Flight Path Optimization for UAV-Aided Reconnaissance Data Collection

Abstract

While UAV-aided reconnaissance data collection grows rapidly, its path optimization is severely hindered by environmental dynamics, node mobility, and overlapping security/interference risks. This paper addresses the problem of data collection from mobile reconnaissance nodes in interference environments, incorporating safety flight constraints and dynamic constraints. We propose an integrated path optimization framework combining initial path guidance with dynamic replanning capabilities. The system first predicts reconnaissance node and interference source positions while analyzing channel conditions to generate an optimal initial path within the designated communication flight corridor. Subsequently, the framework addresses non-convex path planning challenges using slack variables and equivalent constraints, with the successive convex approximation algorithm providing efficient iterative solutions. Numerical results show that in dynamically changing scenarios, the proposed method achieves high reliability and planning efficiency for real-time, data-collection-oriented path optimization.

1. Introduction

The rapid advancement of ubiquitous sensing technologies has significantly expanded the application of UAVs in reconnaissance data collection [1], providing an effective solution for data retrieval from low-power reconnaissance nodes by enabling aerial data gathering and transmission to centralized processing facilities [2,3,4]. As a fundamental enabling technology, UAV path optimization plays a critical role in such scenarios [5,6,7], requiring the generation of optimal flight trajectories that simultaneously fulfill mission objectives [8] while autonomously addressing collision avoidance, interference mitigation, and exposure risks to ensure both real-time and valid data collection [9,10,11]. However, this process faces substantial challenges from high-density obstacles in reconnaissance environments, combined natural and artificial interference sources [12], as well as inherent limitations in UAV hardware/software capabilities and onboard reconnaissance systems [13,14,15], all of which complicate the path optimization process and demand sophisticated solutions.

The timeliness of reconnaissance data stands as one of the most critical metrics for evaluating mission effectiveness, where the end-to-end duration from data generation to processing at the central facility directly determines its quality. In UAV-aided ground node data collection scenarios, the combined duration of flight operations and data collection governs the intelligence-gathering speed, constituting the dominant factor in timeliness assessment. Unlike existing approaches, our model employs a continuous flight paradigm where the UAV completes both data collection and positional arrival simultaneously during its trajectory. The path optimization framework specifically minimizes flight time as its primary objective, thereby ensuring optimal temporal efficiency when delivering reconnaissance information to both data centers and decision-makers.

In adversarial military operations, the implementation of mobility tactics by both hostile interference sources and friendly reconnaissance nodes—aimed at evading counterstrikes—generates a highly dynamic combat environment that introduces formidable spatiotemporal complexities to path optimization challenges. Ref. [16] divides the path optimization process into front-end pathfinding and back-end trajectory refinement, with particular emphasis on the advantages of the A* algorithm as a heuristic search approach during the pathfinding phase. To achieve rapid optimization of UAV flight paths in dynamic scenarios and enhance the quick response to changes in the positions of reconnaissance nodes and interference sources, a method for extracting convex polyhedrons in three-dimensional free space to construct a Safety Flight Corridor (SFC) is proposed. By confining the UAV flight path within the SFC, a convex optimization problem model is established, which can be directly solved using mature convex optimization algorithms. Ref. [17] introduced a partitioning method combined with a multi-phase optimal control formulation to effectively increase the free space for UAV path planning in unstructured environments where complex obstacles in the mission area disrupt the SFC. Ref. [11] proposed an SFC construction method from a computational simplification perspective, generating convex polyhedrons based on the ellipsoid expansion method. Additionally, to generate UAV paths and state parameters within the SFC under hard constraints, ref. [18] employed piecewise Bézier curves based on Bernoulli polynomials to represent the UAV flight trajectory. However, high-order Bézier curves are prone to generating “ill-conditioned” trajectories. To address this issue, ref. [19] introduced B-spline curves, which allow better local adjustments to the UAV path.

Generally, the path planning problem for reconnaissance UAV data collection is modeled as a non-convex optimization problem. For non-convex constraints, solutions typically involve designing equivalent or relaxed problems followed by solving the equivalent convex problem using the Successive Convex Approximation (SCA) or various heuristic optimization algorithms. Although these algorithms perform well in searching for local optimal solutions, they are highly sensitive to initial values [20].

This paper focuses on the application of UAV collecting sensing data from ground nodes, aiming to achieve efficient reconnaissance of mission areas. To address the issue of uncertain positions of reconnaissance nodes in dynamic interference environments, a non-convex path planning method is designed, and a rapid replanning scheme for UAV trajectory is developed. In the planning problem, factors such as the data transmission capability and communication capacity of reconnaissance nodes, as well as the flight characteristics of UAV and interference sources, are comprehensively considered. A rapid replanning method based on initial path guidance is proposed. This method enables efficient execution and rapid response to reconnaissance data collection in dynamic environments, providing a more reasonable and reliable solution for optimizing the timeliness of reconnaissance data. The main contributions and innovations of this paper are as follows:

(a)

To meet the real-time path planning requirements of UAVs in dynamic interference environments, a path planning model based on initial path guidance is proposed. This model comprehensively considers the safe flight constraints, motion characteristics of UAVs, and reconnaissance data collection constraints, establishing a trajectory optimization problem.

(b)

During the path planning phase, by introducing slack variables and constructing equivalent constraints, the non-convex path planning problem is transformed into a convex problem, which is then iteratively solved using SCA. The planning process takes into account the UAV motion characteristics, resulting in a final path suitable for execution by the flight control module.

(c)

To address the rapid replanning requirements when the positions of interference sources and reconnaissance nodes change dynamically, an initial path generation algorithm is designed based on the communication flight corridor (CFC) and collision detection correction. This algorithm guides the optimization search of SCA, thereby achieving rapid replanning of the UAV path.

(d)

The performance of the proposed algorithm under different parameter configurations is validated through numerical simulations, and comparisons are made with the state-of-the-art research. The results demonstrate that in scenarios where interference sources and ground reconnaissance nodes change dynamically, the proposed method exhibits high reliability and planning efficiency in solving the path planning problem with a focus on the timeliness of reconnaissance data.

2. System Model

In this scenario, the reconnaissance data collection task is assigned to a UAV, which is required to take off from a specific airport/waypoint, utilize the Time Division Multiple Access (TDMA) protocol for communication, collect data from mobile reconnaissance nodes within a designated area, and finally arrive at the next airport/waypoint. The process employs path optimization that adheres to the UAV’s dynamic constraints, aiming to maximize the timeliness of reconnaissance data while minimizing flight energy consumption, thereby enabling the UAV to efficiently complete the data collection. As shown in Figure 1, a single UAV is dispatched, and the number of moving ground nodes is N, denoted as $\mathcal{N}=\left\{1,2,\dots ,n,\dots ,N\right\}$. The position of node n is represented by ${\mathbf{w}}_n=\left[x_n,y_n,0\right]$, and it is assumed that the transmission power of each reconnaissance node is $p_n$. The positions of the ground nodes are dynamically changing, meaning ${\mathbf{w}}_n$ varies over time. Consequently, for the UAV, the future positions of the nodes are uncertain, necessitating the prediction of node locations and the adoption of a continuous flight-based data collection mode. When the UAV arrives within the effective communication range of a ground reconnaissance node, the node is activated and establishes communication with the UAV to upload reconnaissance data. Taking into account the need to avoid potential collision risks with the ground and the maximum altitude restrictions imposed by air traffic control, the flight altitude is set to $h\in \left[H_{min},H_{max}\right]$. If the total time required for the UAV to execute the reconnaissance data collection task is T, its flight trajectory is denoted as $\mathbf{w}\left(t\right)=\left[x\left(t\right),y\left(t\right),h\left(t\right)\right],0\le t\le T$. Additionally, there are M obstacles/no-fly zones within the mission area, with the ground-projected center coordinates of these zones denoted as ${\mathbf{w}}_m=\left[x_m,y_m,0\right],m\in \mathcal{M}$. Considering the presence of J interference sources in the scenario, they are represented as the set $\mathcal{J}=\left\{1,2,\dots ,j,\dots ,J\right\}$. The UAV’s flight time is evenly divided into K sufficiently small time slots $\delta$, where flight time $=K\delta$. As a result, the UAV’s 3D flight path is discretized, with the UAV’s position in the k-th time slot denoted as $\mathbf{w}\left(k\right)=\left[x\left(k\right),y\left(k\right),h\left(k\right)\right]$.

