Perception performance evaluation
To verify the effectiveness of LAFA and EIPPM in dynamic scenarios, this chapter deploys test platforms in two typical inspection environments: industrial plants and substations. The experimental setting includes extreme conditions such as sudden changes in illumination (2,000 → 80,000 lux), randomly moving obstacles (5–8/min), and dust interference (visibility < 5 m). Compared with mainstream fusion algorithms (Kalman filter/DNN) and path planning methods (A + DWA/RRT), quantitatively evaluate core indicators such as positioning accuracy, obstacle recognition rate, replanning delay, and energy consumption, and prove the performance advantages of the proposed scheme through statistical significance analysis (p < 0.01). All data are collected from actual industrial plants and substations, totaling 28,000 samples across 6 obstacle categories. All samples are manually annotated. The train/test split ratio is 8:2. An extra 5,000 real-time samples are used for online learning. The environmental feature library is constructed as 12-dimensional multimodal feature vectors. The online learning model is updated incrementally when abnormal samples accumulate for more than 10 consecutive frames, using a fixed learning rate of 0.001. Anomaly labels are defined as sudden obstacles and abnormal equipment states. To prevent catastrophic forgetting, a drift threshold of 0.15 is applied to the data distribution; if the distribution shift exceeds this threshold, the update is temporarily suspended until the incoming data stabilizes, thereby suppressing model drift and maintaining generalization performance. The lightweight online learning module is tested with 5,000 unseen samples. After 10-frame model updating, the accuracy of unknown-obstacle recognition increases by 7.2%, verifying its adaptive optimization capacity for novel environmental targets.
Robot platform: Differential wheel drive, STM32 controller, and Jetson Xavier NX onboard computer. It uses lithium batteries for 8 hours of continuous operation, with a speed of 0.2–1.2 m/s, a max payload of 8 kg, and dual Wi-Fi and 4G communication. Sensors: RPLIDAR A1M8, 10 Hz, 360° FOV; 1080P camera, 30 fps, 120° FOV; 320 x 240 infrared imager; MPU6050 IMU, 200 Hz. All sensors are front-mounted, calibrated uniformly, and synchronized at the microsecond level. Software: Ubuntu 20.04, ROS Noetic, Python and C++, PyTorch framework, equipped with an 8-core CPU and 16 GB GPU for edge computing.
The industrial plant (45 m x 30 m, 120 m route) and substation (50 m x 35 m, 150 m route) include fixed equipment and moving staff. Each test runs 30 times with a safety distance of 0.6 m. Illumination ranges from 2,000 to 80,000 lux, with 5–8 moving obstacles per minute. Dust reduces visibility below 5 m. All conditions are repeatable.
| Method | Localization error (cm) | Obstacle detection rate (%) | False alarm rate (%) | Processing delay (ms) | Robustness (lighting change) | Robustness (dust interference) | p-value |
| LiDAR Only | ±3.2 | 89.6 | 8.7 | 25 | Low | Medium | <0.01 |
| Vision + IMU | ±5.1 | 78.3 | 15.2 | 40 | Very Low | Low | <0.01 |
| Kalman Fusion | ±2.8 | 92.1 | 6.3 | 65 | Medium | Medium | <0.01 |
| DNN Fusion | ±2.5 | 94.8 | 5.1 | 110 | High | Low | <0.01 |
| RAL 2023 | ±1.9 | 96.4 | 4 | 85 | High | Medium | <0.01 |
| Proposed LAFA | ±1.5 | 98.7 | 1.8 | 35 | Very High | Very High | <0.01 |
Table 1: Multi-sensor sensing performance comparison. Robustness is rated on a 5-level scale based on the decline in obstacle detection under lighting changes and dust interference: Very Low, Low, Medium, High, and Very High.
Table 1 compares the performance of different perception methods in a dynamic industrial environment. All experiments were conducted with 30 independent repeated trials (n = 30). A one-way ANOVA combined with Tukey's HSD multiple-comparison test was used for statistical analysis, and all indicators showed significant differences (p < 0.01). The localization error of the proposed LAFA is ±1.5 cm (SD = ±0.25 cm, 95% CI: [1.42, 1.58] cm), and the overall positioning error follows a normal distribution. Its obstacle detection rate reaches 98.7% (SD = ±0.65%, 95% CI: [98.4%, 99.0%]), and the false alarm rate is only 1.8%. The processing latency is only 35 ms (68% faster than mainstream DNN fusion), and the robustness under strong light and dust interference reaches the "Very High" rating, while benchmark methods are rated "Medium" and "Low". The test dataset contains six types of obstacles to ensure reproducibility of results. This fully demonstrates the advantages of LAFA in the adaptive fusion of heterogeneous, multi-source data through spatiotemporal synchronization compensation and a dynamic attention-weighting mechanism.
Path planning performance evaluation
| Method | Re-plan time | Path optimality (%) | Collision rate (%) | Success rate (%) | Dynamic avoidance score | Energy consumption |
| A* + DWA | 2.5 | 82.6 | 7.3 | 88.9 | 6.1 | 0.48 |
| RRT*+APF | 1.8 | 76.4 | 5.1 | 91.2 | 7.3 | 0.52 |
| DRL Planner | 1.2 | 88.7 | 4 | 93.5 | 8.5 | 0.43 |
| ICRA 2024 | 0.9 | 90.2 | 3.2 | 95.1 | 8.9 | 0.41 |
| Proposed EIPPM | 0.8 | 96.3 | 0.9 | 99.2 | 9.7 | 0.37 |
Table 2: Dynamic path planning performance comparison. The dynamic avoidance score ranges from 0 to 10 points and is calculated by weighting the collision rate, path smoothness, replanning latency, and task success rate across 30 repeated trials.
Table 2 evaluates the performance of various path planning methods in a substation scenario with randomly moving obstacles (5-8 obstacles/min) and equipment thermal radiation interference. A total of 12 fixed inspection routes are adopted, and each method is tested 30 times. Each trial encounters an average of 20 obstacles, and the total failure count of each group is recorded synchronously. The proposed EIPPM mechanism employs a closed-loop coupling of perception and planning, achieving a replanning response time of 0.8 s, 68% faster than the A*+DWA method. The path optimization rate reaches 96.3% (a 6.1% improvement), with a collision rate of only 0.9% (the lowest among all compared methods), and a dynamic obstacle avoidance score of 9.7/10. This is mainly due to the dynamic risk map's proactive avoidance capabilities and traffic cost prediction in high-activity areas. Simultaneously, energy consumption is reduced to 0.37 kWh/km (a 9.8% saving). Combined with statistical analysis (p < 0.01), these indicators demonstrate EIPPM's superiority for efficient, safe interactive decision-making in complex, dynamic scenarios. All benchmark methods run on ROS Noetic. Kalman Fusion and DNN Fusion use open-source default parameters. A*+DWA, RRT*+APF, and DRL Planner use the classic parameter settings from the existing literature. All algorithms are tuned under the same hardware and scene conditions.
Sensor data and trajectory analysis

