{array}{l}F\left({\epsilon }_i,\theta \right)\to P\left({\epsilon }_i|{\theta }_{0:t}\right)\\ =\left\{{\displaystyle \frac{1}{{\displaystyle \sum _{p_T^{\prime }\in \aleph \left(p_T^{t-1}\right)}\exp }\left(-\beta \cdot Q\left(p_T^t,p_T^{t-1},{\epsilon }_i,\eta \right)\right)}}\exp \left(-\beta \cdot Q\left(p_T^t,p_T^{t-1},{\epsilon }_i,\eta \right)\right)\right\}P\left({\epsilon }_i|{\theta }_{0:t-1}\right)\end{array}$$

(9)

As shown in Figure 3, the set $\aleph (p_T^{t-1})$ of all possible moving directions of the target can be expressed as follows:

$$\aleph \left(p_T^{t-1}\right)=\left\{p_T^t,{\tilde{p}}_{45}^t,{\tilde{p}}_{90}^t,{\tilde{p}}_{135}^t\right\}$$

(10)

2.4. Threat Model

To more closely approximate real-world scenarios, this paper describes a threat model for the flight process. The model established is as follows [40]:

As shown in Figure 4, the geometric relationship between the parameters can be expressed as follows:

$$\{\begin{array}{l}\begin{array}{l}{x}^{\prime }=x_m-x_r\\ y^{\prime }=y_m-y_r\end{array}\hfill \\ \lambda =\pi -\psi -{\eta }_m\hfill \\ r=\sqrt{x^{\prime 2}+y^{\prime 2}}\hfill \\ \varphi =\arcsin \left({\displaystyle \frac{y}{\sqrt{x^{\prime 2}+y^{\prime 2}}}}\right)\hfill \end{array}$$

(11)

In this paper, we only consider the two-dimensional pitching plane, and so the established threat model can be approximated as a circular area in the plane, and the UAV flies around the boundary when performing its mission. The aircraft trajectory constraint $d$ considered is shown below:

$$d\ge R+\sigma$$

(12)

where $d=\sqrt{{(h-h_z)}^2+{(X-X_z)}^2}$ is the distance between the aircraft and the center of the no-fly zone, $R$ is the radius of no-fly zone, and $\sigma$ is the constraint margin.

3. Main Method

3.1. Prediction Algorithm of BITCN-BIGRU-AAM

3.1.1. BITCN

TCN is mainly composed of causal convolution, inflationary convolution, and residual connectivity [29]. To effectively segment the future data and ensure the forward and backward causality of the temporal data with the tight connectivity of other algorithms, we carry out bidirectional TCN processing on the temporal sequences. The main core of the TCN algorithm involves the construction of accurate residual blocks and the design of a residual connection formula. As shown in Figure 5, the residual block is usually composed of causal dilation convolution, a spatial dropout layer, a residual connection, an activation function, and a weight normalization layer [41].

For a one-dimensional sequence, $X$ is processed into a bidirectionally transmittable sequence that is input into both forward and reverse TCN modules. Through multiple interconnected residual blocks, the sequence is processed and extended in length. Leveraging the flexible receptive field inherent to TCN, the dilation factor is incrementally increased to ensure the effective extraction of both local and global multi-level feature values from the sequence.

The input sequence is set to $X=\left\{x_1, x_2, \cdots , x_{\tau -1}, x_{\tau }\right\}$, and the output sequence is $Y=\left\{y_1, y_2, \cdots , y_{\tau -1}, y_{\tau }\right\}$ after two-layer bidirectional one-dimensional extended causal convolution calculation. For the sequence, after processing with dilated convolutions, the output of the hidden layer at time $\tau$ can be represented as follows:

$$h(\tau )={\displaystyle \sum _{i=0}^{\mathrm{k} -1}f}(\xi )\cdot x_{\tau -m\cdot i}$$

(13)

where $h(\tau )$ is the output of the dilated convolution at time $\tau$, $f(\xi )$ is a factor with position $\xi$ in the convolution kernel, $k$ is the size of the convolution kernel, $x_{\tau -m\cdot i}$ is the corresponding sequence unit after interval sampling, and $m$ is the coefficient of expansion.

