Path deviation control for multi-UAV cooperative task execution based on laser vision guidance and trajectory prediction

2.1. Theoretical implications

This study proposes an integrated multi-drone cooperative control framework at the theoretical and methodological levels, with the following key contributions.

First, in multi-sensor fusion and simultaneous localization and mapping (SLAM), this work innovatively combines the Length- and Ground-Optimized Lidar Odometry and Mapping on Variable Terrain (LeGO-LOAM) algorithm with the Oriented FAST and Rotated BRIEF Simultaneous Localization and Mapping 3 (ORB-SLAM3) algorithm to construct a cooperative mapping method suitable for multiple drones. This approach not only enhances the real-time performance and accuracy of local maps but also addresses map alignment and drift-correction issues in multi-view, multi-source data through a unified world coordinate system and map-fusion mechanism, thereby laying a reliable foundation for future path planning and control in dynamic environments. Second, regarding trajectory prediction, the study improves the classical A* algorithm by incorporating multidimensional constraint fusion. The dynamic characteristics of UAVs and environmental constraints are embedded into the cost function, and a dynamic weight-adjustment mechanism is introduced, enabling the algorithm to maintain high efficiency and adaptability in complex dynamic settings. This provides an extensible heuristic-search framework for multi-agent cooperative path planning. Finally, at the control-strategy level, an integrated closed-loop control process combining fuzzy logic and PID control is constructed, achieving rapid response and accurate correction of path deviations and offering theoretical and methodological support for robust control of multi-UAV systems in uncertain environments.

2.2. Industrial and management implications

Industry refers to economic sectors that utilize science, technology, equipment, and manpower to engage in the production, processing, and construction of material products, including manufacturing, energy, mining, and construction. Management denotes the process of coordinating human, material, financial, and information resources through functions such as planning, organizing, leading, and controlling to achieve organizational goals. The method proposed in this study holds significant practical value for industrial applications and operational management.

At the industrial application level, the method can be widely employed in scenarios such as emergency logistics distribution, urban inspection, agricultural crop protection, and disaster monitoring. For example, in emergency material distribution, it enables precise, efficient, and safe cooperative flight in complex urban environments, thereby substantially improving the efficiency and reliability of material delivery. When applied to power-line inspection or infrastructure monitoring, multiple drones can cooperate to complete large-scale, high-precision data-collection tasks, effectively reducing labor costs and operational risks. Moreover, the method maintains stable operation under harsh conditions such as GPS signal loss and sensor interference, further enhancing the applicability and anti-interference robustness of UAV systems in real-world industrial environments.

From a management perspective, the proposed method provides solid and robust technical support for multi-drone clusters in task scheduling, resource allocation, and cooperative efficiency management. Through real-time trajectory prediction and deviation control, managers can achieve dynamic monitoring and intelligent scheduling of drone clusters, optimize task execution sequences and path planning, reduce collision risks and energy consumption, and improve overall task execution efficiency. Furthermore, the method supports flexible scaling of the number of drones, with low memory usage and high system stability, which facilitates centralized control and distributed cooperation of large-scale drone clusters. This offers a feasible technical pathway and management paradigm for UAV operation and management in future domains such as smart logistics and smart cities.

3.1. Cooperative map construction for multi-UAV systems based on laser vision guidance

The construction of a three-dimensional map for multi-UAV cooperative tasks using laser vision guidance imposes specific requirements on the mapping algorithm, as it must coordinate multi-UAV cooperative actions while demonstrating high tolerance to drift errors and maintaining real-time performance. After comprehensive evaluation, the LeGO-LOAM algorithm is selected. It is used for individual UAV local map construction based on laser vision guidance. The architecture for constructing a local map of a single UAV using this guidance approach is shown in Fig. 2.

Fig. 2 illustrates the process of constructing a local map for a single UAV based on laser vision guidance. The process adopts the LeGO-LOAM algorithm framework, which is divided into front-end and back-end parts. Starting from the point cloud data acquired by LiDAR scanning, the front-end sequentially performs point cloud segmentation, feature extraction, LiDAR odometry computation, and loop-closure detection to estimate the UAV’s pose changes in real time and extract environmental features. The back-end then applies pose-graph optimization to the pose estimates from the front-end, performing global consistency correction to effectively reduce accumulated errors. Finally, the optimized pose information is used for map construction and updating, generating an accurate local 3D point cloud map. The entire process forms a complete closed loop from data acquisition and feature processing to optimized mapping.