2.1. Data Collection Channel with Interference

In the presence of interference sources within the mission area, the UAV collects reconnaissance data from ground nodes while continuously flying. At the k-th time slot, the Euclidean distance between the UAV and the interference source is

$$d_j\left(k\right)=∥\mathbf{w}\left(k\right)-{\mathbf{w}}_j\left(k\right)∥,\forall j\in \mathcal{J}$$

(1)

At the k-th time slot, the Euclidean distance between the UAV and the reconnaissance node is

$$d_n\left(k\right)=∥\mathbf{w}\left(k\right)-{\mathbf{w}}_n\left(k\right)∥,\forall n\in \mathcal{N}$$

(2)

The communication channel between the UAV and the reconnaissance node is divided into two components: large-scale fading and small-scale fading. Here, large-scale fading refers to the path loss during electromagnetic wave propagation, denoted as

$$g_i\left(k\right)=\sqrt{{\mu }_0{\left(d_i\left(k\right)\right)}^{-\alpha }}$$

(3)

The small-scale fading follows an independent and identically distributed Rician channel with a factor of $\mathcal{A}$, and the small-scale fading coefficient is denoted as

$${\widehat{h}}_i=\sqrt{{\displaystyle \frac{\mathcal{A}}{\mathcal{A}+1}}}{\overline{h}}_i+\sqrt{{\displaystyle \frac{1}{\mathcal{A}+1}}}{\tilde{h}}_i$$

(4)

Thus, the total channel coefficient is denoted as

$$h_i\left(k\right)={\widehat{h}}_i{g}_i\left(k\right)$$

(5)

where ${\mu }_0$ is the average power gain at the reference distance, and the path loss exponent satisfies $2\le \alpha \le 5.5$. Here, ${\overline{h}}_i=1$ represents the Line-of-Sight (LoS) channel, while ${\tilde{h}}_i\sim \mathcal{C}\mathcal{N}\left(0,1\right)$ represents the Non-Line-of-Sight (NLoS) channel. The transmission power of the interference source is $p_j$. Therefore, the Signal-to-Interference-plus-Noise Ratio (SINR) of the UAV at the k-th time slot is given by

$${\xi }_n\left(k\right)={\displaystyle \frac{p_n{x}_n{\mu }_0{d}_n{\left(k\right)}^{-\alpha }}{{\displaystyle \sum _{j=0}^{J-1}}{x}_j{\mu }_0{d}_j{\left(k\right)}^{-\alpha }+{\sigma }^2}}$$

(6)

where $x_n$ follows a ${\chi }^2$ distribution. Therefore, using the homogeneous approximation method, the expected SINR is denoted as

$$\mathrm{E}\left[{\xi }_n\left(k\right)\right]={\displaystyle \frac{p_n{\beta }_n{d}_n{\left(k\right)}^{-\alpha }}{{\displaystyle \sum _{j=0}^{J-1}}{p}_j{\beta }_j{d}_j{\left(k\right)}^{-\alpha }+{\sigma }^2}}$$

(7)

where

$${\beta }_n={\int }_0^{\infty }{x}_{n}f\left(x_n\right){\mu }_{0}d{x}_n$$

(8)

$${\beta }_j=\underset{x_0,\cdots x_{J-1}}{{\int }_0^{\infty }\cdots }{\int }_0^{\infty }{x}_j{\mu }_0\prod _j^{J-1}f\left(x_j\right)d{x}_0\cdots d{x}_{J-1}$$

(9)

$$f\left(x\right)={\displaystyle \frac{\mathcal{A}+1}{\mathcal{P}}}exp\left(-\mathcal{A}-{\displaystyle \frac{\left(\mathcal{A}+1\right)x}{\mathcal{P}}}\right)I_0\left(2\sqrt{{\displaystyle \frac{\mathcal{A}\left(\mathcal{A}+1\right)x}{\mathcal{P}}}}\right)$$

(10)

where the signal model parameter $\mathcal{P}=1$, $I_0(·)$ is the zero-order Bessel function, ${\beta }_n$ and ${\beta }_j$ are independent and identically distributed constants generated by the Rician model, and ${\sigma }^2$ is the variance of the independent and identically distributed Gaussian white noise power. When the time slot is sufficiently small, the position of the UAV within each time slot can be approximated as a single point. Therefore, the expected information rate (bit/s) between the UAV and the reconnaissance node $S_n$ at the k-th time slot is given by

$$r_n\left(k\right)={\displaystyle \frac{B}{N}}{log}_2\left(1+\mathrm{E}\left[{\xi }_n\left(k\right)\right]\right)$$

(11)

where B is the communication bandwidth.

2.2. UAV Motion Model

The motion state of the UAV is represented by a vector group as $\mathbf{s}\left(k\right)\in \mathcal{S}$, which includes the three-dimensional coordinates, velocity, and acceleration of the UAV at each discrete time instant k, denoted as $\mathbf{s}\left(k\right)={\left[\mathbf{w}\left(k\right),\mathbf{v}\left(k\right),\mathbf{a}\left(k\right)\right]}^T$. Each discretized parameter in the state vector is recorded individually, forming the discrete states during the reconnaissance data collection period, denoted as $\mathbf{W}={\left[\mathbf{w}\left(1\right),\dots ,\mathbf{w}\left(K\right)\right]}^T$, $\mathbf{V}={\left[\mathbf{v}\left(1\right),\dots ,\mathbf{v}\left(K\right)\right]}^T$, $\mathbf{A}={\left[\mathbf{a}\left(1\right),\dots ,\mathbf{a}\left(K\right)\right]}^T$. The UAV flight control input, i.e., the derivative of acceleration, is denoted as $\mathbf{J}={\left[\mathbf{j}\left(1\right),\dots ,\mathbf{j}\left(K-1\right)\right]}^T$. The relationship between the UAV’s motion state and flight control input is expressed as follows:

$$\mathbf{w}\left(k+1\right)=\mathbf{w}\left(k\right)+\mathbf{v}\left(k\right)\delta +{\displaystyle \frac{1}{2}}·\mathbf{a}\left(k\right)·{\delta }^2+{\displaystyle \frac{1}{6}}·\mathbf{j}\left(k\right)·{\delta }^3,k=0,\cdots ,K-1$$

(12)

$$\mathbf{v}\left(k+1\right)=\mathbf{v}\left(k\right)+\mathbf{a}\left(k\right)\delta +{\displaystyle \frac{1}{2}}·\mathbf{j}\left(k\right)·{\delta }^2,k=0,\cdots ,K-1$$

(13)

$$\mathbf{a}\left(k+1\right)=\mathbf{a}\left(k\right)+\mathbf{j}\left(k\right)\delta ,k=0,\cdots ,K-1$$

(14)

This relationship is abbreviated as

$$\mathbf{W}={\mathbf{T}}_W·\mathbf{J}+{\mathbf{B}}_W$$

(15)

$$\mathbf{V}={\mathbf{T}}_V·\mathbf{J}+{\mathbf{B}}_V$$

(16)

$$\mathbf{A}={\mathbf{T}}_A·\mathbf{J}+{\mathbf{B}}_A$$

(17)

2.3. Path Optimization for Reconnaissance UAVs in Dynamic Scenarios

In practical reconnaissance missions, the positions of interference sources are often dynamically changing, and ground nodes may also need to relocate to acquire spatially distributed reconnaissance information or to evade detected security threats. Therefore, the UAV must assess their real-time positions and predict future locations during the path optimization process to achieve optimal data collection performance. The primary objective of the optimization problem is to ensure that the UAV, after taking off from the current waypoint, maintains stable and energy-efficient continuous flight while collecting a sufficient amount of reconnaissance data and reaching the destination waypoint in the shortest possible time. This process reduces the flight time between waypoints for UAVs operating in continuous flight mode, thereby enhancing the timeliness of reconnaissance data. It also takes into account the UAV’s motion characteristics, energy consumption, and safe flight considerations. To this end, the optimization objective is defined as follows:

$$\begin{array}{c}g\left(\mathbf{J}\right)=c_1{\mathbf{V}}^T\mathbf{V}+c_2{\mathbf{A}}^T\mathbf{A}+c_3{\mathbf{J}}^T\mathbf{J}\hfill \\ ={\mathbf{J}}^T\left(c_1{\mathbf{T}}_V^T{\mathbf{T}}_V+c_2{\mathbf{T}}_A^T{\mathbf{T}}_A+c_3\mathbf{I}\right)\mathbf{J}+2\left(c_1{\mathbf{B}}_V^T{\mathbf{T}}_V+c_2{\mathbf{B}}_A^T{\mathbf{T}}_A\right)\mathbf{J}+c_0\hfill \end{array}$$