In TCN, there will be multiple residual block serial processing sequences. In order to increase the stability of the model and avoid the problem of gradient disappearance, a residual connection method is designed to perform feedback addition processing between multiple residual blocks. The residual connection is as follows:

$$y=F(X,W)+X$$

(14)

where $F(X,W)$ is the feature extracted after model processing. After processing multiple residual blocks, the input sequence $X$ is transformed into $y$, as shown below:

$$y^{(j,p)}=\left[y_0^{(j,p)},\dots ,y_{\tau }^{(j,p)}\right]$$

(15)

$$y_t^{(j,p)}={\displaystyle \sum _{i=0}^{k-1}\left(f(\iota )\cdot y_{\tau -m\cdot i}^{(j-1,p)}\right)}+y_{\tau }^{(1,p)}$$

(16)

where $y^{(j,p)}$ is the $j$ layer in the p-th residual block and $p$ is the number of the residual block.

For a one-dimensional sequence, $X$ is processed by multiple interconnected residual blocks in the forward and reverse directions, and the length of the sequence is finally extended accurately. By using the inherent flexible receptive field of TCN, the scaling factor is gradually increased to ensure the effective extraction of local and global multi-level eigenvalues in the sequence.

3.1.2. BIGRU

After the BITCN output sequence, we use the bidirectional GRU structure for further processing and improve the prediction accuracy by considering contextual information. The GRU network structure performs corresponding operations through the two gated structures in each sub-cell to achieve the forward propagation of the sequence, and then the prediction of the sequence can be achieved [42].

In this paper, the same structure with opposite directions is added to the traditional GRU to form the BIGRU model. When training the BIGRU network structure, the use of additional momentum can prevent the training from falling into local minima. The formula of this method is defined as follows [43]:

$$\Delta w_{jt}(k+1)=(1-mc)\alpha {d_t}^k{b}_j+mc\Delta w_{jt}(k)$$

(17)

$$\Delta {\theta }_t(k+1)=(1-mc)\alpha {d_t}^k+mc\Delta {\theta }_t(k)$$

(18)

where $\Delta w_{jt}(k+1)$ is the weight value, $\Delta {\theta }_t(k+1)$ is the threshold value, $k$ is the training number, $\alpha$ is the training proportion ($0<\alpha <1$), and $mc$ is the momentum factor.

3.1.3. Auto-Attention Mechanism

The auto-attention mechanism is often used in the field of image segmentation semantics [44]. The steps of the auto-attention mechanism in the prediction algorithm of this paper are as follows:

Assuming that the input state matrix input is $R^{(a\times b)}$, the three weight matrices are ${\omega }^q$, ${\omega }^k\in R^{(b\times d)}$, and ${\omega }^v\in R^{(b\times c)}$. The input state matrix and the three weight matrices are linearly transformed to obtain $Q=\mathrm{input}q$, $K=\mathrm{input}{\omega }^k$, and $V=\mathrm{input}{\omega }^v$, where ${\omega }^k\in R^{(b\times d)}$ and ${\omega }^v\in R^{(b\times c)}$.

It is necessary to calculate the attention integral matrix $G$, as shown below:

$$G=Q{K}^T/\sqrt{d_k}$$

(19)

where $d_k$ is the dimension of $k$ and $1/\sqrt{d_k}$ is the scaling factor, which can prevent the inner product value from affecting the learning of the neural network.

The attention weight matrix $W$ is calculated as follows:

$$W=\mathrm{softmax}\left(\left(Q{K}^T\right)/\sqrt{d_k}\right)$$

(20)

In summary, the result matrix $z$ can be represented as follows:

$$z= \mathrm{Attention} (Q,K,V)=\mathrm{softmax}\left(Q{K}^T/\sqrt{d_k}\right)V$$

(21)

In the above formulas, the transformation matrixes ${\omega }^q$, ${\omega }^k$ and, ${\omega }^v$ are the parameters of the neural network. These parameters can be modified with backpropagation, and auto-attention transfer can be achieved by modifying these transformation matrices. Using the above principles, the structure of BITCN-BIGRU-AAM algorithm is shown in Figure 6.

3.2. Online Trajectory Planning

The neural network is a widely parallel interconnected network composed of adaptive simple units and its organization can simulate the interactive response of the biological nervous system to real objects [45]. The general neuron model is shown in Figure 6.

