CKM-Driven Communication-Aware UAV Intelligent Trajectory Optimization for Urban Inspection

# CKM-Driven Communication-Aware UAV Intelligent Trajectory Optimization for Urban Inspection
Source: [https://arxiv.org/html/2606.24979](https://arxiv.org/html/2606.24979)
Xiaomeng Yang†, Ziye Jia†, Qiuming Zhu†and Qihui Wu† This work was supported by National Key R&D Program of China 2025YFF0514704\. \(Corresponding author: Ziye Jia\)

###### Abstract

Unmanned aerial vehicles \(UAVs\) are increasingly employed in urban inspection tasks, where reliable communication is critical but challenging due to the severe spatial channel heterogeneity\. To address the issue, in this paper, we focus on the communication\-aware path planning for multi\-UAV tasks, and propose a channel knowledge map \(CKM\)\-driven trajectory planning framework which integrates the channel modeling and trajectory decision\-making\. Specifically, we apply the diffusion model to construct a time\-accumulated CKM and achieve the accurate perception with low flight overhead, which leverages the sparse observation data to reconstruct the high\-fidelity global channel quality distribution\. Based on the CKM, we propose a global\-to\-local graph attention network soft actor\-critic algorithm\. The graph attention network optimizes the complex combinatorial node ordering problem, generating an optimal and communication\-aware sequence for the inspection targets\. Subsequently, the soft actor\-critic algorithm performs continuous action control to ensure the smoothness of the flight path and dynamically avoid communication attenuation areas\. Simulation results demonstrate that the proposed method effectively guides UAVs through high\-quality channel regions without dependence on real\-time channel feedback, significantly improving both the trajectory efficiency and communication reliability\.

## IIntroduction

THE unmanned aerial vehicle \(UAV\) has emerged as a flexible platform showing unique advantages in urban inspection tasks\[[1](https://arxiv.org/html/2606.24979#bib.bib1),[2](https://arxiv.org/html/2606.24979#bib.bib2)\]\. However, ensuring reliable air\-to\-ground communication during the task remains challenging, particularly in urban environments where dense buildings, street canyons, and dynamic blockages may cause severe path loss and rapid channel variations\[[3](https://arxiv.org/html/2606.24979#bib.bib3)\]\. Thus, it is crucial to perform communication\-aware path planning for urban inspection tasks\.

The conventional UAV path planning approaches typically optimize geometric metrics such as distance or energy consumption, while neglecting essential communication constraints or assuming simplified channel models\[[4](https://arxiv.org/html/2606.24979#bib.bib4)\]\. These assumptions fail to capture the complex spatial heterogeneity of wireless propagation, potentially leading UAVs to traverse regions with severely degraded communication quality\. To address this issue, increasing attention has been paid to the communication\- aware UAV path planning, where the knowledge of the radio environment is incorporated into trajectory design\. For instance,\[[5](https://arxiv.org/html/2606.24979#bib.bib5)\]preconstructs a signal to interference plus noise ratio \(SINR\) map to determine flyable space meeting a given SINR threshold\. Similarly,\[[6](https://arxiv.org/html/2606.24979#bib.bib6)\]achieves continuous control of the UAV during flight by constraining the communication rate to remain above the preset threshold\.\[[7](https://arxiv.org/html/2606.24979#bib.bib7)\]calculates the signal strength and SINR based on the path loss model and integrates them into the path planning of multi\-UAV networks\. Beyond static algorithms, reinforcement learning \(RL\)\-based and active sensing approaches have also been explored\. For example,\[[8](https://arxiv.org/html/2606.24979#bib.bib8)\]and\[[9](https://arxiv.org/html/2606.24979#bib.bib9)\]use deep Q\-networks and periodic environmental observations to jointly optimize the task completion rates and communication quality\. Furthermore, the UAV\-assisted channel mapping is gaining significant attention\. Notably, works such as\[[10](https://arxiv.org/html/2606.24979#bib.bib10)\]and\[[11](https://arxiv.org/html/2606.24979#bib.bib11)\]dynamically couple UAV trajectory planning with real\-time environmental perceptions to achieve autonomous, high\-precision three\-dimensional spatial spectrum mapping\. Despite these advancements, existing methods struggle to balance the environmental uncertainty and task complexity\. These methods typically rely on perfectly known channel models as passive constraints, or focus exclusively on map reconstruction while ignoring the sequential constraints of practical physical tasks\.

To this end, we consider introducing the channel knowledge map \(CKM\) to characterize the spatial distribution of received signal strength \(RSS\) during the inspection task\. However, constructing an accurate CKM in urban environments remains challenging due to the scarcity of spatio\-temporal channel measurement data, which hinders the practical communication\-aware planning\[[12](https://arxiv.org/html/2606.24979#bib.bib12),[13](https://arxiv.org/html/2606.24979#bib.bib13),[14](https://arxiv.org/html/2606.24979#bib.bib14)\]\. Therefore, we construct the diffusion\-enhanced time\-accumulated CKM, which yields a dense and stable channel representation without relying on extensive real\-time sensing infrastructure by aggregating RSS measurements over time\. Building upon the time\-accumulated CKM, a communication\-aware UAV path planning strategy, termed as Graph Attention Network Soft Actor\-Critic \(GATSAC\), is proposed to proactively avoid poor signal zones during urban inspection tasks\. In detail, we reformulate the multi\-target urban inspection issue as a traveling salesman problem \(TSP\) guided by graph attention network \(GAT\)\. The GAT effectively fuses spatial node features with CKM channel indicators, learning both local and global graph representations to infer an optimal visiting order that balances the flight duration and signal quality\. Subsequently, a soft actor\-critic \(SAC\)\-based trajectory planner is designed to ensure the smooth and communication\-efficient UAV trajectory based on the inferred sequence\.

The rest of this paper is arranged as follows\. Section[II](https://arxiv.org/html/2606.24979#S2)presents the system model and problem formulation\. In Section[III](https://arxiv.org/html/2606.24979#S3), we design the CKM\-driven path planning algorithm GATSAC\. In Section[IV](https://arxiv.org/html/2606.24979#S4), we conduct simulations and analyze the results\. Finally, Section[V](https://arxiv.org/html/2606.24979#S5)draws the conclusions\.