The Lightweight and Ground-Optimized Lidar Odometry and Mapping on Variable Terrain (LeGO-LOAM) algorithm is a specialized light detection and ranging (LiDAR) odometry and mapping method designed primarily for real‑time six-degree-of-freedom (6DOF) pose estimation. Developed as an optimization of the LOAM framework, it enables real‑time pose estimation for UAVs even on low‑power embedded systems.

Fig. 2Process for constructing a local map of a single UAV based on laser vision guidance

During the local map construction for a single UAV using the LeGO-LOAM algorithm, three-dimensional point-cloud data of the surrounding environment are acquired by a LiDAR sensor mounted on the drone. The front-end processing comprises four key steps: point-cloud segmentation, feature extraction, LiDAR odometry, and loop-closure detection [11]; the back-end carries out pose-graph optimization. Through the joint operation of the front-end and back-end, the system significantly reduces the UAV’s drift error and enhances the real-time performance of local 3D point-cloud map generation. In the feature-extraction stage, smoothness is computed using Eq. (1):

Depth information is denoted by $r_{ki}$, while the set of points consisting of a specific point in the laser point cloud and five adjacent points on each side within the same row is represented by $S$ [12]. Subsequently, in the LiDAR odometry stage, iterative processing is carried out using Eq. (2):

where, $J$ denotes the Jacobian matrix, $W_k$ represents the pose estimate, and $h$ has a dual interpretation: it refers both to the distance between edge features and to the distance for the planar feature set.

In the back‑end design, the UAV pose‑graph objective function enables the acquisition of accurate UAV pose transformation data:

The pose estimates of all pose nodes are denoted by $W$; the set of all edges is denoted by $\epsilon$; the pose estimation error is denoted by $e_{ij}$; and the covariance matrix is denoted by ${\sum }_{ij}$.

Following the acquisition of the UAV’s pose transformation results, the system performs final loop‑closure detection and map construction to generate the completed local 3D point‑cloud map. The proposed map‑construction method for laser‑vision‑guided multi‑UAV cooperative systems integrates local 3D point‑cloud maps by establishing a unified world coordinate system for each UAV.

(I) World Coordinate System Establishment.

ORB‑SLAM3 (Oriented FAST and Rotated BRIEF Simultaneous Localization and Mapping) is an open‑source real‑time visual SLAM system, developed by extending and enhancing ORB‑feature‑based 3D localization and mapping algorithms such as ORB‑SLAM2 and ORB‑SLAM‑VI, with compatibility for various camera configurations. The ORB‑SLAM3 framework incorporates a DBoW2 (Database of Words) database to store keyframes captured by the multi‑UAV laser‑vision systems. The pose transformation between adjacent keyframes can be computed using Eq. (3). The construction of the world coordinate system for each UAV involves the following steps:

1) Position multiple UAVs performing cooperative tasks with aligned LiDAR orientations to establish inter‑system consensus [13] and ensure sufficient feature‑point acquisition.

2) Initialize each UAV's LiDAR system and store the processed keyframes in the DBoW2 database through ORB‑SLAM3.

3) The keyframes stored in the DBoW2 database serve as reference frames for each UAV to build its world coordinate system.

4) After establishing their respective world coordinate systems, the UAVs generate a cooperative task‑execution map.

(II) Multi‑UAV Cooperative Map Fusion.

After obtaining world coordinate systems from their respective local 3D point‑cloud mapping systems, the UAVs employ the RGB‑L‑integrated ORB‑SLAM3 algorithm to produce a cooperative task‑execution map. The fusion process is illustrated in Fig. 3.

Fig. 3Map fusion framework for multi-UAV cooperative task execution

The multi‑UAV cooperative task map‑fusion process consists of three key steps:

(1) Retrieving local 3D point‑cloud maps and camera images from the keyframe database using laser‑vision guidance;

(2) Establishing coordinate transformations through the keyframe‑tracking model and the Iterative Closest Point (ICP) algorithm when camera‑image consensus is reached, followed by world‑coordinate‑system creation via Robot Operating System 2 (ROS2) data‑transmission topics;

(3) Acquiring UAV pose states and performing loop‑closure detection to generate the final local 3D point‑cloud map.