In Figure 7, $x_1, x_2, x_3, \cdots , x_n$ is the input component of the neuron, $w_1, w_2, w_3, \cdots , w_n$ is the corresponding weight parameter of each input component, $b$ is the offset, $y$ is the neuron output, and $f(\cdot )$ is the activation function. The mathematical model of the neuron model is shown as follows:

$$\{\begin{array}{l}X={\displaystyle \sum _{i=1}^n{w}_i{x}_i+b}\\ Y=f(X)\end{array}$$

(22)

The two-layer neuron model is connected to form a single-layer perceptron, which is the most basic kind of neural network model. A hidden layer is added between the input layer and the output layer to form a multi-layer perceptron, i.e., a multi-layer neural network model [46].

Let the input layer be $X=[x_1, x_2, \cdots , x_n]$ and the output be $Y=[y_1, y_2, \cdots , y_n]$. The output layer node realizes the linear mapping of the hidden layer output node from $R_i(X)\to y_k$, i.e., the hidden layer output node is linearly weighted and summed, and the output layer kth neural network output is expressed as follows:

$${\widehat{y}}_k={\displaystyle \sum _{i=1}^m{\omega }_{ik}{R}_i(X)}, k=1, \cdots , p$$

(23)

where n, p, and m are the number of nodes in the input, output, and hidden layer, and ${\omega }_{ik}$ is the weight connecting the i-th neuron in the hidden layer with the k-th neuron in the output layer. The activation function of the hidden layer corresponds to the RBF network structure. The process of planning the obstacle avoidance trajectory of the RBF network using offline–online modes is shown in Figure 8.

3.3. System Architecture

Working according to the mission requirements of UAV online obstacle avoidance and target capture, the parallel system structure is designed based on the BITCN-BIGRU-AAM and improved RBF algorithm and is shown in Figure 6 and Figure 8. In the structure of the algorithm used in this study, the target and interference state information are first obtained through the seeker unit and then transmitted to the flight status storage unit. The corresponding information is then processed in parallel using prediction and trajectory planning algorithms. The predicted trajectory of the lost target, after actual correction, is transmitted to the UAV’s trajectory online generation unit. The trajectory planning algorithm generates an obstacle avoidance trajectory for the UAV in real time, considering the dynamic interference areas. If the system’s evaluation conditions are met, the trajectory information is transmitted to the integrated guidance and control unit; if not, a new trajectory is replanned, and the above steps are repeated. This process ultimately enables the UAV to successfully avoid dynamic obstacle areas and accurately capture the intermittent target. The detailed steps of the algorithm are shown in Algorithm 1. In summary, the parallel system’s structure, designed based on BITCN-BIGRU-AAM and the improved RBF algorithm, is shown in Figure 9.

Algorithm 1: Complete Algorithm Pseudocode

Input: $X=[x_1, x_2, \dots , x_{\tau }]$; ${l_n|}_{n=1}^N$$, \mathrm{the} \mathrm{component} \mathrm{of} \mathrm{the} \mathrm{neuron}, l_n=\{l_1, l_2,\dots ,l_n\}$; ${w_n|}_{n=1}^N$, $\mathrm{the} \mathrm{weight} \mathrm{parameter}, w_n=\{w_1, w_2, \dots , w_n\}$; Output: optimal_trajectory $\mathrm{Initialize} \mathrm{parameters} n, b, f(•)$$, R_i(X)$ for epoch = 0, …, Nepoch-1 do $\mathbf{for} i\leftarrow \{0, \cdots , K-1\}$ do $\mathrm{In} \mathrm{the} \mathrm{bidirectional} \mathrm{TCN} \mathrm{network}, \mathrm{the} \mathrm{feature} \mathrm{sequence} Y\_forward=\left\{y_0, \dots , y_{\tau }\right\}$$\mathrm{and} Y\_reverse=\left\{y_{\tau }, \dots , y_0\right\}$ using Equations (13)–(16) In the bidirectional GRU network, the feature sequence h using Equations (17) and (18) Compute the Q, K, and V values in the adaptive attention mechanism $c=G *W$; $L(t)\leftarrow FC(c(t)+S(t-1))$ $\mathrm{return} L(t)$  end for $\mathbf{for} n\leftarrow \{1, \cdots , N\}$ do $L\leftarrow {\displaystyle \sum _{i=1}^n{w}_i{l}_i+b}$ $Z\leftarrow f(L)$$, \mathrm{realizes} \mathrm{the} \mathrm{linear} \mathrm{mapping} \mathrm{of} \mathrm{the} \mathrm{hidden} \mathrm{layer} \mathrm{output} \mathrm{node} \mathrm{from} z_k\leftarrow f(L)=R_i(L)$ Predict the output layer k-th $\mathrm{neural} \mathrm{network} \mathrm{output} \mathrm{using} \mathrm{Equation} \left(23\right), \mathrm{obtain} {\widehat{z}}_k$ $\mathbf{if} (|{\widehat{z}}_k-Z|>\epsilon )$ then $L\leftarrow \mathrm{updata}(L)$ continue   end if   $\mathbf{if} \mathrm{valid}\_\mathrm{trajectory}({\widehat{z}}_k$) then    $\mathrm{optimal}\_\mathrm{trajectory} \leftarrow {\widehat{z}}_k$    break   else    $L\leftarrow \mathrm{updata}(L)$   end if end for end for return optimal_trajectory