## IISystem Model and Problem Formulation

In this section, the network model for the multi\-UAV urban inspection scenario and the CKM model are presented, followed by the problem formulation\.

### II\-ANetwork Model

As shown in Fig\.[1](https://arxiv.org/html/2606.24979#S2.F1), we consider an urban UAV inspection scenario, whereMMUAVs must visitNNtarget nodes distributed across an operational area𝒜⊂ℝ2\\mathcal\{A\}\\subset\\mathbb\{R\}^\{2\}at a fixed altitudehh\. The UAVs and target nodes are denoted as𝒰=\{u1,…,uM\}\\mathcal\{U\}=\\\{u\_\{1\},\.\.\.,u\_\{M\}\\\}and𝒱=\{v1,…,vN\}\\mathcal\{V\}=\\\{v\_\{1\},\.\.\.,v\_\{N\}\\\}, respectively\.uiu\_\{i\}represents theii\-th UAV, andvjv\_\{j\}represents thejj\-th target node\. All UAVs are required to depart from and return to a depotv0v\_\{0\}\.

To enable the communication\-aware path planning, we construct the CKM to capture the RSS spatial distribution across𝒜\\mathcal\{A\}\. The CKM is leveraged to guide UAV trajectories toward regions with favorable channel conditions while minimizing the flight distance\. Considering the coordination complexity, the task nodes are clustered intoMMdistinct groups based on the initial positions of UAVs, establishing a one\-to\-one correspondence which is expressed as

𝒱=⋃m=1M𝒱𝐦,𝒱𝐦∩𝒱𝐧=∅,m≠n\.\\mathbf\{\\mathcal\{V\}\}=\\bigcup\_\{m=1\}^\{M\}\\mathbf\{\\mathcal\{V\}\_\{m\}\},\\quad\\mathbf\{\\mathcal\{V\}\_\{m\}\}\\cap\\mathbf\{\\mathcal\{V\}\_\{n\}\}=\\emptyset,m\\neq n\.\(1\)𝒱𝐦\\mathbf\{\\mathcal\{V\}\_\{m\}\}represents the target node cluster withNmN\_\{m\}waypoints of themm\-th UAV\. Each UAV independently serves one cluster, which transforms the multi\-UAV mission into multiple single\-UAV routing problems\. Without loss of generality, we focus on one representative UAVumu\_\{m\}with the cluster𝒱𝐦\\mathbf\{\\mathcal\{V\}\_\{m\}\}\.

### II\-BCKM Model

Considering that RSS is mainly determined by the large\-scale path loss, we assume that the CKM during flight can be regarded as quasi\-static\. To facilitate spatial representation, the area𝒜\\mathcal\{A\}is discretized into a uniform grid of sizeH×WH\\times W, whereHHandWWare determined by the physical dimensions and grid resolution\. The mapping from continuous coordinates\(x,y\)\(x,y\)to discrete indices is denoted as\(gx​\(x\),gy​\(y\)\)\(g\_\{x\}\(x\),g\_\{y\}\(y\)\), given by

gx​\(x\)=clip​\(⌊x−XminXmax−Xmin⋅\(H−1\)⌋,0,H−1\),g\_\{x\}\(x\)=\\mathrm\{clip\}\\left\(\\left\\lfloor\\frac\{x\-X\_\{\\min\}\}\{X\_\{\\max\}\-X\_\{\\min\}\}\\cdot\(H\-1\)\\right\\rfloor,0,H\-1\\right\),\(2\)and

gy​\(y\)=clip​\(⌊y−YminYmax−Ymin⋅\(W−1\)⌋,0,W−1\),g\_\{y\}\(y\)=\\mathrm\{clip\}\\left\(\\left\\lfloor\\frac\{y\-Y\_\{\\min\}\}\{Y\_\{\\max\}\-Y\_\{\\min\}\}\\cdot\(W\-1\)\\right\\rfloor,0,W\-1\\right\),\(3\)whereXminX\_\{\\min\},XmaxX\_\{\\max\},YminY\_\{\\min\}andYmaxY\_\{\\max\}represent the spatial boundaries of the target area𝒜\\mathcal\{A\}, and⌊⋅⌋\\lfloor\\cdot\\rfloorindicates the floor operation\. The clip functions \([2](https://arxiv.org/html/2606.24979#S2.E2)\) and \([3](https://arxiv.org/html/2606.24979#S2.E3)\) restrict the resulting indices within the valid grid dimensions to prevent out\-of\-bound errors, and then each cell stores a channel quality indicator\. In addition, the RSS is used as the channel quality metric, i\.e\.,

𝒦​\(gx,gy\)≜RSS​\(gx,gy\)\.\\mathcal\{K\}\(g\_\{x\},g\_\{y\}\)\\triangleq\\text\{RSS\}\(g\_\{x\},g\_\{y\}\)\.\(4\)With the quasi\-static assumption, RSS samples are accumulated over time to form a fully observed CKM, which serves as the complete CKM for training\. Then, the model is trained to learn the conditional distribution of the complete CKM under sparse measurements, enabling the full CKM reconstruction\.

