Intelligent cruise detection system for aerosols is shown in Fig. 1. The system comprises a control module, an aerosol detection module, an environment sensing and positioning module, and a wire control chassis module, and is integrated into a small electric unmanned vehicle. The control module is composed of industrial controller, computing platform, vehicle controller and gateway. The selected computing platform hosts the Baidu Apollo autonomous driving system. The environment sensing and positioning module includes vehicle LiDAR, binocular camera, and an integrated navigation system (including GPS antenna and inertial navigation). The vehicle LiDAR is a 16-line laser LiDAR, which integrates 16 laser emission channels. It has a maximum detection range exceeding 150 m, a ranging accuracy of ± 2 cm, a point cloud output rate of up to 320 000 points per second, and features a 360° horizontal field of view and a 30° vertical field of view. The binocular camera selected is the “Changjiang-5” binocular stereo camera. In the experimental process of this system, binocular camera serves as an auxiliary sensing method with a relatively low frequency of use and does not act as the primary source of perception information. The wire control chassis module consists of brake module, drive module and steering module.

The aerosol detection module and the unmanned vehicle system each have their own control units. As the “brain” of the whole system, the control module controls the operation of the whole system. The computing platform receives the localization data and environmental data detected by the environment awareness and localization module through the processing gateway. Based on this input, it's dynamically computing the required gear ratio, velocity parameters, and braking force for the unmanned vehicle and transmits these values via the vehicle controller to the wire control chassis module. The wire control chassis module feeds back the state of the moving vehicle parameters (speed, acceleration, rotational speed and braking, etc.) to the computing platform. The environment sensing and positioning module communicates with the computing platform via the Internet, while the Drive-by-Wire Chassis Module communicates with it via the CAN bus. The aerosol detection module installed on top of the unmanned vehicle employs a compact, portable Mie-scattering LiDAR. The overall dimensions of the Mie-scattering LiDAR are controlled within 200 × 200 × 420 mm, with a total weight of 13.5 kg and a power consumption of less than 100 W (Kuang et al., 2023). The LiDAR system comprises a transmitting optical path, a receiving optical path and a dual-channel detection unit. The 1064 nm laser beam is expanded and emitted into the atmosphere. Backscattered light from aerosols and atmospheric molecules is collected by the receiving telescope, then split into two polarization channels by a polarization prism. The beams are focused onto avalanche photodiodes for photoelectric conversion, followed by multi-pulse integration in the data acquisition card. An embedded control board with dedicated Mie-scattering LiDAR software manages system timing, laser triggering, and data acquisition, storage and transmission.

An Nd:YAG solid-state laser emitting 1064 nm eye-safe infrared radiation with a pulse repetition frequency of 10 kHz and a single-pulse energy of 15 µJ is employed in the transmitter. An avalanche photodiode (APD) is used as the photodetector, and a GCC-402053 polarization prism is integrated in the optical path for aerosol depolarization measurement. The LiDAR has a range resolution of 7.5 m and 1800 acquisition channels, with a theoretical maximum detection altitude of 13.5 km. Limited by laser energy attenuation during long-term observation, its practical effective vertical detection altitude stably exceeds 2.5 km, meeting the requirement for vertical pollutant detection in industrial parks.The Mie-scattering LiDAR is equipped with a 1064 nm light source and an APD detector. Developed for aerosol monitoring, it is designed for high-precision detection of the vertical fine structure of aerosols and clouds. Its backscattered LiDAR signals include Mie scattering from aerosol particles and Rayleigh scattering from atmospheric molecules, with Rayleigh scattering generally weaker in the atmospheric boundary layer, where Mie scattering dominates under high aerosol loading (Freudenthaler et al., 2018). The LiDAR system and the industrial controller form an integrated system. All modules within the LiDAR system communicate with the industrial controller via TCP/IP protocols over Ethernet/Wi-Fi networks. The inverter provides a stable 220 V power supply to the LiDAR and computing platform. Figure 1b is the module distribution of the detection system. The relevant technical parameters of the system can be seen in Table 1.

Laser pulses are emitted into the atmosphere by the Mie-scattering LiDAR, and energy attenuation of the laser occurs along its propagation path as a result of the atmospheric extinction effect. A portion of these laser pulses are backscattered by aerosol particles and air molecules and returned along the original propagation path, with extinction attenuation undergone once again during the return propagation (Megie, 1985). The telescope of the LiDAR ultimately captures the returning light, and the acquired backscattered LiDAR signals are substituted into the LiDAR equation (Yang et al., 2021): 1Pz=Cβmz+βaz⋅e{-2∫0zαmz′+αaz′dz′}z2 In Eq. (1), P(z) is the received backscattered LiDAR signals of height z, C is the LiDAR constant. βm and βa are the backscattering coefficients of atmospheric molecules and aerosols respectively. αm and αa are the extinction coefficients of atmospheric molecules and aerosol molecules, respectively. z is the height of aerosol LiDAR detection.