Based on the world coordinate system defined in step (2), each local map is transformed using the pose‑transformation relationship [14], projecting it into the world coordinate system and integrating it into a multi‑UAV cooperative task‑execution map.

In the multi‑UAV cooperative task‑execution map constructed through the above process, an improved A* algorithm is employed for multi‑UAV trajectory prediction to generate the cooperative task‑execution path, while path‑deviation control is achieved by comparing the predicted path with the target path.

3.2. Trajectory prediction for multi-UAV cooperative tasks based on an improved A* algorithm

Fig. 4 illustrates the path-deviation control process for multi-UAV cooperative task execution based on trajectory prediction.

Fig. 4Path deviation control process for multi-UAV cooperative task execution

Fig. 4 illustrates the complete path-deviation control process for multi-UAV cooperative task execution based on trajectory prediction. First, a feasible flight path is determined by constructing a multi-UAV cooperative task map and defining flight-trajectory nodes using laser-vision guidance. Then, a trajectory-prediction module that incorporates safety constraints as well as threat and uncertainty factors generates a feasible and accurate cooperative trajectory. Finally, the deviation between the predicted trajectory and the actual flight position is fed into a PID controller to achieve closed-loop path correction, forming a complete deviation-suppression chain that spans environmental perception, trajectory planning, and real-time control. The multi-UAV cooperative task-execution path-deviation control builds upon the single-UAV trajectory-prediction algorithm [15] and integrates multiple constraints and objective functions for cooperative trajectory prediction. These include collision-avoidance constraints and inter-agent information-sharing constraints [16], while the objective function aims either to minimize the total operational cost of the UAV swarm or to maximize simultaneous target arrival. This framework enables the acquisition of optimal trajectory-prediction data for multi-drone cooperative task execution. The prediction result is compared with the drone's actual position to accurately calculate the deviation. The deviation value is then input to the PID controller. By leveraging the regulating capability of the PID controller, path deviation can be effectively corrected, ensuring stable flight of the drone along the predefined route.

The A* algorithm employs a heuristic strategy that combines characteristics of Dijkstra’s algorithm and the greedy algorithm. It leverages the advantage of Dijkstra’s algorithm in precisely exploring globally optimal paths while also adopting the greedy algorithm’s ability to rapidly approach the target during the search process, thereby enabling efficient and accurate prediction of the optimal trajectory [17-18]. As a classical heuristic algorithm for trajectory prediction, the A* algorithm incorporates heuristic information throughout its computation [19-20]. Its evaluation function is given by:

where, $i$ denotes an arbitrary node in the trajectory-prediction process. $f\left(i\right)$ represents the evaluation function for trajectory generation, indicating the total trajectory cost from the start to the target via node $i$. $g\left(i\right)$ corresponds to the actual trajectory cost (distance) for the UAV to travel from the start to node $i$ in the flight environment, while $u\left(i\right)$ denotes the heuristic function that estimates the optimal trajectory cost from node $i$ to the target point.

The A* algorithm can find an optimal solution under specific conditions [21]. To guarantee optimality, the heuristic function $u\left(i\right)$ used by the A* algorithm must be admissible, meaning it must never overestimate the actual cost $g\left(i\right)$ to reach the goal. If $u\left(i\right)$ is always less than or equal to $g\left(i\right)$, the algorithm is guaranteed to find the optimal solution. However, if $u\left(i\right)$ overestimates $g\left(i\right)$, optimality cannot be ensured.

To enhance the performance of trajectory prediction in multi-drone cooperative task execution and minimize path deviation, the A* algorithm is improved based on its actual cost function. Specifically, the optimization of the actual cost function incorporates multiple factors, including the minimum turning radius, the minimum path length, specific velocity requirements, and spatial constraints of the UAV [22-23]. The detailed procedure is provided in the Appendix.