(18)

The optimization of $g\left(\mathbf{J}\right)$ balances the timeliness of reconnaissance data and the energy consumption of the UAV while also improving the stability of data collection. In (18), $\mathbf{I}$ is the identity matrix, $c_1$, $c_2$, and $c_3$ are multiplicative coefficients, and $c_0=c_1{\mathbf{B}}_V^T{\mathbf{B}}_V+c_2{\mathbf{B}}_A^T{\mathbf{B}}_A$ is a constant. The maximum speed and maximum acceleration constraints for UAV flight are set and denoted as

$$-{\mathbf{V}}_{max}-{\mathbf{B}}_V\le {\mathbf{T}}_V\mathbf{J}\le {\mathbf{V}}_{max}-{\mathbf{B}}_V$$

(19)

$$-{\mathbf{A}}_{max}-{\mathbf{B}}_A\le {\mathbf{T}}_A\mathbf{J}\le {\mathbf{A}}_{max}-{\mathbf{B}}_A$$

(20)

where ${\mathbf{V}}_{max}=v_{max}·{\mathbf{I}}_{K\times 1}$ and ${\mathbf{A}}_{max}=a_{max}·{\mathbf{I}}_{K\times 1}$ represent the maximum speed and maximum acceleration values, respectively. Additionally, the flight altitude constraint for the UAV is set and expressed as

$${\mathbf{H}}_{min}-{\mathbf{B}}_{W_z}\le {\mathbf{T}}_W{\mathbf{J}}_z\le {\mathbf{H}}_{max}-{\mathbf{B}}_{W_z}$$

(21)

To set the starting point and destination point constraints for the UAV, this is expressed as

$$\mathbf{w}\left(0\right)={\mathbf{w}}_{\mathrm{start}},\mathbf{v}\left(0\right)={\mathbf{v}}_{\mathrm{start}},\mathbf{a}\left(0\right)={\mathbf{a}}_{\mathrm{start}}$$

(22)

$$\mathbf{w}\left(N\right)={\mathbf{w}}_{\mathrm{end}},\mathbf{v}\left(N\right)={\mathbf{v}}_{\mathrm{end}},\mathbf{a}\left(N\right)={\mathbf{a}}_{\mathrm{end}}$$

(23)

The UAV’s velocity at these positions is 0. The constraint for the amount of data uploaded by the ground reconnaissance node is denoted as

$$\sum _{k=1}^K{\zeta }_n^k{r}_n\left(k\right)\delta \ge Q_{min}^n,\forall n\in \mathcal{N}$$

(24)

The data transmission rate should satisfy the minimum transmission rate constraint required for demodulation. When the transmission rate falls below the minimum rate, demodulation will fail. This constraint is expressed as

$${\zeta }_n^k=\mathcal{I}\left\{max\left(r_n\left(k\right)-r_{min},0\right)\right\},\forall n\in \mathcal{N},\forall k\in \mathcal{K}$$

(25)

where the indicator function is defined as

$$\mathcal{I}\left(x\right)=\left\{\begin{array}{c}1,x>0\hfill \\ 0,x\le 0\hfill \end{array}\right.$$

(26)

We define the constraints for obstacles and no-fly zones as

$$\mathbf{W}\notin {\Omega }_{\mathrm{obstacles}}$$

(27)

Therefore, the optimization problem is described as

$$\begin{array}{c}\left(P1\right)\underset{\mathbf{J},K}{min}g\left(\mathbf{J}\right)\hfill \\ \mathrm{s}.\mathrm{t}.\left(5–15\right)\sim \left(5–17\right),\left(5–19\right)\sim \left(5–27\right)\hfill \end{array}$$

In (P1), the constraints are related to the number of discrete points in the path, making them implicit functions of the path, which significantly increases the difficulty of handling. On the other hand, constraints (24), (25), and the safety constraint (27) representing the avoidance of no-fly zones are all non-convex, leading to challenges in solving the optimization problem. To address this, slack variables are introduced to transform the original problem into a relaxed problem, and the SCA is then employed to compute the flight path.

3. Algorithm Design

The difficulty in solving (P1) lies in the uncertainty of the number of discrete path points; the non-convex constraints (24), (25), and (27); and the complexity of handling the indicator function in (26). Therefore, based on the discretization approach, the UAV path is divided into several connected straight-line segments, transforming the solution of (P1) into determining a set of path points that serve as the starting and ending points of each segment while optimizing the UAV’s motion state along these segments. The overall process is illustrated in Figure 2.

First, the perception module is utilized to construct an environmental map, determine the real-time positions of reconnaissance nodes and interference sources, and employ a Model Predictive Control (MPC) model to predict the location of ground nodes and interference sources. Under the premise of the minimum discrete time interval, a communication flight corridor for interference avoidance is established, and the discrete initial path of the UAV is computed. Then, the SCA is applied to calculate the global path to satisfy the various constraints in (P1). Finally, the path is transmitted to the flight control system to guide the UAV in executing the reconnaissance mission.

3.1. Reconnaissance Node and Interference Source Position Prediction

In constraint (24), due to the dynamic changes in the positions of reconnaissance nodes and interference sources, the MPC method is employed in advance for position prediction. The MPC method determines the optimal control input at each sampling time by solving an online optimization problem, thereby achieving optimal control of the system. This subsection models the motion of reconnaissance nodes and interference sources as a discrete-time dynamic system, uses this model to predict future positions, and performs path optimization based on these predictions.

The MPC method primarily involves using the current system state and a predictive model over a future time horizon at each sampling time to compute the optimal control sequence. The first control input in the sequence is then applied as the result. This process is repeated continuously, updating the estimated state with new measurements and recalculating the optimal control sequence. This predictive control approach effectively handles multi-variable, multi-constraint, and nonlinear problems and theoretically provides closed-loop optimization performance. When dealing with the positions of mobile reconnaissance nodes and interference sources, the UAV needs to continuously adjust its motion strategy based on the predicted positions. In this section, the position prediction is modeled as an unconstrained MPC problem, where the position of the n-th node is calculated as follows:

$${\mathbf{w}}_n=\mathbf{A}\mathbf{x}+\mathbf{B}\mathbf{u}$$

(28)

where $\mathbf{A}$ and $\mathbf{B}$ are known. Additionally, the optimization objective at time t is constructed as

$$J={\sum }_{\tau =t}^{\tau +\infty }x{\left(\tau \right)}^T\mathbf{Q}x\left(\tau \right)+u{\left(\tau \right)}^T\mathbf{R}u\left(\tau \right)$$

(29)

In practical reconnaissance missions, this problem adopts a finite observation time. Let the prediction horizon be K. Then, the above problem can be simplified as

$$J={\sum }_{\tau =t}^{\tau +K}x{\left(\tau \right)}^T\mathbf{Q}x\left(\tau \right)+u{\left(\tau \right)}^T\mathbf{R}u\left(\tau \right)$$

(30)

In cases where future states and inputs are unknown, it is necessary to predict the state values. Therefore, the objective is reformulated as

$$J={\sum }_{k=0}^{K}x{\left(t+k|t\right)}^T\mathbf{Q}x\left(t+k|t\right)+u{\left(t+k|t\right)}^T\mathbf{R}u\left(t+k|t\right)$$

(31)

where $x(t+k|t)$ and $u(t+k|t)$ are the predicted values of the state and input at time t for time $t+k$, denoted as $x\left(k\right|t)$ and $u\left(k\right|t)$, respectively. This yields the following form of the objective:

$$J={\sum }_{k=0}^{K}x{\left(k|t\right)}^T\mathbf{Q}x\left(k|t\right)+u{\left(k|t\right)}^T\mathbf{R}u\left(k|t\right)$$