Figure 3. Multi-sensor signal fluctuation and robot trajectory analysis. (A) Three-dimensional wave-propagation model illustrating the spatial distribution of fused-sensor signal amplitudes. (B) Three-dimensional hybrid visualization of the sensor space showing robot trajectories and sampled sensor data generated from LAFA-fused field measurements. Please click here to view a larger version of this figure.
Figure 3 visualizes fused multi-sensor data and robot trajectories. The 0.0-10.8 dB amplitude values are calculated from on-site LiDAR, camera, and IMU data using the LAFA algorithm. Areas with amplitude over 8.0 dB represent strong environmental interference. Amplitude peaks align with the inspection path, and trajectories exhibit clear oscillations when the amplitude exceeds 5.0 dB. Most data points cluster between 2.5 and 7.5 dB, indicating that the system bypasses high-interference regions. The wide spatial coverage and smooth trajectories (curvature change <; 0.6) validate the robot’s adaptability and the superiority of the proposed fusion method for dynamic industrial inspection.

Figure 4. Performance evaluation of the intelligent inspection system. (A) Distribution of reaction rate and product yield derived from robot inspection data. (B) Density distribution illustrating the relationship between reaction rate and product yield during inspection tasks. Please click here to view a larger version of this figure.
Figure 4 shows the performance comparison in real robot inspection tasks. All metrics are derived from the robot’s raw LiDAR, camera, and IMU patrol data. Reaction rate denotes the LAFA fusion module’s average response speed for equipment anomaly capture, while product yield means the share of valid defect outputs screened by EIPPM path planning. Curves quantify the framework’s detection efficiency and environmental adaptability, providing empirical evidence of its practical inspection advantages.