![Refer to caption](https://arxiv.org/html/2606.24979v1/scene3.png)Figure 1:Multi\-UAV urban inspection scenario\. The trajectory is generated based on the constructed CKM\.
### II\-CProblem Formulation

To achieve efficient urban inspection with guaranteed communication quality, we formulate the trajectory optimization problem𝒫​0\\mathscr\{P\}0over the continuous trajectory𝐩m​\(t\)\\mathbf\{p\}\_\{m\}\(t\)of UAVumu\_\{m\}withNmN\_\{m\}nodes in cluster𝒱m\\mathcal\{V\}\_\{m\}\. For notational brevity, the spatial channel quality at the continuous UAV position is mapped to the discrete grid indices, which is defined as

𝒦​\(𝐩m​\(t\)\)≜𝒦​\(gx​\(px,m​\(t\)\),gy​\(py,m​\(t\)\)\),\\mathcal\{K\}\(\\mathbf\{p\}\_\{m\}\(t\)\)\\triangleq\\mathcal\{K\}\\big\(g\_\{x\}\(p\_\{x,m\}\(t\)\),\\,g\_\{y\}\(p\_\{y,m\}\(t\)\)\\big\),\(5\)where\(px,m​\(t\),py,m​\(t\)\)\(p\_\{x,m\}\(t\),p\_\{y,m\}\(t\)\)is the instantaneous spatial coordinate of the UAVumu\_\{m\}at timett\. Besides, the UAV follows a second\-order kinematic model during flight, where𝐩˙m​\(t\)=𝝃m​\(t\)\\dot\{\\mathbf\{p\}\}\_\{m\}\(t\)=\\bm\{\\xi\}\_\{m\}\(t\)and𝝃˙m​\(t\)=𝐚m​\(t\)\\dot\{\\bm\{\\xi\}\}\_\{m\}\(t\)=\\mathbf\{a\}\_\{m\}\(t\), with\(˙\)\(\\dot\{\\ \}\)denoting time derivative\.𝝃m​\(t\)\\bm\{\\xi\}\_\{m\}\(t\)and𝐚m​\(t\)\\mathbf\{a\}\_\{m\}\(t\)are the velocity and acceleration vectors of UAVumu\_\{m\}, respectively\. In addition, to avoid nested minimization in the objective function, an auxiliary variableqmq\_\{m\}is introduced to represent the worst communication quality along the trajectory\. The optimization problem is formulated as

𝒫​0:\\displaystyle\\mathscr\{P\}0:\\quadmin𝐩m​\(t\),qm​∫0Tm‖𝝃m​\(t\)‖​𝑑t−λ​qm\\displaystyle\\min\_\{\\mathbf\{p\}\_\{m\}\(t\),\\,q\_\{m\}\}\\;\\int\_\{0\}^\{T\_\{m\}\}\\\|\\bm\{\\xi\}\_\{m\}\(t\)\\\|\\,dt\-\\lambda q\_\{m\}\(6a\)s\.t\.‖𝐩m​\(tk\)−𝐩vk‖≤r,k=1,…,Nm,\\displaystyle\\\|\\mathbf\{p\}\_\{m\}\(t\_\{k\}\)\-\\mathbf\{p\}\_\{v\_\{k\}\}\\\|\\leq r,\\quad k=1,\\ldots,N\_\{m\},\(6b\)𝒦​\(𝐩m​\(t\)\)≥qm,∀t∈\[0,Tm\],\\displaystyle\\mathcal\{K\}\(\\mathbf\{p\}\_\{m\}\(t\)\)\\geq q\_\{m\},\\quad\\forall t\\in\[0,T\_\{m\}\],\(6c\)‖𝝃m​\(t\)‖≤ξmax,∀t∈\[0,Tm\],\\displaystyle\\\|\\bm\{\\xi\}\_\{m\}\(t\)\\\|\\leq\\xi\_\{\\max\},\\quad\\forall t\\in\[0,T\_\{m\}\],\(6d\)‖𝐚m​\(t\)‖≤amax,∀t∈\[0,Tm\],\\displaystyle\\\|\\mathbf\{a\}\_\{m\}\(t\)\\\|\\leq a\_\{\\max\},\\quad\\forall t\\in\[0,T\_\{m\}\],\(6e\)𝝃m​\(0\)=𝝃m​\(Tm\)=𝟎,\\displaystyle\\bm\{\\xi\}\_\{m\}\(0\)=\\bm\{\\xi\}\_\{m\}\(T\_\{m\}\)=\\mathbf\{0\},\(6f\)𝐩m​\(0\)=𝐩m​\(Tm\)=𝐩vm,0,\\displaystyle\\mathbf\{p\}\_\{m\}\(0\)=\\mathbf\{p\}\_\{m\}\(T\_\{m\}\)=\\mathbf\{p\}\_\{v\_\{m,0\}\},\(6g\)𝒦min≤qm≤𝒦max,\\displaystyle\\mathcal\{K\}\_\{\\mathrm\{min\}\}\\leq q\_\{m\}\\leq\\mathcal\{K\}\_\{\\mathrm\{max\}\},\(6h\)0≤tk≤Tm,k=1,…,Nm,\\displaystyle 0\\leq t\_\{k\}\\leq T\_\{m\},\\quad k=1,\\ldots,N\_\{m\},\(6i\)𝐩m​\(t\)∈𝒜,∀t∈\[0,Tm\]\.\\displaystyle\\mathbf\{p\}\_\{m\}\(t\)\\in\\mathcal\{A\},\\quad\\forall t\\in\[0,T\_\{m\}\]\.\(6j\)The objective function minimizes the total flight path length∫0Tm‖𝝃m​\(t\)‖​𝑑t\\int\_\{0\}^\{T\_\{m\}\}\\\|\\bm\{\\xi\}\_\{m\}\(t\)\\\|dtwhile maximizing the communication qualityqmq\_\{m\}, whereTmT\_\{m\}represents the total task time, andλ\>0\\lambda\>0balances the flight efficiency and communication reliability\. Constraint \([6b](https://arxiv.org/html/2606.24979#S2.E6.2)\) ensures that the UAV passes within capture radiusrrof each waypoint𝐩vk\\mathbf\{p\}\_\{v\_\{k\}\}at timetkt\_\{k\}\. In detail,𝐩vk\\mathbf\{p\}\_\{v\_\{k\}\}is the position of the waypointvkv\_\{k\}in cluster𝒱m\\mathcal\{V\}\_\{m\}, andtkt\_\{k\}is the arrival time in continuous trajectory𝐩m​\(t\)\\mathbf\{p\}\_\{m\}\(t\)atvkv\_\{k\}\. Constraint \([6c](https://arxiv.org/html/2606.24979#S2.E6.3)\) requires that the RSS value𝒦​\(𝐩m​\(t\)\)\\mathcal\{K\}\(\\mathbf\{p\}\_\{m\}\(t\)\)along the entire trajectory remains no less thanqmq\_\{m\}, for all timest∈\[0,Tm\]t\\in\[0,T\_\{m\}\], thereby imposingqmq\_\{m\}as a global lower bound on the communication quality throughout the flight\. Constraints \([6d](https://arxiv.org/html/2606.24979#S2.E6.4)\) and \([6e](https://arxiv.org/html/2606.24979#S2.E6.5)\) impose speed and acceleration limits, bounding the first and second derivatives of𝐩m​\(t\)\\mathbf\{p\}\_\{m\}\(t\), respectively\. Constraint \([6f](https://arxiv.org/html/2606.24979#S2.E6.6)\) enforces zero velocity at departure and return, and constraint \([6g](https://arxiv.org/html/2606.24979#S2.E6.7)\) requires the UAV to return to the depot𝐩vm,0\\mathbf\{p\}\_\{v\_\{m,0\}\}\. In constraint \([6h](https://arxiv.org/html/2606.24979#S2.E6.8)\),qmq\_\{m\}is restricted within the interval\[𝒦min,𝒦max\]\[\\mathcal\{K\}\_\{\\mathrm\{min\}\},\\mathcal\{K\}\_\{\\mathrm\{max\}\}\], where𝒦min\\mathcal\{K\}\_\{\\mathrm\{min\}\}and𝒦max\\mathcal\{K\}\_\{\\mathrm\{max\}\}represent the minimum and maximum RSS values stored in the CKM, respectively\. Constraint \([6i](https://arxiv.org/html/2606.24979#S2.E6.9)\) enforces that the arrival time of each waypoint is within the horizon\[0,Tm\]\[0,T\_\{m\}\]\. Constraint \([6j](https://arxiv.org/html/2606.24979#S2.E6.10)\) confines the trajectory within the operational area𝒜\\mathcal\{A\}\.