(32)

At the same time, the future states and inputs satisfy the following relationship:

$$\mathbf{w}\left(k+1|t\right)=\mathbf{A}x\left(k|t\right)+\mathbf{B}u\left(k|t\right)$$

(33)

Thus, the final form of the objective is obtained as

$$\begin{array}{cc}\hfill & \underset{\mathbf{x},\mathbf{u}}{min}{\sum }_{k=0}^{K}x{\left(k|t\right)}^T\mathbf{Q}x\left(k|t\right)+u{\left(k|t\right)}^T\mathbf{R}u\left(k|t\right)\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.\left(a\right)\mathbf{w}\left(0|t\right)=\mathbf{w}\left(t\right)\hfill \\ \hfill & \left(b\right)\mathbf{w}\left(k+1|t\right)=\mathbf{A}x\left(k|t\right)+\mathbf{B}u\left(k|t\right)\hfill \end{array}$$

(34)

where $x={\left[\begin{array}{cccc}x\left(0|t\right)& x\left(1|t\right)& \dots & x\left(K|t\right)\end{array}\right]}^{\mathrm{T}}$, $u={\left[\begin{array}{cccc}u\left(0|t\right)& u\left(1|t\right)& \dots & u\left(K|t\right)\end{array}\right]}^{\mathrm{T}}$. The solution to this problem is relatively straightforward, and the resulting computational output provides a prediction of the future motion states. This prediction takes into account the system’s state deviations, changes in control inputs, and potential prediction errors.

3.2. Initial Path Generation

To address the complexity of (P1), a subproblem decomposition and relaxation approach is employed. Since the SCA is highly sensitive to initial values, a poor set of initial values may even lead to convergence difficulties. Therefore, this subsection proposes a method to quickly generate an initial path by constructing an interference-avoiding communication flight corridor, which meets the requirements of data collection and enables rapid replanning in dynamic interference environments. This approach also ensures the speed and reliability of the global path planning solution based on SCA. After obtaining the interference-avoiding communication flight corridor, a trapezoidal strategy is used to quickly acquire path points, and the minimum flight time of the UAV is calculated based on these points, thereby optimizing the timeliness of the reconnaissance data.

As shown in Figure 3, the starting point ${\mathbf{w}}_1$ of the current path and the ground reconnaissance node ${\mathbf{w}}_3$ are connected to generate the segment $l_{1,3}$. Similarly, ${\mathbf{w}}_3$ and the endpoint ${\mathbf{w}}_5$ are connected to generate the segment $l_{3,5}$. The intersection points of segments $l_{1,3}$ and $l_{3,5}$ with the interference-avoiding communication flight corridor are ${\mathbf{w}}_2$ and ${\mathbf{w}}_4$, respectively. The path points on segments $l_{1,2}$ and $l_{4,5}$ are generated using the trapezoidal velocity strategy, i.e., the UAV accelerates to its maximum speed as quickly as possible after departure, maintains a period of constant-speed flight, and then decelerates to zero speed as quickly as possible upon reaching the endpoint of the current path. This flight mode achieves the shortest flight time, thereby optimizing the timeliness of the reconnaissance data. Meanwhile, the path points on segments $l_{2,3}$ and $l_{3,4}$ are generated using a combination of the fastest flight strategy that meets the data collection requirements and the trapezoidal strategy.

Assume that the flight time for segment $l_{1,2}$ is $t_1$. According to the trapezoidal strategy, it can be divided into three parts, denoted as $t_1=t_{11}+t_{12}+t_{13}$, where $t_{11}$ represents the flight time for the UAV to accelerate from the starting point to its maximum speed, $t_{12}$ represents the flight time for the UAV to maintain constant-speed flight, and $t_{13}$ represents the flight time for the UAV to decelerate to zero speed and simultaneously reach the endpoint of the current path. Assume that the length of $l_{1,2}$ is $d_1$. Then, we have $t_{11}=v_{max}/\phantom{v_{max}{a}_{max}}{a}_{max}=t_{13}$ and $t_{12}=d_1/\phantom{d_1{v}_{max}}{v}_{max}-v_{max}/\phantom{v_{max}{a}_{max}}{a}_{max}$. From this, the number of discretized path points for $l_{1,2}$ can be derived as

$$K_{11}=\mathrm{round}\left({\displaystyle \frac{v_{max}}{a_{max}·\delta }}\right)=K_{13}$$

(35)

$$K_{12}=\mathrm{round}\left({\displaystyle \frac{d_1}{v_{max}·\delta }}-{\displaystyle \frac{v_{max}}{a_{max}·\delta }}\right)$$

(36)

$$K_1=K_{11}+K_{12}+K_{13}$$

(37)

Furthermore, the discretized path points are calculated and denoted as

$${\mathbf{w}}_1\left(k\right)=\left\{\begin{array}{c}{\mathbf{w}}_{\mathrm{init}}+\frac{1}{2}{a}_{max}{\left(k\delta \right)}^2,k=0,\cdots ,K_{11}-1\hfill \\ {\mathbf{w}}_1\left(K_{11}-1\right)+v_{max}k\delta ,k=K_{11},\cdots ,K_{12}+K_{11}-1\hfill \\ {\mathbf{w}}_1\left(K_{12}+K_{11}-1\right)+v_{max}k\delta \hfill \\ -\frac{1}{2}{a}_{max}{\left(k\delta \right)}^2,k=K_{12}+K_{11},\cdots ,K_{13}+K_{12}+K_{11}\hfill \end{array}\right.$$

(38)

On the other hand, for the path segments $l_{2,3}$ and $l_{3,4}$ within the interference-avoiding communication flight corridor, the UAV collects reconnaissance data at a fixed communication rate $r_{min}$. The collection times $t_2^{\prime }$ and $t_3^{\prime }$ satisfy the following relationship:

$$t_2^{\prime }+t_3^{\prime }={\displaystyle \frac{Q_{min}}{r_{min}}}$$

(39)

$$K_2^{\prime }+K_3^{\prime }={\displaystyle \frac{Q_{min}}{r_{min}\delta }}$$

(40)

Let the lengths of path segments $l_{2,3}$ and $l_{3,4}$ be $d_2$ and $d_3$, respectively. Then,

$$K_2^{\prime }={\displaystyle \frac{Q_{min}}{r_{min}·\delta }}·{\displaystyle \frac{d_2}{d_2+d_3}}$$

(41)

$$K_3^{\prime }={\displaystyle \frac{Q_{min}}{r_{min}·\delta }}·{\displaystyle \frac{d_3}{d_2+d_3}}$$

(42)

In practical terms, when the UAV completes data collection or the remaining data volume is small, excessively small discrete values may lead to planning failure. In such cases, the aforementioned planning strategy is no longer followed. Instead, the trapezoidal strategy is adopted to achieve the minimum UAV flight times $t_2^{″}$ and $t_3^{″}$, as well as the corresponding numbers of path points $K_2^{″}$ and $K_3^{″}$. After comprehensive consideration, the larger values from the two strategies are selected to ensure the existence and optimality of the solution, enabling the algorithm to converge correctly. These values are denoted as $t_2=max\left\{t_2^{\prime },t_2^{″}\right\}$, $t_3=max\left\{t_3^{\prime },t_3^{″}\right\}$, $K_2=max\left\{K_2^{\prime },K_2^{″}\right\}$, and $K_3=max\left\{K_3^{\prime },K_3^{″}\right\}$.

Subsequently, the points on the path segments are uniformly discretized to obtain

$${\mathbf{w}}_{\mathbf{2}}\left(k\right)=\left(1-{\displaystyle \frac{k}{K_2}}\right)·{\mathbf{w}}_{\mathbf{2}}+{\displaystyle \frac{k}{K_2}}·{\mathbf{w}}_{\mathbf{3}},k=1,\cdots ,K_2$$

(43)

$${\mathbf{w}}_{\mathbf{3}}\left(k\right)=\left(1-{\displaystyle \frac{k}{K_3}}\right)·{\mathbf{w}}_{\mathbf{3}}+{\displaystyle \frac{k}{K_3}}·{\mathbf{w}}_{\mathbf{4}}\left(K_3-1\right),k=1,\cdots ,K_3$$

(44)

In the same manner, the discretized path points for $l_{1,2}$ and $l_{4,5}$ are obtained, resulting in the complete UAV flight path, denoted as ${\mathbf{w}}_{\mathrm{CFC}}=\left\{{\mathbf{w}}_{\mathbf{1}},{\mathbf{w}}_{\mathbf{2}},{\mathbf{w}}_{\mathbf{3}},{\mathbf{w}}_{\mathbf{4}},{\mathbf{w}}_{\mathbf{5}}\right\}$. This algorithm is described in Algorithm 1.