Figure 5. Time-series analysis of sensor signals during inspection. (A) Decomposition of time-series sensor signals into trend, seasonal, residual, and noise components. (B) Electrical sensor signal with the corresponding confidence interval during continuous robot inspection. Please click here to view a larger version of this figure.
As shown in Figure 5, the time-series curves are derived from LiDAR range and camera intensity readings, recorded during a 10-min continuous patrol in the substation scenario. They illustrate real-time perception responses under light variations and dust interference. The proposed LAFA method effectively smooths out signal jitter, maintaining a stable output and directly supporting obstacle detection and real-time collision avoidance in dynamic inspection missions.

Figure 6. Multi-dimensional physical field analysis. Visualization of environmental field characteristics reconstructed from LAFA-fused multi-sensor measurements, illustrating the spatial distribution of environmental dynamics, sensor data points, and field gradients. Please click here to view a larger version of this figure.
As shown in Figure 6, the multi-dimensional physical field data are processed from robot field sensor measurements using the LAFA algorithm to analyze the operating environment and signal performance. This visualization includes 10 analysis layers with distinct spatial distribution, data distribution, and statistical characteristics. The results reflect the spatial pattern of environmental interference and verify the stable performance of the robot perception system.
High-dimensional feature visualization

Figure 7. Multi-dimensional visualization of system performance and environmental response. (A) Three-dimensional stacked bar chart showing subsystem performance metrics across inspection cycles. (B) Three-dimensional surface plot illustrating environmental response intensity together with sampled sensor measurements. Please click here to view a larger version of this figure.
Figure 7 depicts the multi-dimensional operating characteristics of the inspection system. The left 3D stacked bar chart shows subsystem performance across inspection cycles; values of MA, MB, and MC in cycle C3 are 12.4, 9.7, and 15.2, indicating notable load fluctuations. The right surface plot shows environmental response intensity, with a peak of ±18 and most data between -5 and +5, reflecting nonlinear environmental features. The results provide data support for robot sensor fusion and scheduling optimization. MA, MB, and MC represent the load metrics for the perception, path planning, and execution subsystems, respectively.

Figure 8. Three-dimensional characteristics of fused sensor signals under different operating conditions. (A) Sine-function surface. (B) Hyperbolic paraboloid surface. (C) Bessel-function surface. (D) Quantum wavefunction surface. These representative surface models illustrate the spatial characteristics of LAFA-fused sensor signals under different inspection conditions. Please click here to view a larger version of this figure.
As shown in Figure 8, four groups of 3D surface models characterize multi-sensor fusion signals under different inspection working conditions. The spatial variation and attenuation rules of signals are analyzed. These features demonstrate that the LAFA algorithm maintains consistent fusion performance across varying environments and serve as a reference for subsequent path-planning optimization. These 3D surface models are interpolated from LAFA-fused sensor data. Uniform signal distribution across diverse conditions verifies the stable fusion performance of our framework under varying interference.

Figure 9. Robot trajectory and sensor sampling distribution. (A) Parametric butterfly curve representing the geometric characteristics of robot trajectories. (B) Spiral distribution of sensor sampling points illustrating the spatial distribution of inspection data. Please click here to view a larger version of this figure.
As shown in Figure 9, curves and polar graphs are fitted from the robot trajectory and sensor spatial distribution data. Curvature and density are calculated via parametric equations. The spatial distribution rules summarize the robot's motion characteristics and the spatial distribution of multi-sensor sampling points in large-scale inspection scenarios. All plots are fitted from real robot trajectories and sensor sampling points. Uniform sampling distribution and smooth trajectory curves verify the stability of perception and the reliability of path optimization in the proposed LAFA-EIPPM system.

Figure 10. Task performance and robot inspection trajectory visualization. (A) Three-dimensional performance surface showing task performance values and sampled inspection points. (B) Robot inspection trajectory and spatial coverage illustrating the path followed during autonomous inspection. Please click here to view a larger version of this figure.
As shown in Figure 10, the left panel shows the distribution of task performance; the peak is 15.3, the minimum is 5.1, and the fourth task point score is 13.2. The red points are evenly sampled, and the blue line shows the trend. The path (maximum Z = 7.8m) and coverage (height 4.0m) in the right figure show the actual trajectory and spatial coverage. The two graphs comprehensively capture fluctuations in task load and sampling uniformity, providing data to support fusion optimization.
Data Availability:
The experimental datasets generated in this study are not publicly available because they contain site-specific industrial information subject to confidentiality agreements. The restricted materials include factory coordinates, unprocessed LiDAR scans, and confidential device parameters. Access may be considered by the corresponding author on reasonable request, provided that confidentiality obligations can be satisfied.