𝒫​0\\mathscr\{P\}0is challenging to solve due to the non\-differentiable CKM, nonconvex coverage constraints, and continuous kinematic constraints\. Accordingly, we propose the CKM\-driven GATSAC algorithm, which decomposes the problem into a discrete waypoint ordering stage and a continuous trajectory optimization stage solved in sequence\.

## IIIAlgorithm Design

In this section, we present the CKM\-driven GATSAC framework for communication\-aware urban inspection, as illustrated in Fig\.[2](https://arxiv.org/html/2606.24979#S3.F2)\. We firstly present the construction of a complete CKM via a diffusion\-based generative model\. Then, we divide task\-level path planning problem into two layers, which jointly addresses the communication\-aware node ordering and continuous trajectory planning\. In detail, a graph\-based model firstly serves as the upper layer to determine the communication\-aware visiting sequence of task nodes\. Then, a continuous trajectory planner generates feasible UAV paths between consecutive nodes while avoiding regions with poor channel quality\. The overall framework enables efficient and communication\-aware urban UAV inspection tasks, detailed in Algorithm[1](https://arxiv.org/html/2606.24979#alg1)\.

![Refer to caption](https://arxiv.org/html/2606.24979v1/framework2.png)Figure 2:The overall framework of CKM\-driven GATSAC algorithm\.### III\-ATime\-Accumulated CKM Construction

The CKM serves as the fundamental information layer that supports communication\-aware trajectory planning\.

#### III\-A1Temporal Accumulation under Quasi\-Static Assumption

Exploiting the assumption of urban propagation quasi\-static nature, RSS measurements across sequential episodes can be regarded as a sampling accumulation dimension and aggregated to form progressively denser spatial maps\. Specifically, we useδrt​\(i,j\)≜𝕀​\[\(i,j\)=\(gx​\(t,r\),gy​\(t,r\)\)\]\\delta\_\{r\}^\{t\}\(i,j\)\\triangleq\\mathbb\{I\}\\bigl\[\(i,j\)=\(g\_\{x\}\(t,r\),\\,g\_\{y\}\(t,r\)\)\\bigr\]to denote whether the channel measurements of receiverrrmapping to grid cell\(i,j\)\(i,j\)at time stepttare available\. The accumulated signal sum and measurement count are updated via

𝐒t​\(i,j\)=𝐒t−1​\(i,j\)\+∑r∈ℛtRt,r⋅δrt​\(i,j\),\\mathbf\{S\}\_\{t\}\(i,j\)=\\mathbf\{S\}\_\{t\-1\}\(i,j\)\+\\sum\_\{r\\in\\mathcal\{R\}\_\{t\}\}\\mathrm\{R\}\_\{t,r\}\\cdot\\delta\_\{r\}^\{t\}\(i,j\),\(7\)and

𝐂t​\(i,j\)=𝐂t−1​\(i,j\)\+∑r∈ℛtδrt​\(i,j\),\\mathbf\{C\}\_\{t\}\(i,j\)=\\mathbf\{C\}\_\{t\-1\}\(i,j\)\+\\sum\_\{r\\in\\mathcal\{R\}\_\{t\}\}\\delta\_\{r\}^\{t\}\(i,j\),\(8\)where𝐒t​\(i,j\)\\mathbf\{S\}\_\{t\}\(i,j\)and𝐂t​\(i,j\)\\mathbf\{C\}\_\{t\}\(i,j\)denote the accumulated signal sum and measurement count at grid\(i,j\)\(i,j\),ℛt\\mathcal\{R\}\_\{t\}is the receiver set, andRt,r\\mathrm\{R\}\_\{t,r\}is the RSS value of receiverrrat time steptt\. An observation mask𝐌t​\(i,j\)=𝕀​\[𝐂t​\(i,j\)\>0\]\\mathbf\{M\}\_\{t\}\(i,j\)=\\mathbb\{I\}\\left\[\\mathbf\{C\}\_\{t\}\(i,j\)\>0\\right\]is defined to indicate the measured cells\. Then, the accumulated CKM at time stepttcan be expressed as