Algorithm 1 generates a path that satisfies the data collection volume constraints with the minimum flight time. However, it is still necessary to avoid obstacles within the reconnaissance area. Algorithm 2 further describes the obstacle avoidance algorithm, detailing the specific steps.

Algorithm 1: Initial path generation algorithm for communication flight corridors with interference avoidance.

1. Input: Start point coordinates ${\mathbf{w}}_{\mathrm{init}}$ and end point coordinates ${\mathbf{w}}_{\mathrm{end}}$ of the path segment; predicted location of the reconnaissance node ${\mathbf{w}}_n$; location and signal strength of interference sources perceived by the UAV; reconnaissance data collection volume $Q_{\mathrm{current}}$; current position of the UAV ${\mathbf{w}}_{\mathrm{UAV}}$. 2. Calculation: Substitute the perceived interference source parameters into constraint (25) to obtain the communication flight corridor ${\Omega }_{\mathrm{CFC}}$ for interference avoidance. 3. Initialization: Set ${\mathbf{w}}_1$, ${\mathbf{w}}_2$, ${\mathbf{w}}_3$, ${\mathbf{w}}_4$, ${\mathbf{w}}_5$. 4.                        ${\mathbf{w}}_1={\mathbf{w}}_{\mathrm{start}}$; 5.                        ${\mathbf{w}}_2=l_{1,3}\cap {\Omega }_{\mathrm{CFC}}$; 6.                        ${\mathbf{w}}_3={\mathbf{w}}_n$; 7.                        ${\mathbf{w}}_4=l_{3,5}\cap {\Omega }_{\mathrm{CFC}}$; 8.                        ${\mathbf{w}}_5={\mathbf{w}}_{\mathrm{end}}$; 9. if  ${\mathbf{w}}_{\mathrm{UAV}}\notin {\Omega }_{\mathrm{CFC}}\&Q_{\mathrm{current}}<Q_{min}$ 10.    Calculate path segments $l_{1,2}$, $l_{2,3}$, $l_{3,4}$, $l_{4,5}$ and obtain the initial path point ${\mathbf{w}}_{\mathrm{CFC}}=\left\{{\mathbf{w}}_1,{\mathbf{w}}_2,{\mathbf{w}}_3,{\mathbf{w}}_4\right\}$. 11. else if  ${\mathbf{w}}_{\mathrm{UAV}}\in {\Omega }_{\mathrm{CFC}}\&{\mathbf{w}}_{\mathrm{CFC}}=\left\{{\mathbf{w}}_1,{\mathbf{w}}_2,{\mathbf{w}}_3,{\mathbf{w}}_4\right\}$ 12.    Calculate path segments $l_{2,3}$, $l_{3,4}$, $l_{4,5}$ and obtain the initial path point ${\mathbf{w}}_{\mathrm{CFC}}=\left\{{\mathbf{w}}_3,{\mathbf{w}}_4\right\}$. 13. else 14.    Calculate path segment $l_{4,5}$ and obtain the initial path point ${\mathbf{w}}_{\mathrm{CFC}}=\left\{{\mathbf{w}}_4\right\}$. 15. end if 16. Output: The initial path ${\mathbf{w}}_{\mathrm{CFC}}$.

3.3. SCA-Based Path Optimization

Based on the initial path described above, this subsection first addresses the non-convex constraints (24), (25), and (27) in (P1) by introducing auxiliary variables, resulting in a relaxed convex problem.

Lemma 1. 

In (24) and (25), by introducing the slack variable ${\kappa }_n\left(k\right)$, the problem can be transformed into the following equivalent form:

$$\sum _{k=1}^K{\kappa }_n\left(k\right)r_n\left(k\right)·\delta \ge Q_{min},\forall n\in \mathcal{N}$$

(45)

$${\kappa }_n\left(k\right)r_n\left(k\right)\ge {\kappa }_n\left(k\right)r_{min},\forall n\in \mathcal{N}$$

(46)

$${\kappa }_n\left(k\right)\in \left\{0,1\right\},\forall n\in \mathcal{N}$$

(47)

Proof. 

Constraint (46) indicates that when $r_n\left(k\right)<r_{min}$, ${\kappa }_n\left(k\right)$ must be 0 to hold, whereas when $r_n\left(k\right)>r_{min}$, ${\kappa }_n\left(k\right)$ can be either 1 or 0. Therefore, (45) and (46) imply that the UAV collects reconnaissance data while flying through the flight corridor that satisfy the communication demodulation threshold. Here, ${\kappa }_n\left(k\right)$ in (47) takes the same form as in (26), representing a binary integer indicator function.    □

Algorithm 2: Path correction for obstacles and no-fly zones.

1. Input: Path in communication flight corridor ${\mathbf{w}}_{\mathrm{CFC}}$; obstacle coordinates ${\mathbf{w}}_m$; safety distance $d_{\mathrm{safe}}$; search precision $\lambda$; 2. for  $i=1:\mathrm{size}\left({\mathbf{w}}_{\mathrm{CFC}}\right)-1$ 3.    Calculate the straight path segment between point ${\mathbf{w}}_{\mathrm{CFC}\left(i\right)}$ and point ${\mathbf{w}}_{\mathrm{CFC}(i+1)}$; 4.    $\mathbf{a}=\left[{\mathbf{w}}_{\mathrm{CFC}(i+1)}-{\mathbf{w}}_{\mathrm{CFC}\left(i\right)}\right]$; $\Lambda =\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$; 5.    for $m=1:M$ 6.       if ${\displaystyle \frac{\left|{\mathbf{a}}^T\Lambda {\mathbf{w}}_m-{\mathbf{a}}^T\Lambda {\mathbf{w}}_{\mathrm{CFC}\left(i\right)}\right|}{∥\mathbf{a}∥}}<d_{\mathrm{safe}}$ 7.          The perpendicular line ${\overline{l}}_{{\mathbf{w}}_{\mathrm{CFC}}\left(i\right),{\mathbf{w}}_m}$ to the connection between this risk point and ${\mathbf{w}}_m$ is calculated as ${\mathbf{a}}^T{\mathbf{w}}_m={\mathbf{a}}^T{\mathbf{w}}_{\mathrm{CFC}\left(i\right)}$; 8.          Search for a safe point ${\mathbf{w}}_{\mathrm{safe}}$ on this perpendicular line that satisfies the safety distance ${\mathbf{a}}_{\mathrm{safe}}=\left[{\mathbf{w}}_{\mathrm{safe}}-{\mathbf{w}}_{\mathrm{CFC}\left(i\right)}\right]$; 9.          while ${\displaystyle \frac{\left|{\mathbf{a}}_{\mathrm{safe}}^T\Lambda {\mathbf{w}}_m-{\mathbf{a}}_{safe}^T\Lambda {\mathbf{w}}_{\mathrm{safe}}\right|}{∥{\mathbf{a}}_{\mathrm{safe}}∥}}<d_{\mathrm{safe}}$ 10.             ${\mathbf{w}}_{\mathrm{safe}}={\mathbf{w}}_{\mathrm{safe}}-\lambda {\displaystyle \frac{{\mathbf{w}}_{\mathrm{safe}}-{\mathbf{w}}_{\mathrm{CFC}(i+1)}}{∥{\mathbf{w}}_{\mathrm{safe}}-{\mathbf{w}}_{\mathrm{CFC}(i+1)}∥}}$; ${\mathbf{a}}_{\mathrm{safe}}=\left[{\mathbf{w}}_{\mathrm{safe}}-{\mathbf{w}}_{\mathrm{CFC}\left(i\right)}\right]$ 11.          end while 12.          ${\mathbf{w}}_{\mathrm{CFC}(i+1)}={\mathbf{w}}_{\mathrm{safe}}$. 13.       end if 14.    end for 15. end for 16. Output: ${\mathbf{w}}_{\mathrm{CFC}}^{\mathrm{safe}}={\mathbf{w}}_{\mathrm{CFC}}$.