During cooperative task execution, assuming that each drone maintains a constant-speed flight state, its flight distance and flight time exhibit a proportional relationship. Consequently, the distance between different drones can be derived by calculating the position of each drone at a specific time point t.

Based on the above analysis, the trajectory for cooperative task execution is predicted. The flight trajectories predicted by the improved A* algorithm during multi-drone cooperative task execution, together with the inter-drone deviation data, serve as input to the PID controller, enabling effective control of path deviation in multi-drone cooperative task execution [24].

Simultaneously, a dynamic weight-adjustment mechanism is introduced into the algorithm. This mechanism can adjust the influence weights of various constraints on the cost function in real time and flexibly, depending on different task scenarios and the specific performance of the drone. This process enhances the adaptability and flexibility of the algorithm. In handling spatial constraints, the algorithm calculates the position of each drone in real time, dynamically ensures a safe distance between drones, and maintains a minimum safe distance between drones and obstacles. It can effectively cope with complex and varying flight environments, significantly improving the safety and reliability of trajectory planning. Moreover, by comprehensively considering multidimensional constraints, the algorithm also optimizes the heuristic function to produce a more accurate estimate of the optimal-path cost from the current node to the target node, thereby accelerating convergence to the optimal solution.

Overall, the improved A* algorithm achieves substantial improvements in the accuracy, efficiency, safety, and reliability of trajectory planning across multiple key dimensions, providing essential algorithmic support for path-deviation control in multi-UAV cooperative task execution.

The research objective is to verify the effectiveness of the improved A* algorithm in predicting trajectories for multi-UAV cooperative tasks, and to conduct comparative experiments with three alternative trajectory-prediction methods: the Model Predictive Control (MPC)-based trajectory-length method combining optimization and learning, the deep-learning-based trajectory-prediction method, and the improved Rapidly-exploring Random Tree star (RRT*)-based trajectory-prediction method. In the experiment, the trajectory length between the predicted endpoint and the target position obtained by each method is recorded and compared; the results are presented in Table 1.

According to the analysis in Table 2, on all tested drones the trajectory length predicted by the improved A* algorithm is shorter than those obtained by the optimization-and-learning-based MPC method, the deep-learning method, and the improved RRT* algorithm. Its average trajectory length is 124.7 m, which is 6.0 %, 11.1 %, and 8.3 % shorter than the lengths produced by the MPC, deep-learning, and improved RRT* methods, respectively, indicating higher prediction accuracy. This improvement mainly stems from the deep integration of multidimensional constraints in the improved A* algorithm, which incorporates both the dynamic characteristics of UAVs and spatial safety requirements into the cost function, thereby avoiding the path redundancy or feasibility risks caused by fragmented constraint handling in traditional methods. The dynamic weight-adaptation mechanism of the algorithm can adjust constraint weights in real time according to the task objectives; for example, it reduces safety-distance weights to shorten paths in emergency tasks, whereas the MPC and deep-learning methods employ fixed weights and the improved RRT* algorithm relies on manually set parameters, which lack such flexibility. Furthermore, the algorithm intelligently optimizes the heuristic function by implicitly incorporating multiple constraints into the path-cost estimation, which improves search efficiency and overcomes the problems of local optima in the conventional A* algorithm and the low search efficiency of the improved RRT* algorithm.

3.3. Path deviation control based on PID

The UAV adjusts its movement direction according to the trajectory generated by the A* algorithm through a path‑control cycle that follows the sequence perception → decision → execution → correction. During cooperative operations, trajectory deviations may arise due to obstacles or environmental disturbances, requiring corrective directional adjustments. Based on the UAV control‑system architecture, a path‑deviation control methodology that integrates fuzzy logic with PID speed‑control algorithms is developed [25-26], as illustrated in Fig. 5.

In Fig. 5, $∆\alpha$ denotes the angular deviation between the UAV and the predicted trajectory, and $∆q$ represents the lateral-distance deviation between the UAV and the predicted trajectory. The fuzzy-control algorithm performs path-deviation correction over multiple control cycles [27-28]. For each adjustment cycle, the algorithm takes $\left(∆{\alpha }_t,∆q_t\right)$ as input parameters, where $∆{\alpha }_t$ is the angular-deviation input for the $t$-th cycle and $∆q_t$ is the lateral-distance-deviation input for the $t$-th cycle [29-30]. In summary, the path-deviation control process for multi-UAV cooperative task execution based on laser-vision guidance and trajectory prediction is illustrated in Fig. 6.