𝐊traw​\(i,j\)=\{𝐒t​\(i,j\)𝐂t​\(i,j\),if​𝐌t​\(i,j\)=1,0,otherwise,\\mathbf\{K\}\_\{t\}^\{\\mathrm\{raw\}\}\(i,j\)=\\begin\{cases\}\\frac\{\\mathbf\{S\}\_\{t\}\(i,j\)\}\{\\mathbf\{C\}\_\{t\}\(i,j\)\},&\\mathrm\{if~\}\\mathbf\{M\}\_\{t\}\(i,j\)=1,\\\\ 0,&\\text\{otherwise\},\\end\{cases\}\(9\)where𝐊traw​\(i,j\)\\mathbf\{K\}\_\{t\}^\{\\mathrm\{raw\}\}\(i,j\)depicts the average sparse measurement value of grid\(i,j\)\(i,j\)at time steptt\. RSS samples collected over multiple time steps are projected onto a unified spatial grid, forming a sparse CKM as

𝐊accum​\(i,j\)=𝐊traw​\(i,j\),\\mathbf\{K\}\_\{\\mathrm\{accum\}\}\(i,j\)=\\mathbf\{K\}\_\{t\}^\{\\mathrm\{raw\}\}\(i,j\),\(10\)where the observed grid cells are masked as a matrix, expressed as𝐊accum\\mathbf\{K\}\_\{\\mathrm\{accum\}\}, and𝐊accum​\(i,j\)\\mathbf\{K\}\_\{\\mathrm\{accum\}\}\(i,j\)represents the value of the grid\(i,j\)\(i,j\)in the accumulated CKM\. After sufficient accumulation, certain scenes achieve full coverage, yielding complete maps that serve as ground truth for model training\.

#### III\-A2Diffusion\-Based CKM Generation

While the time accumulation densifies the CKM, practical missions must plan trajectories based on the sparse observations from limited flight time, which typically cover only a small portion of the operational area\. To enable reliable planning from such sparse data, we train a diffusion model on historical dense CKMs to learn the spatial propagation patterns\.

Given the time\-accumulated CKM as ground truth, represented as𝐊0=𝐊accum\\mathbf\{K\}\_\{0\}=\\mathbf\{K\}\_\{\\mathrm\{accum\}\}, we simulate sparse observations by randomly sampling to form training pairs, denoted as\(𝐊sparse,𝐌\)\(\\mathbf\{K\}\_\{\\text\{sparse\}\},\\mathbf\{M\}\)\.𝐊sparse\\mathbf\{K\}\_\{\\text\{sparse\}\}is the sparse observations, and𝐌∈\{0,1\}H×W\\mathbf\{M\}\\in\\\{0,1\\\}^\{H\\times W\}is the observation mask\. The forward diffusion process gradually adds Gaussian noise to𝐊0\\mathbf\{K\}\_\{0\}overTTsteps, i\.e\.,

𝐊t=α¯t​𝐊0\+1−α¯t​ϵ,ϵ∼𝒩​\(0,𝐈\),\\mathbf\{K\}\_\{t\}=\\sqrt\{\\bar\{\\alpha\}\_\{t\}\}\\mathbf\{K\}\_\{0\}\+\\sqrt\{1\-\\bar\{\\alpha\}\_\{t\}\}\\bm\{\\epsilon\},\\bm\{\\epsilon\}\\sim\\mathcal\{N\}\(0,\\mathbf\{I\}\),\(11\)whereα¯t\\bar\{\\alpha\}\_\{t\}controls the noise level at diffusion steptt\. Then, a UNet\-based denoising networkϵθ\\epsilon\_\{\\theta\}learns to predict the noise component conditioned on sparse observations, which is detailed as

ϵθ=fθ​\(𝐊t,t,𝐊sparse,𝐌\)\.\\epsilon\_\{\\theta\}=f\_\{\\theta\}\(\\mathbf\{K\}\_\{t\},t,\\mathbf\{K\}\_\{\\text\{sparse\}\},\\mathbf\{M\}\)\.\(12\)During the inference, the reverse process iteratively denoises from𝐊T∼𝒩​\(0,𝐈\)\\mathbf\{K\}\_\{T\}\\sim\\mathcal\{N\}\(0,\\mathbf\{I\}\)to𝐊0\\mathbf\{K\}\_\{0\}\. The observed radio measurements are strictly preserved by replacing𝐊t\\mathbf\{K\}\_\{t\}at each denoising step as

𝐊t←𝐊t⊙\(1−𝐌t\)\+𝐊sparse⊙𝐌t,\\mathbf\{K\}\_\{t\}\\leftarrow\\mathbf\{K\}\_\{t\}\\odot\(1\-\\mathbf\{M\}\_\{t\}\)\+\\mathbf\{K\}\_\{\\text\{sparse\}\}\\odot\\mathbf\{M\}\_\{t\},\(13\)where𝐌t\\mathbf\{M\}\_\{t\}denotes the mask signal which take the value of 1 in grid with sparse observation, and 0 otherwise\. The training objective minimizes the noise prediction error as

ℒ=𝔼t,𝐊0,ϵ​\[\|ϵ−ϵθ​\(𝐊t,t,𝐊sparse,𝐌\)\|2\]\.\\mathcal\{L\}=\\mathbb\{E\}\_\{t,\{\\mathbf\{K\}\_\{0\}\},\\bm\{\\epsilon\}\}\\left\[\|\\bm\{\\epsilon\}\-\\epsilon\_\{\\theta\}\(\\mathbf\{K\}\_\{t\},t,\\mathbf\{K\}\_\{\\text\{sparse\}\},\\mathbf\{M\}\)\|^\{2\}\\right\]\.\(14\)

### III\-BGraph\-Based TSP Solver

We employ the GAT to better aggregate the channel state and the spatial information of target nodes and 3\-opt\[[15](https://arxiv.org/html/2606.24979#bib.bib15)\]to dynamically adjust the node order in the TSP problem\. Firstly, we combine the information of nodes and edges to construct the graph\. For a single UAV assigned with task nodes set𝒱\\mathcal\{V\}, we construct a complete graph as