To further address the new non-convex constraints (45) and (46), new auxiliary variables $S_n\left(k\right)$ and $I_n\left(k\right)$ are introduced, resulting in

$$\sum _{k=1}^K{\kappa }_n\left(k\right){\tilde{r}}_n\left(k\right)\delta \ge Q_{min},\forall n\in \mathcal{N}$$

(48)

where $r_n\left(k\right)\ge {\tilde{r}}_n\left(k\right)=B·{log}_2\left(1+{\displaystyle \frac{S_n{\left(k\right)}^{-1}}{I_n\left(k\right)}}\right),\forall n\in \mathcal{N}$. The auxiliary variables $S_n\left(k\right)$ and $I_n\left(k\right)$ satisfy

$$S_n{\left(k\right)}^{-1}\le {\beta }_0{p}_0{d}_n^{-\alpha }\left(k\right),S_n\left(k\right)>0,\forall n\in \mathcal{N}$$

(49)

$$I_n\left(k\right)\ge \sum _j{\beta }_j{p}_j{d}_j{\left(k\right)}^{-\alpha }+{\sigma }^2,\forall n\in \mathcal{N}$$

(50)

The convex constraint (49) is rewritten as

$$d_n^{\alpha }\left(k\right)-{\beta }_0{p}_0{S}_n\left(k\right)\le 0,S_n\left(k\right)>0,\forall n\in \mathcal{N}$$

(51)

To further address the non-convex constraint (50), a first-order Taylor expansion is applied.

$$\begin{array}{c}{d_j}^{-\alpha }\left(k\right)={\left[{\left({\mathbf{w}}_x-{\mathbf{w}}_{jx}\right)}^2+{\left({\mathbf{w}}_y-{\mathbf{w}}_{jy}\right)}^2+{\left({\mathbf{w}}_z-{\mathbf{w}}_{jz}\right)}^2\right]}^{-\alpha /\phantom{\alpha 2}2}\hfill \\ \ge L_j^r{\left(k\right)}^{-\alpha /2}-\alpha L_j^r{\left(k\right)}^{-\alpha /2-1}\left[{\left({\mathbf{w}}^r-{\mathbf{w}}_j\right)}^T·\left(\mathbf{w}-{\mathbf{w}}^r\right)\right],\forall n\in \mathcal{N},\forall j\in \mathcal{J}\hfill \end{array}$$

(52)

where $L_j\left(k\right)={\left({\mathbf{w}}_x-{\mathbf{w}}_{jx}\right)}^2+{\left({\mathbf{w}}_y-{\mathbf{w}}_{jy}\right)}^2+{\left({\mathbf{w}}_z-{\mathbf{w}}_{jz}\right)}^2$. $L_j^r\left(k\right)$ and ${\mathbf{w}}^r$ are the benchmark values for the r-th iteration of the SCA. Substituting into constraint (52), another relaxed form of (50) is obtained, denoted as the new convex constraint (53).

$$I_n\left(k\right)\ge \sum _j{\beta }_j{p}_j\left(L_j^r{\left(k\right)}^{-\alpha /2}-A_j^r\left(k\right)\right)+{\sigma }^2,\forall n\in \mathcal{N},\forall j\in \mathcal{J}$$

(53)

$$A_j^r\left(k\right)=\alpha L_j^r{\left(k\right)}^{-\alpha /2-1}\left[{\left({\mathbf{w}}^r-{\mathbf{w}}_j\right)}^T\left(\mathbf{w}-{\mathbf{w}}^r\right)\right],\forall n\in \mathcal{N},\forall j\in \mathcal{J}$$

(54)

For constraint (48), an auxiliary variable $\epsilon \left(k\right)$ is further introduced, and its first-order Taylor expansion for values less than ${\tilde{r}}_n\left(k\right)$ is

$${\epsilon }_n\left(k\right)\le U_n^r\left(k\right)+V_n^r\left(k\right)\left(S_n\left(k\right)-S_n^r\left(k\right)\right)+W_n^r\left(k\right)\left(I_n\left(k\right)-I_n^r\left(k\right)\right),\forall n\in \mathcal{N}$$

(55)

where

$$U_n^r\left(k\right)=B·{log}_2\left(1+{\displaystyle \frac{1}{S_n^r\left(k\right)I_n^r\left(k\right)}}\right),\forall n\in \mathcal{N}$$

(56)

$$V_n^r\left(k\right)={\displaystyle \frac{-B·{log}_{2}e}{S_n^r\left(k\right)+S_n^r{\left(k\right)}^2{I}_n^r\left(k\right)}},\forall n\in \mathcal{N}$$

(57)

$$W_n^r\left(k\right)={\displaystyle \frac{-B·{log}_{2}e}{I_n^r\left(k\right)+I_n^r{\left(k\right)}^2{S}_n^r\left(k\right)}},\forall n\in \mathcal{N}$$

(58)

Thus, the relaxed form of Equation (48) is obtained.

$$\sum _{k=1}^K{\kappa }_n\left(k\right){\epsilon }_n\left(k\right)\delta \ge Q_{min},\forall n\in \mathcal{N}$$

(59)

Equation (59) remains a non-convex constraint. To address this, the indicator function is further relaxed, resulting in

$$0\le {\kappa }_n\left(k\right)\le 1,\forall n\in \mathcal{N}$$

(60)

$${\kappa }_n\left(k\right)\left({\kappa }_n\left(k\right)-1\right)\ge 0,\forall n\in \mathcal{N}$$

(61)

The relationship between ${\kappa }_n\left(k\right)$ and ${\epsilon }_n\left(k\right)$ is introduced as follows:

$${\kappa }_n\left(k\right){\epsilon }_n\left(k\right)={\displaystyle \frac{{\left({\kappa }_n\left(k\right)+{\epsilon }_n\left(k\right)\right)}^2-{\left({\kappa }_n\left(k\right)-{\epsilon }_n\left(k\right)\right)}^2}{4}},\forall n\in \mathcal{N}$$

(62)

Next, a first-order Taylor expansion is applied to (46), (59), and (61), yielding

$$H_n^r{\left(k\right)}^2-2H_n^r\left(k\right)\left({\kappa }_n\left(k\right)+{\epsilon }_n\left(k\right)\right)+{\left({\kappa }_n\left(k\right)-{\epsilon }_n\left(k\right)\right)}^2\ge 4{\kappa }_n\left(k\right)r_{min},\forall n\in \mathcal{N}$$

(63)

$$\sum _{k=1}^K\left[H_n^r{\left(k\right)}^2-2H_n^r\left(k\right)\left({\kappa }_n\left(k\right)+{\epsilon }_n\left(k\right)\right)+{\left({\kappa }_n\left(k\right)-{\epsilon }_n\left(k\right)\right)}^2\right]·\delta \ge 4Q_{min},\forall n\in \mathcal{N}$$

(64)

$$2{\kappa }_n^r\left(k\right){\kappa }_n\left(k\right)-{\kappa }_n\left(k\right)-{\kappa }_n^r{\left(k\right)}^2\ge 0,\forall n\in \mathcal{N}$$

(65)

where

$$H_n^r\left(k\right)=\left({\kappa }_n^r\left(k\right)+{\epsilon }_n^r\left(k\right)\right),\forall n\in \mathcal{N}$$

(66)

At this point, constraints (24) and (25) in (P1) have been equivalently transformed into convex constraints (63), (64), and (65). Next, the non-convex constraint (27) in (P1) is addressed. The obstacles within the reconnaissance mission area are modeled as cylindrical structures. The horizontal distance between the UAV and the center coordinates of the obstacles must be greater than the safety distance $d_{safe}$ or the UAV’s flight altitude must exceed the maximum height of the obstacles. This safety constraint is denoted as

$$∥{\mathbf{w}}_{xy}\left(k\right)-{\mathbf{w}}_{xy,m}∥\ge d_{safe},\forall m\in \mathcal{M}$$