Fig. 6 illustrates the complete path-deviation control process for multi-UAV cooperative task execution based on laser-vision guidance and trajectory prediction. First, a local 3D point-cloud map is constructed through multi-sensor data acquisition, and a global cooperative task map is generated. Then, an A* algorithm is employed to predict the cooperative trajectory of multiple UAVs, producing the optimal cooperative trajectory under multi-constraint fusion. Subsequently, control commands are generated via fuzzy logic, and UAV attitude control is implemented using a PID controller. After verifying whether the path deviation has been eliminated, the UAV is guided to the target point. Finally, the entire task-execution process – from environmental perception and cooperative map construction through trajectory prediction to closed-loop control – is completed.

Fig. 5Implementation process of the PID‑based UAV path deviation control algorithm

Fig. 6Path deviation control process for multi-UAV cooperative task execution based on laser vision guidance and trajectory prediction

4.1. Map construction

4.1.1. Local map construction

To validate the actual performance of 3D map construction using LiDAR mounted on drones, experiments are conducted to generate 3D point-cloud maps. All experiments are carried out in an outdoor environment; corresponding images are presented in Fig. 8.

Fig. 8Construction results of a local 3D point cloud map

a) City-scene map

b) Local 3D point-cloud map

Fig. 8 shows the construction results of a local 3D point cloud map in urban scenes. From the original urban scene in Fig. 8(a), it can be seen that the experimental environment includes various complex land structures such as buildings, roads, and trees, which are highly representative. The local 3D point cloud map in Fig. 8(b) clearly reproduces the three-dimensional geometric shape of the main objects in the scene, with distinct building contours, distinguishable ground undulations, and densely distributed point clouds of trees. This result indicates that the LeGO-LOAM algorithm used in this paper can effectively extract environmental features in outdoor urban scenes, and the generated point cloud maps have high geometric fidelity, providing a reliable local data foundation for subsequent multi-drone collaborative map fusion.

4.1.2. Global map construction

The map-fusion results for multi-UAV cooperative task execution are presented in Fig. 9.

Fig. 9Map fusion results of multi-UAV collaborative task execution

a) Local 3D point‑cloud map 1

b) Local 3D point‑cloud map 2

c) Fusion result

Fig. 9 shows the map fusion results during the collaborative task execution process of multiple drones. Among them, Fig. 9(a) and Fig. 9(b) are the local 3D point cloud maps independently constructed by two drones, and Fig. 9(c) is the global collaborative task map fused from the two. From the fusion results, it can be seen that the common features such as buildings and roads in the two local maps have been accurately aligned, and the fused map does not show obvious ghosting or misalignment in the overlapping areas, with smooth edge transitions. This indicates that the world coordinate system method based on the ORB-SLAM3 framework and keyframe consensus mechanism in this paper can effectively achieve accurate registration and fusion of multi-source point cloud data, providing a spatially consistent global map for collaborative trajectory planning of multiple drones in a common environment.

4.2. Obstacle-avoidance navigation planning results

The obstacle-avoidance navigation-planning results under different test environments are presented in Fig. 10.

Fig. 10Obstacle‑avoidance trajectory planning results

a) Fixed obstacles

b) Moving obstacles

As shown in Fig. 10(a), when obstacles are stationary, the method proposed in this paper can accurately capture their position information and, based on this information together with factors such as obstacle density, autonomously plan a trajectory to avoid the obstacles. Simultaneously, with the support of the path-deviation control algorithm presented in this work, the actual flight path of the drone closely follows the pre-predicted trajectory, flying along the predicted path, successfully avoiding all static obstacles, and smoothly reaching the target point from the starting point. As shown in Fig. 10(b), when obstacles are moving, the method can analyze the motion trajectory of the moving obstacles in real time and perform obstacle-avoidance maneuvers on this basis. It predicts its own flight trajectory according to the motion trajectory of the moving obstacles and then uses path-deviation control to bring the actual flight path close to the predicted trajectory, ultimately enabling the UAV to reach the endpoint smoothly from the starting point. Based on the above observations, it is clearly demonstrated that the proposed method can effectively ensure the safety of UAVs during flight.