4. Experiments

In this section, we set up a series of complex experimental scenarios to verify the performance of the designed system. Specifically, the performance of the prediction algorithm is tested by using different maneuvering target trajectories and the different prediction algorithms are used to prove the superior performance of the prediction algorithm in the predictor. Then, we show the adaptability of online planning to the dynamic interference region under the condition that the target future trajectory prediction point is known and verify the anti-interference performance of the online planning algorithm when the target prediction point has errors. Finally, the real-time performance of the designed system structure is proved using the planning time and CPU occupancy rate. The experimental environment is a 12th Gen Intel (R) Core (TM) i7-12700H 2.30 GHz and the MATLAB version is 2023a.

4.1. Experimental Arrangement and Parameter Setting

To reasonably and accurately verify the performance of the system proposed in this paper, we arrange the following experimental scenarios. In Section 4.2, three different maneuvering forms are used to verify the prediction algorithm in this paper, and then four commonly used prediction algorithms are compared with the proposed algorithm. In Section 4.3, we use three different scenarios to verify the system. The accuracy and real-time performance of UAV planning trajectory are verified under the conditions of a dynamic interference area and target prediction trajectory error. The simulation parameters of this paper are outlined in

Table 1. Experiment-related parameters.

Parameters	Value
Pitch plane (km)	10 × 2
Initial position of online planning (m)	[2000, 578]
Initial speed for online planning (m/s)	500
Target speed (m/s)	600
$\mathrm{Craft} \mathrm{control} \mathrm{constraints}$(°)	$[-30,30]$
Comparisons of dynamic pressure (kPa)	$[120,240]$
Radius of interference and blind area released by aerial fighters (m)	$[200\pm \Delta r]$
Position of interference and blind area released by aerial fighters (m)	$[(5500, 1300)\pm \Delta o]$
Alert radars (m)	$\left[2750,675\right]\cup \left[7350,1180\right]$
Radar detection parameters	$c_1=1.01$$, c_2=1.25\times {10}^{-18}$

. In the experimental setup, the target is configured to fly from position A to position B at a speed of 600 m/s, with allowance for non-repetitive maneuvers. The launch position of the aircraft is set as the origin of the flight pitch plane coordinate system. The initial velocity used for trajectory planning is not less than 500 m/s. The radius and position variation ranges of the interference blind zone during flight are $[200\pm \Delta r]$ and $[(5500, 1300)\pm \Delta o]$, respectively. In these figures, $\Delta r$ and $\Delta o$ represents the variation deviations of the radius and position. The known information about the ground deployment environment traversed by the aircraft includes two ground-based joint detection and early warning radars located at [2750, 675] meters and [7350, 1180] meters, respectively. The random elements include the sudden appearance of intercepting fighter aircraft, which conduct aerial detection and release jamming missiles, creating dynamic threats throughout the flight process.

4.2. Verification of Online Prediction Algorithm for Maneuvering Target

Firstly, we utilize the set of target historical trajectories with motion intention features in both directions as the input sequence of the prediction algorithm. In the algorithm, we divide the input sequence containing 1300 sample points into 30 sample sets, of which 29 are training sets and 1 is a testing set. The sliding window is set to 10, and the prediction algorithm trains, derives, and verifies the entire input sequence. Then, we set the following key parameters: the convolution kernel is set to 128 × 64 × 32, the convolution kernel size is set to 1 × 3, the expansion coefficient is set to 1, 2, 4, the dropout rate is set to 0.5, the GRU layer number is set to 2, the learning rate is set to 0.003, and the algorithm is iterated 1000 times. To better evaluate the prediction effect, we introduced four commonly used prediction evaluation indicators, namely, MSE, RMSE, MAE, and MAPE [47]. When the values of the four indicators are smaller, the prediction effect of the algorithm is the best.