In this study, the original backscattered LiDAR signals are mainly processed by range-squared correction to obtain the Range-Corrected Signal (RCS), which is used to qualitatively reflect the trends in aerosol concentration and vertical distribution characteristics. The equation of Range-corrected signal is: 2X(z)=P(z)⋅z2

Considering experimental safety, the speed is maintained at a low level, all wheels are in a rolling state, and the influence of lateral force is ignored; vehicle dynamics are ignored, so only the vehicle kinematic model is considered.

In Fig. 2 L, f, r and d are the wheelbase, front overhang, rear overhang and width of the vehicle respectively; point R(x, y) is the center of the rear axle of the vehicle; v is the velocity of point R along the longitudinal axis of the vehicle; O is the instantaneous steering center of the vehicle; φ is the equivalent swing angle of the front wheel; θ is the heading angle of the vehicle; A, B, C and D are the four contour vertices of the vehicle body respectively.

During the vehicle movement process, the state variables of point R(x, y) in the ground coordinate system include: lateral displacement x, longitudinal displacement y, velocity of the rear axle center point v, vehicle acceleration a, vehicle heading angle θ, and equivalent swing angle of the front wheel φ; The control variables include the vehicle acceleration rate j and the angular velocity of the front wheel's equivalent swing angle ω. Thus, the kinematic differential equations of the vehicle can be obtained as follows: 3ddtx(t)y(t)v(t)a(t)θ(t)φ(t)=v(t)⋅cos⁡θ(t)v(t)⋅sin⁡θ(t)a(t)j(t)v(t)⋅tan⁡φ(t)/Lω(t),t∈t0,tf In Eq. (3): t0 and tf are the initial and termination moments respectively of the unmanned vehicle respectively.

Vehicle collision avoidance constraints are important when solving trajectory planning problems. The actual top-view projection shape of the vehicle is close to a rectangle. Here the vehicle contour is depicted with an enlarged rectangle. dsafe is the safety threshold to ensure that the vehicle is collision free.

As shown in Fig. 3 the red area around the vehicle is the safety threshold to ensure a collision-free vehicle. If the vehicle does not collide with point M while traveling, the point M coordinates are always outside the rectangular ABCD region. Remember that the four sides of the rectangle are the lines LAB, LBC, LCD, and LAD, and their linear equations are as follows:

4LAB=k1⋅x+y1LCD=k1⋅x+y2LAD=k2⋅x+y3LBC=k2⋅x+y4 k1 is the slope of the lines LAB, and LCD, k2 is the slope of the lines LAD, and LBC. If the line LAB is parallel or perpendicular to the X-axis so that the point M is outside the rectangle ABCD, then the coordinates of the point M must satisfy the following conditions: 5Mix<Dx(t)orMix>Ax(t)orMiy<Cy(t)orMiy>Ay(t),θ=0°Mix<Dx(t)orMix>Cx(t)orMiy<Dy(t)orMiy>Ay(t),θ=90°Mix<Ax(t)orMix>Dx(t)orMiy<Dy(t)orMiy>Cy(t),θ=180°Mix<Dx(t)orMix>Cx(t)orMiy<Ay(t)orMiy>Dy(t),θ=270° In Eq. (5), i= 1, 2, 3, 4 represent the four vertices of the rectangle. For a line LAB that is neither parallel nor perpendicular to the X-axis, if point M lies outside the quadrilateral ABCD, the following conditions must hold: 6(Miy-k1⋅Mix)<y2or(Miy-k1⋅Mix)>y1(Miy-k2⋅Mix)<y4or(Miy-k2⋅Mix)>y3

The motion of a vehicle is fundamentally a problem of solving a dynamic system. Incorporating constraints and an objective function then forms an optimal control problem. This paper employs the segmented Gaussian pseudo-spectral method to solve the optimal control problem. The method constructs Lagrange interpolation polynomials to approximate the state and control variables after discretizing the continuous optimization problem at the Legendre-Gauss (LG) collocation point. And replace the differential equation constraints with algebraic constraints, thus transforming the optimal control problem into a Nonlinear Programming (NLP) problem to be solved. Qiu et al. (2021) proposed a hierarchical trajectory planning and tracking control algorithm for unmanned vehicles combining Model Predictive Control (MPC) and Gaussian Pseudo-spectral Method (GPM).