These metrics are compared and analyzed with baseline planning methods based on DQN, Particle Swarm Optimization (PSO), and Genetic Algorithm (GA). All data are averaged over 10 repeated runs under the same experimental conditions. The results are presented in Table 5.

Analysis of Table 5 shows that the method proposed in this paper significantly outperforms the three mainstream planning baseline methods across all key performance metrics. In terms of path-control accuracy, the RMS path error of the proposed method is only 0.92 m, representing reductions of 67.7 %, 65.9 %, and 66.5 % compared with the DQN, PSO, and GA methods, respectively. This improvement stems from precise environmental perception enabled by laser-vision fusion mapping and from the deeply integrated multidimensional constraints and dynamic weight-adjustment mechanism of the improved A* algorithm. These features make trajectory prediction more consistent with UAV dynamics and the actual environment, significantly suppressing cumulative error. Regarding real-time performance, the proposed method demonstrates a notable advantage, with an average system delay of only 85 ms. Compared with the DQN, PSO, and GA methods, latency is reduced by 73.4 %, 58.5 %, and 64.6 %, respectively. This achievement is attributed to the lightweight and efficient processing pipeline jointly constructed by LeGO-LOAM and the improved A* algorithm, as well as the optimized sensor-data fusion and trajectory-search mechanisms, which allow control commands to be generated and responded to quickly in dynamic and complex environments. In terms of energy efficiency, the proposed method also performs well, exhibiting an energy consumption per unit flight distance of 112 J/m. Compared with the baseline methods, energy consumption is reduced by 18.6 % to 39.5 %. This reflects that, by planning smooth and feasible trajectories and implementing precise closed-loop deviation control, the method reduces unnecessary maneuvers and speed adjustments, thereby lowering overall kinetic-energy consumption. With respect to computational-resource utilization, the proposed method maintains a stable CPU utilization of 58 %, which is 17.9 % to 25.6 % lower than that of the baseline methods. This indicates that the proposed algorithm achieves a good balance between computational complexity and task-scheduling efficiency; its modular design and efficient data-processing flow reduce the dependence on hardware resources. In terms of system reliability, the proposed method performs exceptionally well, with a task-failure probability controlled at 1.2 %, far below the 5.5 % to 8.5 % range of the baseline methods. This outcome fully validates the effectiveness of the full-chain design - from robust multi-sensor fusion mapping, through trajectory prediction that considers physical and cooperative constraints, to fast-response fuzzy-PID closed-loop control. This design effectively addresses environmental uncertainty, sensor interference, and multi-agent cooperative conflicts, greatly enhancing the stability and task-completion rate of the system in real-world complex scenarios. In summary, the cooperative control framework integrating laser-vision guidance and trajectory prediction proposed in this paper exhibits comprehensive and significant technical advancement and practical advantages for multi-UAV cooperative task execution compared with mainstream planning baseline methods.

To further validate the effectiveness of the laser‑vision‑guided path‑deviation control method for multi‑UAV cooperative tasks incorporating trajectory prediction, the previously described multi‑UAV cooperative emergency material‑distribution task is selected as the benchmark scenario. The methods from references [5]-[8] are employed as comparative approaches, with performance metrics including the magnitude of path deviation during navigation, task completion time, computational time per image frame, and UAV collision rate. The comparison results of these metrics are presented in Table 6.

According to Table 4, in terms of path-deviation distance, the methods in references [5]-[8] yield 3.2 m, 2.8 m, 2.5 m, and 2.0 m, respectively, while the proposed method achieves only 1.0 m. Regarding task execution time, the methods in references [5]-[8] require 18 min, 16 min, 15 min, and 13 min, respectively, whereas the proposed method requires only 10 min. In terms of image-processing time per frame, the methods in references [5]-[8] take 0.35 s, 0.30 s, 0.28 s, and 0.25 s, respectively, while the proposed method takes 0.20 s. For the UAV flight collision-rate metric, the methods in references [5]-[8] result in 12 %, 10 %, 8 %, and 6 %, respectively, whereas the proposed method yields only 2 %. Overall, the method proposed in this paper outperforms the comparative methods across all evaluated metrics and better satisfies the stringent requirements for precision, timeliness, and safety in emergency material-distribution scenarios.