Scenario 1: Considering the maneuverability of the target, we set the initial position of the target to (5000, 0) meters and the initial speed as 0 m/s. In the simulation, the target speed increases rapidly to 600 m/s, and the target is set to perform irregular maneuvers. The maneuvering mode is set as follows: firstly, the target plunges and dives at a pitch angle of 35 degrees. Then, it performs two cycles with sinusoidal motion, and finally performs a straight diagonal rise. To closely resemble a real application scenario, we allow the observation state variables to be updated. The experimental setting can fully verify the real-time correction speed and adaptive learning ability of the prediction algorithm.

As shown in Figure 10, the prediction algorithm is relatively accurate in predicting the future trajectory of the target, and it can quickly adapt to the maneuvering situation of the target to adjust the predicted trajectory. When the target is moving in a straight line, the error between the predicted distance and the actual distance is 0.2 m. This result demonstrates that the algorithm proposed in this study achieves high accuracy in predicting linear motion trajectories, with its performance metrics reflected by MAE and MSE. Lower values indicate stronger prediction stability. When the target is moving in a sinusoidal motion, the error between the predicted distance and the actual distance is 1.12 m. Further, when further evaluating slightly more complex motion trajectories, the results obtained from RMSE better reflect the algorithm’s adaptability. For Scenario 1, when the target suddenly maneuvers, the error changes in the range of 7 m to 10 m and quickly converges to the actual trajectory. At the junction of the last two linear motions with different pitch angles, the predicted trajectory shows a slight oscillation. This phenomenon produces a distance error of about 16 m in the horizontal axis direction and a distance error of about 60 m in the vertical axis direction, but it quickly converges to the actual trajectory.

To more clearly compare the prediction performance of algorithms for different types of trajectories, we evaluated the prediction results of target motion trajectories under different maneuver forms using four common performance indicators for prediction algorithms, as shown in

Table 2. Comparison of performance indicators of four prediction algorithms.

	Rectilinear Maneuver	Sinusoidal Maneuver	Irregular Maneuver
MSE	9.6197 × 10−17	15.1888	179.2565
RMSE	9.808 × 10−9	3.8973	13.3887
MAE	9.808 × 10−9	3.4995	7.181
MAPE (%)	1.0621 × 10−10	0.06	0.097

. The data demonstrate that the algorithm achieves optimal performance in predicting linear motion target trajectories, with MSE, RMSE, and MAE values approaching 0, and MAPE as low as 1.0621 × 10⁻¹⁰%; this indicates that the algorithm exhibits extremely high accuracy for simple motion trajectories. For sinusoidal motion, the errors increase, with MSE at 15.1888, RMSE at 3.8973, MAE at 3.4995, and MAPE at 0.06%; this suggests that the algorithm can effectively capture regular trajectories, though some errors persist. When predicting irregular motion targets, the errors increase significantly, with MSE at 179.2565, RMSE at 13.3887, MAE at 7.181, and MAPE at 0.097%; this indicates that the algorithm’s predictive capability declines substantially for complex and irregular trajectories. However, despite its relatively lower accuracy, the proposed prediction algorithm still demonstrates an impressive performance for irregular maneuver (MAPE at 0.097%). This favorable outcome can be credited to the algorithm’s ability to infer the target’s historical motion intentions.

Since each prediction algorithm demonstrates excellent performances when predicting straight and regular curved trajectories, and because targets in practical applications rarely exhibit simple and regular movements while being pursued, this study focuses on comparing the performance of different prediction algorithms to predict irregular trajectories. In the following validation experiments, we selected four traditional trajectory prediction algorithms for further comparative verification, namely, extreme learning machine (ELM), bidirectional time convolution network (BITCN), long short-term memory (LSTM) network, and support vector regression (SVR) machine.