𝒢=\(𝒱∪\{v0\},ℰ\),\\mathcal\{G\}=\(\\mathcal\{V\}\\cup\\\{v\_\{0\}\\\},\\mathcal\{E\}\),\(15\)wherev0v\_\{0\}is the initial position of the UAV, andℰ\\mathcal\{E\}contains all pairwise edges\. Additionally, the feature vector of each nodevi∈𝒱v\_\{i\}\\in\\mathcal\{V\}is defined as𝐱i=\[xi,yi,ki\]\\mathbf\{x\}\_\{i\}=\[x\_\{i\},y\_\{i\},k\_\{i\}\], consisting of spatial coordinates\(xi,yi\)\(x\_\{i\},y\_\{i\}\)and the corresponding RSS valuekik\_\{i\}extracted from the CKM\. The edge feature between nodesviv\_\{i\}andvjv\_\{j\}consists of the Euclidean distance and the minimum channel qualityki​jk\_\{ij\}along the straight\-line path between the two nodes\. Then, GAT is employed to aggregate the node and edge information and learn expressive node embeddings, depicted as

𝐡i=GAT​\(𝐱i,\{𝐱j,𝐞i​j\}j∈𝒩​\(i\)\),\\mathbf\{h\}\_\{i\}=\\mathrm\{GAT\}\(\\mathbf\{x\}\_\{i\},\\\{\\mathbf\{x\}\_\{j\},\\mathbf\{e\}\_\{ij\}\\\}\_\{j\\in\\mathcal\{N\}\(i\)\}\),\(16\)where𝐱j\\mathbf\{x\}\_\{j\}and𝐞i​j\\mathbf\{e\}\_\{ij\}represent the nodes and edges in the graph structure, respectively\. Through iterative message passing, GAT captures both geometric relationships and communication\-aware interactions among task nodes\. Based on the learned node embeddings, a decoding module generates a visiting sequenceπ0\\pi\_\{0\}that starts and ends at the depotv0v\_\{0\}\. The decoding process is implemented using the attention\-based selection strategy\.

Algorithm 1CKM\-Driven GATSAC for UAV Urban Inspection0:Target nodes

𝒱=\{v1,…,vN\}\\mathcal\{V\}=\\\{v\_\{1\},\\ldots,v\_\{N\}\\\}, depot

v0v\_\{0\}, dense CKM

𝐊CKM\\mathbf\{K\}^\{\\text\{CKM\}\}, trained GAT

ϕ∗\\phi^\{\*\}, and trained SAC policy

πθ∗\\pi\_\{\\theta\}^\{\*\}\.

0:UAV trajectory

𝐩​\(t\)\\mathbf\{p\}\(t\)for all UAVs\.

1:Partition

𝒱\\mathcal\{V\}into

MMclusters

\{𝒱1,…,𝒱M\}\\\{\\mathcal\{V\}\_\{1\},\\ldots,\\mathcal\{V\}\_\{M\}\\\}of

NmN\_\{m\}waypoints via K\-means clustering\.

2:foreach UAV

umu\_\{m\}with assigned cluster

𝒱m\\mathcal\{V\}\_\{m\}do

3:Construct graph

𝒢m=\(𝒱m∪\{v0\},ℰm\)\\mathcal\{G\}\_\{m\}=\(\\mathcal\{V\}\_\{m\}\\cup\\\{v\_\{0\}\\\},\\mathcal\{E\}\_\{m\}\)\.

4:Extract node features

𝐱i=\[xi,yi,ki\]\\mathbf\{x\}\_\{i\}=\[x\_\{i\},y\_\{i\},k\_\{i\}\]and edge features

\[di​j,ki​j\]\[d\_\{ij\},k\_\{ij\}\]from

𝐊CKM\\mathbf\{K\}^\{\\text\{CKM\}\}\.

5:Compute node embeddings according to \([16](https://arxiv.org/html/2606.24979#S3.E16)\)\.

6:Decode initial visiting sequence

πm,0\\pi\_\{m,0\}via attention\-based selection\.

7:Refine

πm,0\\pi\_\{m,0\}with 3\-opt and obtain

πm∗\\pi\_\{m\}^\{\*\}\.

8:Convert

πm∗\\pi\_\{m\}^\{\*\}to sequence

\{vm,0,vi1,…,viNm,vm,0\}\\\{v\_\{m,0\},v\_\{i\_\{1\}\},\\ldots,v\_\{i\_\{N\_\{m\}\}\},v\_\{m,0\}\\\}\.

9:Initialize UAV at

𝐩m​\(0\)=𝐩vm,0\\mathbf\{p\}\_\{m\}\(0\)=\\mathbf\{p\}\_\{v\_\{m,0\}\},

ξm​\(0\)=𝟎\\mathbf\{\\xi\}\_\{m\}\(0\)=\\mathbf\{0\}, and waypoint index

k←1k\\leftarrow 1\.

10:while

k≤Nmk\\leq N\_\{m\}do

11:Observe state

st=\[p~x,p~y,ξ~x,ξ~y,g~x,g~y,d~,qnorm\]s\_\{t\}=\[\\tilde\{p\}\_\{x\},\\tilde\{p\}\_\{y\},\\tilde\{\\xi\}\_\{x\},\\tilde\{\\xi\}\_\{y\},\\tilde\{g\}\_\{x\},\\tilde\{g\}\_\{y\},\\tilde\{d\},q\_\{\\text\{norm\}\}\]\.

12:Inquire

𝐊CKM\\mathbf\{K\}^\{\\text\{CKM\}\}at current position to obtain

qnormq\_\{\\text\{norm\}\}\.

13:Select action

𝐚𝐭∼πθ∗\(⋅\|st\)\\mathbf\{a\_\{t\}\}\\sim\\pi\_\{\\theta\}^\{\*\}\(\\cdot\|s\_\{t\}\)\.

14:Execute

ata\_\{t\}, then update

ξm​\(t\+1\)\\mathbf\{\\xi\}\_\{m\}\(t\+1\)and

𝐩m​\(t\+1\)\\mathbf\{p\}\_\{m\}\(t\+1\)\.