To evaluate the adaptability of the proposed method under different scenarios, adverse conditions such as GPS signal loss, LiDAR interference, and extreme weather are simulated, and the five methods mentioned earlier are tested. During this process, the path-deviation distance is selected as the key metric to assess the actual effectiveness of each method in path control. The test results of path deviation under different conditions are presented in Table 7.

The data in Table 7 demonstrate that the proposed method exhibits outstanding advantages in controlling UAV path deviation under adverse conditions such as GPS loss, LiDAR interference, and extreme weather. When GPS is unavailable, the path-deviation distances of the methods in references [5]-[8] are 4.5 m, 4.0 m, 3.7 m, and 3.2 m, respectively, whereas the proposed method achieves only 1.8 m. Under LiDAR interference, the deviation distances of the methods in references [5]-[8] are 4.2 m, 3.8 m, 3.5 m, and 3.0 m, while the proposed method yields 1.6 m. In extreme weather, the deviation distances of the methods in references [5]-[8] reach 5.0 m, 4.3 m, 3.9 m, and 3.4 m, compared with 2.0 m for the proposed method. These results indicate that the method proposed in this paper can control deviations more effectively and ensure flight stability, because it employs laser-vision guidance and multi-sensor fusion to assist UAV positioning and tracking when GPS is unavailable; it improves the classical A* algorithm to plan feasible trajectories under interference or extreme-weather conditions; and it designs a path-deviation control strategy that forms a complete correction loop, enabling rapid and accurate deviation correction. In contrast, the methods in the literature rely excessively on GPS, their trajectory prediction does not fully account for complex situations, and their control strategies lack sufficient response speed and accuracy, leading to larger deviations under adverse conditions. Therefore, the method proposed in this paper possesses stronger adaptability and stability in complex environments.

The memory-usage results of the different methods are presented in Table 8.

Analysis of the data in Table 8 shows that as the number of drones increases, the memory usage of all methods exhibits an upward trend. However, the proposed method consistently maintains a low level of memory consumption, demonstrating that the path-deviation control method for multi-UAV cooperative task execution based on laser-vision guidance and trajectory prediction possesses significant advantages in resource utilization. It ensures smooth task execution and achieves the intended outcomes while effectively reducing system memory usage, thereby enhancing system efficiency and stability.

Regarding path-control accuracy, the RMS error of the proposed method is only 0.92 m, which is 67.7 % lower than that of the deep-reinforcement-learning-based method, 58.2 % lower than that of the attention-mechanism-based method, 63.2 % lower than that of the NFMGOA-based method, and 48.9 % lower than that of the data-driven cascade-control method. In terms of real-time performance, the average system delay is 85 ms, representing an improvement of 43.3 % to 73.4 % over the comparative methods. With respect to energy efficiency, the energy consumption per unit flight distance is 112 J/m, which is 18.6 % to 39.5 % better than that of the comparative methods. Concerning system reliability, the task-failure probability is controlled at 1.2 %, corresponding to a reduction of 65.7 % to 85.9 % compared with the comparative methods. Under complex conditions such as GPS signal denial, LiDAR interference, and extreme weather, the proposed method can consistently maintain path deviation within 2 m, whereas other comparative methods typically exhibit deviations exceeding 3 m. This demonstrates that the proposed method possesses significant advantages in coping with environmental uncertainty and enhancing multi-agent cooperative stability, offering a superior-performance solution for the practical application of UAVs in dynamic and complex scenarios.

In practical applications, the method significantly improves the flight safety, energy-utilization efficiency, and cluster-cooperation capability of UAV systems. It integrates high-precision environmental perception with multi-safety-constrained trajectory planning, reliably avoiding collisions and ensuring the safety of dense multi-UAV flight. By optimizing control strategies, it reduces unnecessary maneuvering adjustments, lowers energy consumption, and extends mission endurance. Its scalable design supports stable cooperative operations of large-scale drone swarms under harsh conditions, delivering a highly robust and deployable cooperative-control solution for logistics distribution, disaster response, and wide-area inspection.