The simulation results and performance indicators are shown in Figure 11 and Figure 12. The analysis of the results shows that the other prediction algorithms do not show a good prediction effect, and each algorithm has a relatively obvious deviation. In the last section of the trajectory, the deviations between the predicted results of ELM, BITCN, LSTM, and SVR and the actual trajectory are 450 m, 80 m, 40 m, and 35 m, respectively; this effect does not meet the stringent requirements of the mission parameters of the UAV. In comparison, the algorithm proposed in this paper only has a trajectory deviation of about 9.5 m, and its prediction effect is the best among those compared. To facilitate the comparison and analysis of performance metrics for each algorithm, we normalized the indicators, as shown in Figure 12b and

Table 3. The data of the four normalized performance metrics for different prediction algorithms.

	ELM	BITCN	LSTM	SVR	BITCN-BIGRU-AAM
MSE	0.9234	0.0343	0.0187	0.0173	0.0062
RMSE	0.6433	0.1239	0.0921	0.0882	0.053
MAE	0.6861	0.1197	0.0792	0.0792	0.0451
MAPE (%)	0.69	0.23	0.19	0.18	0.097

.

The normalized performance metrics, shown in Table 3, quantitatively evaluate the performance of different algorithms in predicting random target motion. By combining the prediction results from Figure 11 and the data in Table 3, we can analyze and compare them to learn that the BITCN-BIGRU-AAM achieves an MSE of 0.0062, the lowest among all algorithms, demonstrating the model’s exceptional capability to fit target trajectories and its absolute advantage in terms of controlling overall error. Its RMSE of 0.053 further validates its stability and reliability in minimizing large deviations. The MAE of 0.0451 indicates that it has the smallest average prediction error, ensuring high precision, while an MAPE of 0.097% signifies an almost negligible relative error, highlighting its excellent adaptability to target motion trends. BITCN, with an MSE of 0.0343, RMSE of 0.1239, MAE of 0.1197, and MAPE of 0.23%, ranks second to BITCN-BIGRU-AAM but surpasses traditional methods, showcasing good accuracy and applicability. LSTM achieves an MSE of 0.0187, an RMSE of 0.0921, an MAE of 0.0792, and an MAPE of 0.19%, further reflecting the potential of deep learning models to handle complex nonlinear target motion. SVR, with an MSE of 0.0173, RMSE of 0.0882, MAE of 0.0792, and MAPE of 0.18%, performs similarly to LSTM but slightly falls short in certain complex scenarios. In contrast, ELM shows an MSE of 0.9234, an RMSE of 0.6433, an MAE of 0.6861, and a significantly high MAPE of 0.69%, indicating its difficulty in terms of adapting to complex trajectory changes. Through the comparative analysis of these specific metrics, it is evident that BITCN-BIGRU-AAM demonstrates a clear advantage in every performance indicator, comprehensively outperforming other algorithms and delivering optimal target trajectory prediction results, providing robust theoretical support and practical value for the achievement of high-precision trajectory prediction.

In summary, the algorithm proposed in this paper has strong adaptability to the target trajectory prediction in the form of random motion, but there is still a small prediction oscillation in the case of more rapid maneuvering changes. Compared with the traditional trajectory prediction algorithms, the performance of the proposed prediction algorithm is much better than that of the ordinary algorithm, which is attributed to the inference model of the target motion intention. The above experiments provide convincing evidence for the advancement and performance advantages of the proposed algorithm.

4.3. Overall System Verification

4.3.1. Design of Offline Trajectory Sample Library

• Generation of trajectory sample library

Before employing the online planning algorithm proposed in this paper, an offline sample library was generated using the pseudospectral method [39]. To optimize online performance, we established corresponding parameter offsets to generate a trajectory sample library. In

Table 4. Deviation change setting.

Deviation	Range
$\Delta X_f$ (m)	$\pm 300$
$\Delta h_f$ (m)	$\pm 100$
$\Delta r_{circ}$ (m)	$\pm 50$
$\Delta o_{circ}$ (m)	$(\pm 500, \pm 50)$
$\Delta X_f$ (m)	$\pm 300$

, the horizontal range deviation is set to $\pm 300$ m, the vertical range deviation is set to $\pm 100$ m, the interference zone radius deviation is set to $\pm 50$ m, and the centroid displacement deviation of the interference zone is set to $(\pm 500, \pm 50)$ m. Under these deviation conditions, 200 trajectories are generated to serve as the sample library for online trajectory planning. The results of this process are illustrated in Figure 13. Under the sample library with the established parameter offsets, the UAV can plan online obstacle avoidance trajectories that adapt to dynamic disturbances in unknown environments.