15:if

‖𝐩m​\(t\)−𝐩vik‖≤r\\\|\\mathbf\{p\}\_\{m\}\(t\)\-\\mathbf\{p\}\_\{v\_\{i\_\{k\}\}\}\\\|\\leq rthen

16:Advance to next waypoint,

k←k\+1k\\leftarrow k\+1\.

17:endif

18:endwhile

19:Record trajectory

𝐩m​\(t\)\\mathbf\{p\}\_\{m\}\(t\)\.

20:endfor

21:return

\{𝐩m​\(t\)\}m=1M\\\{\\mathbf\{p\}\_\{m\}\(t\)\\\}\_\{m=1\}^\{M\}\.

### III\-CSAC\-Based Continuous Trajectory Planning

To further account for UAV kinematic constraints and environmental dynamics, the TSP solution is used as an initial policy for a SAC agent\. Specifically, given the visiting sequenceπ=\{v0,vi1,…,vin,v0\}\\pi=\\\{v\_\{0\},v\_\{i\_\{1\}\},\\ldots,v\_\{i\_\{n\}\},v\_\{0\}\\\}, the UAV is required to generate a continuous trajectory connecting consecutive nodes\. The trajectory planning objective is to minimize the mission completion timeTTwhile maintaining the communication quality\. In this work, the problem is formulated as a Markov decision process, which mainly consists of the following three parts:

#### III\-C1State Space

At time steptt, the statests\_\{t\}encodes the UAV normalized position\(c~x,c~y\)=\(cx/W,cy/H\)\(\\tilde\{c\}\_\{x\},\\tilde\{c\}\_\{y\}\)=\(\{c\_\{x\}\}/\{W\},\{c\_\{y\}\}/\{H\}\), velocity\(ξ~x,ξ~y\)=\(ξx/ξmax,ξy/ξmax\)\(\\tilde\{\\xi\}\_\{x\},\\tilde\{\\xi\}\_\{y\}\)=\(\{\\xi\_\{x\}\}/\{\\xi\_\{\\max\}\},\{\\xi\_\{y\}\}/\{\\xi\_\{\\max\}\}\), next waypoint position\(g~x,g~y\)\(\\tilde\{g\}\_\{x\},\\tilde\{g\}\_\{y\}\), distance to goald~\\tilde\{d\}, and the current RSS qualityqnorm∈\[0,1\]q\_\{\\text\{norm\}\}\\in\[0,1\]extracted from the CKM\.\(cx,cy\)\(c\_\{x\},c\_\{y\}\)and\(ξx,ξy\)\(\{\\xi\_\{x\}\},\{\\xi\_\{y\}\}\)represent the mapping grid position and the velocity of the UAV\.

#### III\-C2Action Space

The continuous action𝐚~t=\[a~x,a~y\]T∈\[−1,1\]2\\mathbf\{\\tilde\{a\}\}\_\{t\}=\[\\tilde\{a\}\_\{x\},\\tilde\{a\}\_\{y\}\]^\{T\}\\in\[\-1,1\]^\{2\}is a two\-dimensional vector representing normalized acceleration commands along thexxandyyaxes, respectively\.𝐚~t\\mathbf\{\\tilde\{a\}\}\_\{t\}maps to the physical UAV acceleration via𝐚t=𝐚~t​amax\\mathbf\{a\}\_\{t\}=\\mathbf\{\\tilde\{a\}\}\_\{t\}a\_\{\\max\}, whereamaxa\_\{\\max\}is the maximum UAV acceleration\.

#### III\-C3Reward Function

The reward function is designed to encourage the progress toward the target node while penalizing communication bottlenecks and excessive control effort, which is modeled as

rt=λ1​Δ​dtprog−λ2​max⁡\(0,qmint−1−qt\)​𝕀​\[qt<qmint−1\]−λ3​‖at‖,r\_\{t\}=\\lambda\_\{1\}\\Delta d\_\{t\}^\{\\text\{prog\}\}\-\\lambda\_\{2\}\\max\(0,q\_\{\\min\}^\{t\-1\}\-q\_\{t\}\)\\mathbb\{I\}\[q\_\{t\}<q\_\{\\min\}^\{t\-1\}\]\-\\lambda\_\{3\}\\\|a\_\{t\}\\\|,\(17\)whereΔ​dtprog\\Delta d\_\{t\}^\{\\text\{prog\}\}denotes the progress increment towards the target,qtq\_\{t\}denotes the communication quality from the CKM, and‖at‖\\\|a\_\{t\}\\\|penalizes the excessive control actions\.

#### III\-C4Objective Function

The policy networkπθ​\(at\|st\)\\pi\_\{\\theta\}\(a\_\{t\}\|s\_\{t\}\)parameterizes a Gaussian distribution over actions conditioned on the current state\. The SAC maximizes the entropy\-regularized expected return, i\.e\.,

maxθ𝔼πθ\[∑t=0Tγt\(rt\+αℋ\(πθ\(⋅\|st\)\)\)\],\\max\_\{\\theta\}\\ \\mathbb\{E\}\_\{\\pi\_\{\\theta\}\}\\left\[\\sum\_\{t=0\}^\{T\}\\gamma^\{t\}\(r\_\{t\}\+\\alpha\\mathcal\{H\}\(\\pi\_\{\\theta\}\(\\cdot\|s\_\{t\}\)\)\)\\right\],\(18\)whereγ∈\(0,1\)\\gamma\\in\(0,1\)is the discount factor,α\>0\\alpha\>0is the entropy coefficient, andℋ​\(⋅\)\\mathcal\{H\}\(\\cdot\)denotes entropy\. The optimized objective via the soft policy iteration is

ℒSAC=𝔼st,at​\[α​log⁡πθ​\(at\|st\)−Qϕ​\(st,at\)\],\\mathcal\{L\}\_\{\\text\{SAC\}\}=\\mathbb\{E\}\_\{s\_\{t\},a\_\{t\}\}\\left\[\\alpha\\log\\pi\_\{\\theta\}\(a\_\{t\}\|s\_\{t\}\)\-Q\_\{\\phi\}\(s\_\{t\},a\_\{t\}\)\\right\],\(19\)whereQϕ​\(st,at\)Q\_\{\\phi\}\(s\_\{t\},a\_\{t\}\)is the soft Q\-function approximated by a critic network\. The entropy term encourages exploration while the Q\-value guides exploitation, enabling stable and efficient learning\.