(67)

or

$${\mathbf{w}}_z\left(k\right)\ge h_m+d_{safe},\forall m\in \mathcal{M}$$

(68)

where ${\mathbf{w}}_{xy}\left(k\right)$ represents the two-dimensional coordinates of the UAV projected onto the ground and ${\mathbf{w}}_z\left(k\right)$ is the UAV’s flight altitude. By introducing binary integer variables ${\lambda }_{xy,m}$ and ${\lambda }_{z,m}$, constraint (27) in (P1) can be equivalently expressed as

$$∥{\mathbf{w}}_{xy}\left(k\right)-{\mathbf{w}}_{xy,m}∥+C{\lambda }_{xy,m}\left(k\right)\ge d_{safe},\forall m\in \mathcal{M}$$

(69)

$${\mathbf{w}}_z\left(k\right)+C{\lambda }_{z,m}\left(k\right)\ge h_m+d_{safe},\forall m\in \mathcal{M}$$

(70)

$${\lambda }_{xy,m}\left(k\right)+{\lambda }_{z,m}\left(k\right)\le 1,\forall m\in \mathcal{M}$$

(71)

$${\lambda }_{xy,m}\left(k\right),{\lambda }_{z,m}\left(k\right)\in \left\{0,1\right\},\forall m\in \mathcal{M}$$

(72)

where C is a sufficiently large positive constant that ensures constraints (69) and (70) hold; Equation (71) ensures that at most one of ${\lambda }_{xy,m}\left(k\right)$ and ${\lambda }_{z,m}\left(k\right)$ is 1, meaning that at least one of constraints (69) and (70) does not hold. This constraint is further relaxed to obtain

$${\displaystyle \frac{{\left({\mathbf{w}}_{xy}^r\left(k\right)-{\mathbf{w}}_{xy,m}\right)}^T·\left({\mathbf{w}}_{xy}\left(k\right)-{\mathbf{w}}_{xy}^r\left(k\right)\right)}{A_m^r\left(k\right)}}\ge d_{safe}-C{\lambda }_{xy,m}\left(k\right)-A_m^r\left(k\right),\forall m\in \mathcal{M}$$

(73)

where

$$A_m^r\left(k\right)=∥{\mathbf{w}}_{xy}^r\left(k\right)-{\mathbf{w}}_{xy,m}∥,\forall m\in \mathcal{M}$$

(74)

The variables ${\lambda }_{xy,m}$ and ${\lambda }_{z,m}$ are relaxed and denoted as

$$0\le {\lambda }_{i,m}\left(k\right)\le 1,i\in \left\{xy,z\right\},\forall m\in \mathcal{M}$$

(75)

$${\lambda }_{i,m}\left(k\right)\left({\lambda }_{i,m}\left(k\right)-1\right)\ge 0,i\in \left\{xy,z\right\},\forall m\in \mathcal{M}$$

(76)

Continuing with the Taylor expansion of the non-convex constraint (76), we obtain

$$-{\lambda }_{i,m}^r{\left(k\right)}^2+2{\lambda }_{i,m}^r\left(k\right){\lambda }_{i,m}\left(k\right)-{\lambda }_{i,m}\left(k\right)\ge 0,i\in \left\{xy,z\right\},\forall m\in \mathcal{M}$$

(77)

where ${\lambda }_{i,m}^r\left(k\right)$ is the result of the r-th iteration of ${\lambda }_{i,m}\left(k\right)$. At this point, (P1) has been transformed into a convex problem, denoted as

$$\begin{array}{c}\left(\mathrm{P}2\right)\underset{\mathbf{J}}{min}g\left(\mathbf{J}\right)\hfill \\ \mathrm{s}.\mathrm{t}.\left(5–15\right)\sim \left(5–17\right),\left(5–19\right)\sim \left(5–23\right),\hfill \\ \left(5–63\right)\sim \left(5–65\right),\left(5–70\right),\left(5–73\right),\hfill \\ \left(5–75\right),\left(5–77\right)\hfill \end{array}$$

For the transformed convex problem (P2), standard convex optimization techniques or CVX (e.g., interior-point methods) are used to solve it, and the SCA iterative method is employed to compute the optimal solution. The path planned within the communication flight corridor is used as the initial solution for the algorithm, enabling rapid convergence to the optimal solution and avoiding the negative impact of poor initial values on the convergence speed and solution quality of SCA. The steps of this algorithm are outlined in Algorithm 3.

In this scenario, since the positions of ground reconnaissance nodes and interference sources change in real time, the UAV iteratively performs MPC position prediction for the nodes and interference sources, initial path planning within the communication flight corridor, and SCA-based path planning during its flight. This achieves real-time path optimization for the UAV. This optimization focuses on effective global path planning and is performed at a certain frequency during the UAV’s flight to guide its real-time navigation.

Algorithm 3: SCA path optimization based on the initial path in the communication flight corridor.

1. Input: Initial path in the interference-avoiding communication flight corridor ${\mathbf{w}}_{\mathrm{CFC}}^{\mathrm{safe}}$, minimum data collection volume $Q_n^{min}$, communication bandwidth B, minimum communication rate $r_{min}$, algorithm iteration count r, and maximum iteration count $Inte{r}_{max}$; 2. Initialization: Set $\omega \left(k\right),{\kappa }_n^r\left(k\right),{\epsilon }_n^r\left(k\right),{\lambda }_{i,m}^r\left(k\right),i\in \left\{xy,z\right\},\forall m\in \mathcal{M},\forall k\in \mathcal{K},\forall n\in \mathcal{N}$ 3. for  $r=1:Inte{r}_{max}$ 4.     Solve the optimal solution of (P2) using the CVX toolbox; 5.     ${\mathbf{w}}^{*}\left(k\right),{\kappa }_n^{*}\left(k\right),{\epsilon }_n^{*}\left(k\right),{\lambda }_n^{*}\left(k\right),i\in \left\{xy,z\right\},\forall m\in \mathcal{M},\forall k\in \mathcal{K},\forall n\in \mathcal{N}$; 6.     Update the reference values of optimization variables and slack variables: 7.     ${\mathbf{w}}^{r+1}\left(k\right)={\mathbf{w}}^{*}\left(k\right),\forall n\in \mathcal{N}$; 8.     ${\kappa }_n^{r+1}\left(k\right)={\kappa }_n^{*}\left(k\right),\forall k\in \mathcal{K},\forall n\in \mathcal{N}$; 9.     ${\epsilon }_n^{r+1}\left(k\right)={\epsilon }_n^{*}\left(k\right),\forall k\in \mathcal{K},\forall n\in \mathcal{N}$; 10.   ${\lambda }_{i,m}^{r+1}\left(k\right)={\lambda }_{i,m}^{*}\left(k\right),i\in \left\{xy,z\right\},\forall m\in \mathcal{M},\forall n\in \mathcal{N}$; 11. end for

The complete algorithm workflow shown in Algorithm 4 incorporates six critical constraints for UAV path planning: obstacle avoidance, velocity limits, starting/ending position requirements, state equations, and communication/data collection thresholds, with an overall computational complexity of $\mathcal{O}\left(R\left(5MK+12K+4NK\right)+2NM+NJ+K\right)$ where R, N, M, and K represent iteration count, ground nodes, obstacles, and time slots, respectively. This complexity arises from three core components: the initial CFC-based path optimization $\mathcal{O}\left(NJ\right)$, obstacle-adaptive refinement $\mathcal{O}\left(2NM\right)$, and iterative resolution $\mathcal{O}\left(R\left(5MK+12K+4NK\right)\right)$, collectively ensuring real-time performance while addressing all constraints in dynamic reconnaissance scenarios.

Algorithm 4: Real-time path optimization for data collection of mobile reconnaissance nodes in dynamic interference environments.