• Offline sample library training

Building upon the experimental parameter settings outlined in Section 4.1, we configure one hidden layer in the RBF neural network. The input layer, hidden layer, and output layer each have 15 neurons. The hidden layer activation function employs the Gaussian function within the Radbs function. For the output layer activation function, the Purelin linear function is utilized. The Nguyen–Widrow algorithm is employed to initialize the weights and thresholds of each layer, with the weight initialization function set to the Initwb function. The Mean Squared Error (MSE) is selected as the loss function. The gradient descent method is chosen as the optimization algorithm. The dataset is partitioned into training data, validation data, and test data in a ratio of 70%: 15%: 15%. The learning rate is set to 0.01 and the maximum number of training iterations is set to 1000.

Boundary conditions are randomly designated so that $X_f$ equals 8680 m, $h_f$ equals 1686 m, $r$ equals 400 m, and $o$ equals (5153, 1040) meters. These values are adopted to test the trained network. The training metrics are illustrated in Figure 14.

• Performance verification of offline sample library

As evident from Figure 14, the neural network’s predictive outputs in terms of training, validation, and testing all exceed 0.93. The R is greater than 0.93, and higher R values indicate more precise neural network fitting. Figure 15 and Figure 16 show that the trajectory planned by the pseudospectral method under the same conditions is used as a benchmark for comparison with the training test results. This benchmark can better verify the effectiveness of online prediction than others. The error is defined as the variation between the predicted and nominal values, serving to verify the accuracy of the online prediction.

In the above performance verification, the online predicted trajectory closely approximates the best nominal trajectory while perfectly avoiding the interference zones. The prediction trajectory error fluctuates within the range of [−9, 1] meters, with a terminal error of 0.31 m, meeting the precision requirements for online target interception.

4.3.2. Performance Verification of Online Trajectory Planning

Scenario 2: In this scenario, we verify the online obstacle avoidance trajectory planning performance of the UAV in the face of different radius interference areas. The environmental settings are shown in

Table 5. Scenario environment parameter setting.

Interference Zone	Dynamic Interference Zone	Static Interference Zone 1	Static Interference Zone 2
Radius (m)	(150$\to$200$\to$240)	100	200
Position (m)	(5000, 1200)	(3620, 650)	(7300, 1190)

. In the environment with dynamic and static radius interference zones, the online trajectory planning experiment is carried out for the UAV based on the new neural network. The experiment setup algorithm is updated 1000 times online. To facilitate observation, we selected three state variables that were representative of performance to undergo analysis. The results are shown in Figure 17 and Figure 18.

As shown in Figure 17, the online obstacle avoidance trajectory of UAV is relatively smooth, and it can adjust its flight trajectory according to changes in the dynamic region. Among these changes, the drone can gradually adapt to the change in the radius of the interference area during flight and complete fast obstacle avoidance trajectory planning, which provides a safe reference trajectory for subsequent control. It can be seen from Figure 18 that the state variables and control variables of the UAV in the presence of static and dynamic interference regions meet the predetermined constraints. Figure 18b shows the distance error between the 1000 trajectories planned online and the interference area, and the values are all within 8 m.

Table 6. Obstacle avoidance distance of UAV under different dynamic interference radius.

radius of interference area (m)	150	200	240
shortest distance (m)	152	201	243

describes the error of obstacle avoidance distance in the initial, middle, and end states of the whole planning. The experiment shows that no matter how the radius changes of the dynamic interference zone, the UAV can plan the obstacle avoidance trajectory online efficiently and accurately.

Scenario 3: In this scenario, we verify the online obstacle avoidance planning performance of UAVs in the presence of dynamic interference areas with position changes. The scene environmental settings are shown in

Table 7. Scenario environment parameter settings.

Interference Zone	Dynamic Interference Zone	Static Interference Zone 1	Static Interference Zone 2
Radius (m)	200	100	200
Position (m)	(5000, 1200)$\to$(5500, 1300)$\to$(6000, 1330)	(3620, 650)	(7300, 1190)

. In the simulation, we also set the trajectory update frequency of 1000 times to conduct the performance verification of UAV in this scenario. The verification results are shown in Figure 19 and Figure 20.

As shown in Figure 19, the online obstacle avoidance trajectory of UAV is relatively smooth, and it can adjust its flight trajectory according to changes in the dynamic region. As shown in Figure 20 and

Table 8. Obstacle avoidance distance of UAV under different dynamic interference positions.