## IVSimulation Analysis

![Refer to caption](https://arxiv.org/html/2606.24979v1/x1.png)Figure 3:Diffusion\-based time\-accumulated CKM Construction\.![Refer to caption](https://arxiv.org/html/2606.24979v1/x2.png)Figure 4:Multi\-UAV cooperative trajectory planning\.### IV\-AExperiment Setup

To evaluate the effectiveness of the proposed CKM\-driven GATSAC joint framework, comprehensive simulations are conducted in an urban UAV inspection scenario\. The simulation environment is constructed based on the Raymobtime urban dataset\[[16](https://arxiv.org/html/2606.24979#bib.bib16)\], which provides ray\-tracing\-based channel measurements and accurate geographical information\. In detail, the target area for UAV network simulation is divided into64×6464\\times 64grids\. Besides, to reduce the inference latency, we adopt the denoising diffusion implicit model sampling withT=20T=20steps, achieving a5050\-fold acceleration over the standard denoising diffusion probabilistic model while maintaining comparable reconstruction quality\. To accurately evaluate the communication quality of a flight segment over a discretized CKM, the edge communication cost is defined as the minimum RSS among all grid cells intersected by the path between two nodes\. Aimed at demonstrating the performance of the proposed algorithm, five related methods are compared as follows\.

#### IV\-A1Distance\-Only TSP without CKM

This baseline solves the TSP using greedy and 3\-opt algorithms based solely on Euclidean distance\.Subsequently, its continuous trajectories are generated by a basic proportional controller\.

#### IV\-A2Distance\-Only TSP\-SAC

This method combines the distance\-based TSP ordering with a pre\-trained SAC agent for communication sensing and continuous trajectory planning\. It enables the UAV to bypass poor communication areas, verifying the SAC module’s independent contribution\.

#### IV\-A3TSP\-A\*

After determining the node order, this baseline replaces our SAC\-based continuous trajectory planner with the classical A\* algorithm\. It is implemented to evaluate the superiority of RL in continuous control\.

#### IV\-A4SAC without GAT\-TSP Initialization

Instead of utilizing GAT\-TSP for sequence optimization, this approach adopts a random node visiting order and purely relies on the pre\-trained SAC agent to achieve communication\-aware continuous trajectory planning\.

#### IV\-A5Joint SAC

The method relies solely on the SAC agent to jointly optimize the discrete node ordering and continuous trajectory control, verifying the necessity of TSP initialization\.

### IV\-BPerformance Analysis

![Refer to caption](https://arxiv.org/html/2606.24979v1/x3.png)Figure 5:Trajectory comparisons of multiple planning methods\.![Refer to caption](https://arxiv.org/html/2606.24979v1/x4.png)Figure 6:Comparison performance of six planning methods\.Fig\.[3](https://arxiv.org/html/2606.24979#S4.F3)shows the process and performance of the CKM construction, where the discrete measurement points are shown in Fig\.[3](https://arxiv.org/html/2606.24979#S4.F3)\(a\), and marked in the form of a mask in Fig\.[3](https://arxiv.org/html/2606.24979#S4.F3)\(b\)\. Then, the reconstructed CKM in Fig\.[3](https://arxiv.org/html/2606.24979#S4.F3)\(c\) is obtained through the pre\-trained diffusion model, and Fig\.[3](https://arxiv.org/html/2606.24979#S4.F3)\(d\) is the ground truth in the current region, which is relatively intuitive to observe that the error between the reconstructed CKM and ground truth is extremely small\. Fig\.[4](https://arxiv.org/html/2606.24979#S4.F4)shows the results of trajectory planning for two UAVs, where Fig\.[4](https://arxiv.org/html/2606.24979#S4.F4)\(a\) shows the node division results for multiple UAVs, and Fig\.[4](https://arxiv.org/html/2606.24979#S4.F4)\(b\) is the final planning trajectory\.

Moreover, the trajectory planning results and performance comparison results of various algorithms are shown in Figs\.[5](https://arxiv.org/html/2606.24979#S4.F5)and[6](https://arxiv.org/html/2606.24979#S4.F6)\. As observed in Fig\.[5](https://arxiv.org/html/2606.24979#S4.F5), compared with other algorithms, the planned trajectory of the proposed algorithm effectively avoids low\-quality communication areas while maintaining a relatively low route cost\. Furthermore, it can be observed from Fig\.[6](https://arxiv.org/html/2606.24979#S4.F6)\(a\) that the total flight distance of the proposed method is significantly shorter than most baseline methods\. Besides, since the RSS in dBm is inherently negative,−MinRSS\-\\text\{MinRSS\}is used as the vertical axis, such that a smaller value indicates better communication quality\. It is obvious that our algorithm achieves the optimal communication performance from Fig\.[6](https://arxiv.org/html/2606.24979#S4.F6)\(b\)\. Compared with the Distance\-Only TSP and TSP\+A\*, the CKM\-driven GATSAC algorithm reduces the path length while incorporating communication awareness\. Additionally, although Dist\-TSP\+SAC yields the shortest distance, it does not explicitly optimize the communication quality and tends to traverse regions with poor communication quality due to the lack of channel awareness\. Meanwhile, the Joint SAC algorithm improves performance by incorporating learning\-based planning, but it is still inferior to our proposed method due to the lack of structured global guidance\. The SAC \(No TSP\) method performs the worst, which further highlights the importance of combining global planning with local optimization\.

## VConclusions

In this paper, we propose the CKM\-driven GATSAC algorithm for urban UAV inspection, simultaneously optimizing the flight efficiency and communication quality\. By constructing the diffusion\-based time\-accumulated CKM and integrating the graph\-based TSP planning with SAC trajectory optimization, the method can effectively avoid low\-quality communication regions while maintaining a relatively short flight distance\. Simulation results validate the effectiveness of the proposed diffusion\-based CKM and the hierarchical planning framework\.

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