1. Initialization: UAV position ${\mathbf{w}}_{\mathrm{UAV}}$; 2. while  $∥{\mathbf{w}}_{\mathrm{UAV}}-{\mathbf{w}}_{\mathrm{end}}∥\le \xi$ 3.    Solve (34) to calculate the predicted positions of the reconnaissance node and the interference source; 4.    Use Algorithm 1 to compute the initial path ${\Omega }_{\mathrm{CFC}}$ in the communication flight corridor; 5.    Use Algorithm 2 to correct ${\Omega }_{\mathrm{CFC}}$ and compute a safe, collision-free initial path ${\Omega }_{\mathrm{CFC}}^{\mathrm{safe}}$; 6.    Use Algorithm 3 to compute the optimal flight path ${\Omega }^{*}$; 7.    Transmit the calculated path to the UAV flight controller and update the UAV position; 8. end while

4. Numerical Results

4.1. Parameter Settings

In this section, numerical results are presented to compare the proposed method with the A* algorithm and the Dynamic Window Approach (DWA). The simulations are conducted using MATLAB R2021a. The scenario involves moving interference sources and static obstacles within the reconnaissance area, where a UAV is dispatched to collect data from moving ground nodes in continuous flight mode. For the A* algorithm, a discrete path is first determined, and path points that satisfy the minimum communication rate requirement $r_{min}$ are identified from the path point set. The total data collection volume at these path points is calculated. If the volume requirement is not met, additional discrete points are inserted between these path points to supplement the path, ensuring it satisfies the data collection volume constraint. For DWA, two different heuristic functions are designed for the two stages of planning, including the stage before completing the data collection mission, denoted as

$$g\left(t\right)={\theta }_1\sum _{k=1}^{K}r\left(k\right)-{\theta }_2\sum _{k=0}^{K-1}{\left|\mathbf{u}\left(k\right)\right|}^2-{\theta }_3\sum _{k=0}^{K-1}{\left|\mathbf{v}\left(k\right)\right|}^2-{\theta }_4\sum _{k=0}^{K-1}{\left|\mathbf{w}\left(k\right)\right|}^2$$

(78)

and the stage after completing the data collection mission, denoted as

$$g\left(t\right)=\sum _{k=0}^{K-1}{\left|\mathbf{u}\left(k\right)\right|}^2-{\theta }_3\sum _{k=0}^{K-1}{\left|\mathbf{v}\left(k\right)\right|}^2-{\theta }_4\sum _{k=0}^{K-1}{\left|\mathbf{w}\left(k\right)\right|}^2$$

(79)

where $\mathbf{u}\left(k\right)$ represents the control variable, $\mathbf{v}\left(k\right)$ represents the velocity variable, $\mathbf{w}\left(k\right)$ represents the position variable, and $r\left(k\right)$ represents the normalized data collection volume. The terms ${\theta }_1$, ${\theta }_2$, ${\theta }_3$, and ${\theta }_4$ are weighting coefficients.

Table 1. Parameter settings.

Parameter	Value
Interference power $p_j$	$1000\mathrm{mW}$
Channel bandwidth B	$10\mathrm{kHz}$
Maximum flight speed $v_{max}$	$25\mathrm{m}/\phantom{\mathrm{m}\mathrm{s}}\mathrm{s}$
Maximum flight acceleration $a_{max}$	$5{\mathrm{m}/\phantom{\mathrm{m}\mathrm{s}}\mathrm{s}}^2$
Noise power spectral density $n_0$	$-169\mathrm{dBm}/\phantom{-169\mathrm{dBm}\mathrm{Hz}}\mathrm{Hz}$
Path loss factor $\alpha$	2
Minimum flight altitude $H_{min}$	$10\mathrm{m}$
Maximum flight altitude $H_{max}$	$200\mathrm{m}$
Carrier frequency $f_c$	$2\mathrm{GHz}$
Minimum communication rate $r_{min}$	$2.4\mathrm{kbps}$
Discrete time slot width $\delta$	$0.1\mathrm{s}$

shows the key parameter settings used in the simulation.

4.2. Result Analysis and Discussion

In this section, we conduct comparative experiments evaluating our proposed CFC-guided path optimization method against two benchmark approaches: an A*-initialized path planning algorithm and the DWA. The results systematically demonstrate the superior performance of our methodology in addressing the specified operational scenario, particularly in terms of the entire flight path of UAV.

As shown in Figure 4, the dashed lines in different colors represent optimizing results using different initialization methods: the red dashed line indicates the optimized path using the CFC initial path, the blue dashed line denotes the optimized path with the A* initial path, and the green dashed line represents the optimized path employing the DWA initial path. The light green area illustrates the effective communication range of ground reconnaissance nodes. When there is no interference in the reconnaissance area, this range appears circular in the top view; when two interference sources are present in the area, the range takes on a pear shape in the top view. The results demonstrate that all three schemes are effective in obstacle avoidance, with none of the optimized paths colliding with obstacles.

In Figure 4, the positions of the ground reconnaissance nodes and the interference source both vary over time, with the data collection volume being $200\mathrm{kbits}$. It can be observed that in a dynamic scenario, the communication range of the reconnaissance nodes, i.e., the central position and shape of the flight corridor for interference-avoidance communication, change over time.

Figure 5 illustrates the changes in the remaining data volume of the nodes during the reconnaissance data collection. When the communication power is $100\mathrm{mW}$, the SCA optimization strategy based on CFC initialization and the DWA optimization strategy can complete the task in approximately 50 s, while the optimization strategy based on A* initialization requires about 200 s. When the communication power is $200\mathrm{mW}$, all three optimization strategies can complete the data collection in around 60 s. When the communication power is $500\mathrm{mW}$, all three strategies can complete the data collection in approximately 50 s. This demonstrates that under low communication rates, the A*-initialized optimization path only considers spatial shortest paths and performs moderately in terms of data timeliness. However, under the other two communication power settings, the proposed algorithm can complete the reconnaissance data collection in a shorter time.

Figure 6 illustrates the variation in instantaneous communication rates, where the pink markers represent the communication rate threshold. It can be observed that compared to the benchmark algorithms, the proposed algorithm exhibits relatively stable fluctuations in communication rates, with concentrations occurring when the UAV is in close proximity to reconnaissance nodes. This demonstrates superior “tracking” performance for mobile reconnaissance nodes and offers more intuitive rationality.

Figure 7 presents a comparative visualization of UAV trajectories generated by the three optimization strategies. All methodologies successfully maintain continuous tracking of mobile reconnaissance nodes, as evidenced by their path convergence in the time–space diagram. The proposed algorithm exhibits smoother flight trajectories compared to the benchmark algorithms, enhancing compatibility with standard flight control systems. Conversely, the A*-guided approach exhibits pronounced waypoint discontinuity, while the DWA-optimized path, due to its higher redundancy for obstacle avoidance, requires longer flight times, which is less favorable for data timeliness.

Figure 8 compares the normalized energy consumption of the UAV, represented by the integral of acceleration. The results show that among the three optimization strategies, the DWA-optimized path consumes significantly more energy than the other two algorithms. Under higher communication power levels, the energy consumption of the A*-initialized optimization strategy is comparable to that of the proposed algorithm. However, under lower communication power levels, the proposed algorithm demonstrates notably lower energy consumption. Additionally, the computational complexity of the former is $\mathcal{O}\left(N{log}_{2}N\right)$, while the latter achieves a computational complexity of only $\mathcal{O}\left(NJ+2NM+K\right)$. These findings highlight the superior energy efficiency of the proposed algorithm in this scenario.

Figure 9 and Figure 10 compare the variations in UAV flight speed and altitude under different communication power levels. It can be observed that the proposed algorithm enables the UAV to fly toward the reconnaissance node at maximum power before reaching the CFC. Upon entering the CFC, the UAV gradually reduces its flight speed and altitude to approach the reconnaissance node, achieving stable tracking while collecting data. Finally, it follows a smooth flight trajectory to reach the destination. Compared to the benchmark algorithms, the proposed algorithm better aligns with the dynamic characteristics of rotor-wing UAVs. It not only achieves superior data timeliness but also demonstrates the highest feasibility for practical UAV system applications.

5. Conclusions

This paper investigates the path planning problem for UAVs assigned to collect data from mobile ground reconnaissance nodes in dynamic interference environments. The proposed methodology exhibits two inherent limitations: (1) pronounced dependence on sensor accuracy for localizing both interference sources and reconnaissance nodes, and (2) stringent requirements for precise detection of structured obstacles. Crucially, elevated sensing and positioning errors may induce significant deviations between optimized flight paths and theoretically optimal trajectories, potentially culminating in catastrophic UAV failures. These limitations define our immediate research priorities: first, validating the algorithm’s efficacy through live UAV trials under controlled real-world conditions; second, systematically quantifying its tolerance of perception uncertainties to establish rigorous practicality benchmarks for field deployment.