Position of interference area (m)	(5000, 1200)	(5500, 1300)	(6000, 1330)
Radius of interference area (m)	200	200	200
Shortest distance (m)	200	202	201

, similar to the experimental result of Scenario 3, the drone can gradually adapt to the change in the positions of the interference area during flight and complete the fast obstacle avoidance trajectory planning. When the position of the dynamic interference area changes, the UAV switches the optimal avoidance strategy and bypasses the interference in the optimal form to avoid the threat. The experiment shows that no matter how the position of the dynamic interference zone changes, the UAV can plan the obstacle avoidance trajectory online efficiently and accurately.

Scenario 4: In this scenario, we verify the performance of online obstacle avoidance trajectory planning and accurate target capture when the UAV faces errors related to the target prediction position. We selected five points from the target prediction trajectory for verification, and the flight environment was set as is shown in

Table 9. Scene parameter settings.

Interference Zone	Dynamic Interference Zone	Static Interference Zone 1	Static Interference Zone 2
Radius (m)	360	100	200
Position (m)	(1820, 1060)	(3620, 650)	(7300, 1190)
Position of target Capture area (m)	(8680, 1610)$\to$(8680, 1630)$\to$(8680, 1650)$\to$(8680, 1670)$\to$(8680, 1690)

. In the environment with static interference area, the trajectory planning experiment of UAV online obstacle avoidance and disturbance target capture is carried out based on the new neural network. The experimental results are shown in Figure 21 and Figure 22.

As shown in Figure 21, the online obstacle avoidance trajectory of the UAV is relatively stable, and the flight trajectory can be adjusted according to the trajectory change predicted by the target. The drone can gradually capture the predicted trajectory points of the target online, and quickly and accurately achieve obstacle avoidance. As shown in Figure 22, the state variables of the UAV meet the predetermined constraints under the condition that the static interference region exists, the online planned trajectory is accurate when the target predicted trajectory point is the end point, and the average error of each plan is 1.2 m (Figure 22b). Experiments show that, under the condition that the prediction algorithm guarantees a certain trajectory prediction error, the trajectory error of online planning will not increase the error of the whole system, which ensures the miss rate of the UAV.

In this section, we verify the performance of the algorithm in the UAV flight system by setting different experimental scenarios. Working from the results of each scene, the flight system can complete the task of obstacle avoidance and target capture under the condition of satisfying the flight performance in the complicated flight environment.

Due to the high flight speed of UAVs, the system imposes extremely high demands on computational resources and real-time performance. As the complexity of the environment increases, the complexity of the system’s mathematical model also grows, leading to a heavier computational burden during operation. In addition, when validating the algorithm proposed in this study, variations in results can also arise from the use of different computer systems and simulation software. Specifically, the higher the performance of the computer system used, the better the real-time performance achieved, as shown in Figure 23. According to the iteration time of the system in the simulation and the occupancy rate of the algorithm in relation to the CPU of simulation platform, the time required for 1000 iterations in each scene is less than 0.3 s, which meets the time required for the online trajectory planning of long UAV flights at high altitudes (Figure 23a). The prediction algorithm only takes up a small amount of running space when predicting the future trajectory of the target, which ensures the smooth operation of the subsequent online trajectory planning (Figure 23b).

5. Conclusions

This paper addresses the trajectory planning problem for UAVs, capturing intermittently lost targets in flight environments with dynamic obstacles, and proposes an online obstacle avoidance trajectory planning method that considers the real-time prediction of target motion. Considering the UAV system’s control methods and operational processes, a parallel processing algorithm structure is designed. To estimate the motion state of intermittently lost targets, a predictor of the UAV is designed using a prediction algorithm (BITCN-BIGRU-AAM) based on motion intention reasoning. Subsequently, using the target state information obtained by the predictor, an online obstacle avoidance trajectory planner for the UAV is designed using an improved RBF network and offline–online methods. The simulation results demonstrate that, regardless of the form of dynamic disturbances in the environment, the designed method can quickly and accurately avoid dynamic obstacles and successfully reach the target capture area. Furthermore, the system enables the UAV to precisely capture the target, even when prediction errors exist in the predictor.

There are many different types of UAVs in the real flight environment, which is a three-dimensional airspace. In future work, we will extend the dynamic disturbance regions and target motion trajectories to three-dimensional space. Building on the foundation of this study, we will also employ more advanced algorithms to address more complex flight scenarios.