However, although the method exhibits excellent cooperative control and path accuracy, its practical deployment also faces limitations. When extended to large-scale drone swarms, the complexity of system communication and cooperative decision-making increases considerably, potentially leading to real-time scheduling delays and decision conflicts. The high-frequency data processing required by modules such as mapping demands substantial on-board computational resources, which can affect real-time responsiveness under hardware constraints. Furthermore, sensor noise and dynamic environmental disturbances may degrade perception and positioning stability in extreme scenarios, necessitating further optimization of algorithmic robustness and adaptability.

Future research could validate the method’s performance in more complex, long-term outdoor real-world scenarios, evaluating its behavior under strong winds, rain, fog, and dynamic-obstacle interference. It may also explore intelligent decision-making mechanisms that incorporate reinforcement learning to enable UAVs to autonomously adapt to unknown environments and optimize cooperative strategies. Designing an adaptive PID parameter-tuning algorithm that dynamically adjusts the control response based on real-time state and environmental feedback could improve stability and accuracy under nonlinear disturbances. Additionally, investigating lightweight models and edge-computing deployment schemes would help reduce the computational load and enhance the feasibility of real-time cooperation for large-scale swarms.

In summary, the collaborative control method based on laser vision guidance and trajectory prediction proposed in this paper is significantly superior to existing representative methods in terms of path accuracy, real-time performance, energy efficiency, and system robustness. In terms of path control accuracy, the RMS error of our method is only 0.92 m, which is 67.7 % lower than the method based on deep reinforcement learning, 58.2 % lower than the method based on attention mechanism, 63.2 % lower than the method based on NFMGOA, and 48.9 % lower than the method based on data-driven cascade control. In terms of real-time performance, the average system delay is 85 ms, which is 43.3 % to 73.4 % lower than the comparative methods. In terms of energy efficiency, the unit flight energy consumption is 112 J/m, which is 18.6 % to 39.5 % better than the comparative methods. In terms of system reliability, the probability of task failure is controlled at 1.2 %, which is 65.7 % to 85.9 % lower than the comparative methods. In complex situations such as GPS signal rejection, LiDAR interference, and extreme weather conditions, this method can stably control the path deviation within 2.0 m, while other comparative methods generally have deviations exceeding 3.0 m. This proves that the proposed method has significant advantages in dealing with environmental uncertainty and improving multi-machine collaborative stability, providing a better-performance solution for the practical application of UAVs in dynamic and complex scenarios. In practical applications, this method significantly enhances the flight safety, energy utilization efficiency, and cluster collaboration capability of UAV systems. It integrates high-precision environmental perception with multi-safety-constrained trajectory planning, reliably avoiding collisions to ensure the safety of multi-aircraft dense flight. It optimizes control strategies to reduce unnecessary maneuvering adjustments, lower energy consumption, and extend mission endurance. Its scalable design supports stable collaborative operations of large-scale drone swarms under harsh conditions, providing highly robust and deployable collaborative control solutions for logistics distribution, disaster response, and wide-area inspections. However, although this method has excellent collaborative control and path accuracy, its practical application also faces limitations. When extended to large-scale drone clusters, the complexity of system communication and collaborative decision-making increases significantly, leading to real-time scheduling delays and decision conflicts. The high-frequency data processing required by mapping and other modules demands substantial on-board computing resources, which affects real-time responsiveness under hardware constraints. Sensor noise and environmental dynamic interference may also degrade perception and positioning stability in extreme scenarios, requiring further optimization of algorithm robustness and adaptability. Future research can verify its performance in more complex outdoor real-world scenarios over long durations, evaluating its behavior under strong winds, rain and fog, and dynamic obstacle interference. It may explore intelligent decision-making mechanisms that integrate reinforcement learning to enable drones to autonomously adapt to unknown environments and optimize collaborative strategies. An adaptive PID parameter adjustment algorithm can be designed to dynamically adjust control response based on real-time status and environmental feedback, improving stability and accuracy under nonlinear disturbances. Lightweight models and edge-computing deployment schemes should be investigated to reduce the computational load and enhance the real-time collaboration feasibility of large-scale clusters.