An optimal control problem typically comprises: the system dynamics differential equations, physical constraints, obstacle avoidance constraints, boundary constraints, and a performance index function. The optimal control parameters are obtained by minimizing the performance index function while satisfying all constraints. The Bolza problem in nonlinear optimization is one of the main problems in classical calculus of variations that deals with the conditions for extreme points under certain constraints (Wang et al., 2021). This problem has a special feature of the mixed nature of the functional represented as the sum of an integral functional and a function on the boundary. It not only emphasizes the system state at the terminal moment, but also stresses the requirements for the control system process. Without loss of generality, the Bolza problem for nonlinear optimal control can be described as: 7minψ=ϕ(ξt0,t0,ξtf,tf)+∫t0tfg(ξt,μt,t)dt In Eq. (7): ξ(t) and μ(t) are the state and control variables of the system, respectively. The state variables ξ(t) encompass the vehicle's longitudinal displacement x, lateral displacement y, velocity v, acceleration a, heading angle θ, and wheel steering angle φ. The control variables include the wheel angular velocity ω and jerk ξ(t)∈Rn and μ(t)∈Rm satisfy. 8s.t.ξ˙(t)=f(ξ(t),μ(t),t)M(ξ(t),μ(t),t)≤0N(ξt0,t0,ξtf,tf)=0t∈t0,tf In Eq. (8): In the first line, describes the differential equation of state of the system. In the second line, M(ξ(t),μ(t),t)≤0 represents the inequality constraints in the vehicle's path planning, including collision avoidance constraints and the physical limitations of the vehicle system (such as maximum speed, maximum steering angle, acceleration limits, etc.).In the third line, N(ξ(t0),t0,ξ(tf),tf)=0 represents the equality constraints in the vehicle's path planning, including the condition that the vehicle is stationary at both the initial and final times, as well as the continuity constraints in multi-stage planning (i.e., the terminal state of the previous stage must equal the initial state of the subsequent stage).

Based on the above context, the nonlinear optimal control problem for vehicle trajectory planning can be described as follows: the objective is to minimize tf, that is min tf. Meanwhile, within the time interval t∈ [t0, tf], the vehicle system must satisfy the state differential equations, physical system constraints, obstacle avoidance constraints, and boundary condition constraints. The detailed solution procedure of the optimal control problem via the Gaussian pseudospectral method can be found in the Appendix.

Kinematic Eq. (3) defines the feasible motion capability of the vehicle. This equation characterizes the relationship between control inputs (jerk and front-wheel angular velocity) and the evolution of the vehicle states. The obstacle locations provided by the perception module are incorporated as path constraints in the trajectory planning problem, such that all obstacles must remain outside the vehicle's safety envelope throughout the planned path, thereby restricting the feasible state space. The optimal control algorithm searches within this constrained space to solve for the optimal control inputs, ensuring that the generated trajectory avoids obstacles while also adhering to the vehicle's kinematic constraints.

We conducted continuous fixed-point outdoor detection in Hefei (31.8593° N, 117.2160° E) on 24 February 2025. Figure 4a shows the Range-corrected signal data of that day. In Fig. 4a, the temporal evolution of the vertical distribution of the near-surface aerosol layer is illustrated. The height of the aerosol layer was maintained at about 1.5 km for a long period of time. The Range-corrected signal intensity of aerosol exhibits relatively high values below 1 km. The signal intensity shows pronounced temporal variability, gradually decreasing from 1 to 0.2 ∼ 0.3 W × km² between 06:00 and 17:00 UTC. After 17:00 UTC, the signal intensity recovers and stabilizes at approximately 0.5 W × km². Clouds were also detected at 2 to 2.5 km.

Many previous studies have correlated multi-source data with LiDAR data to investigate variations in aerosol concentration (Tu et al., 2022; Xiao et al., 2023). In order to verify the accuracy of the system's detection, we also selected the hourly particulate matter concentration observed at the ground station in Hefei City on 24 February. Figure 4b shows the variation curve of particulate matter concentration on the 24th (daily average concentration thresholds of 150 and 75 µg m⁻³ for PM₁₀ and PM_2.5, respectively). When the PM_2.5 / PM₁₀ ratio is below 0.5, it means large particle pollutants account for the main part of the air. When the ratio is 0.5 or above, it indicates that air pollution is dominated by fine particle pollutants. PM_2.5 and PM₁₀ concentrations were higher than 100 µg m⁻³ from 00:00 to 05:00 UTC. PM_2.5 / PM₁₀ values were around 0.8, indicating that the pollution in this phase is local fine particulate matter. Then, the three curves dropped rapidly reaching a minimum at 10:00 UTC (56 µg m⁻³ for PM₁₀; 23 µg m⁻³ for PM_2.5 and 0.41 for PM_2.5 / PM₁₀). At 16:00 UTC, the subsequent concentrations all rebounded, and the PM_2.5 / PM₁₀ value stabilized between 0.5 and 0.6. The variation trend of the particulate matter concentration data is consistent with the detection results of the LiDAR.

To verify the physical rationality of the observation results, the vertical aerosol distribution from this cruise detection is compared with contemporaneous MERRA-2 reanalysis data. As a large-scale product, MERRA-2 reflects the regional aerosol spatiotemporal variation and transport background, while the LiDAR captures fine local vertical structures, showing complementary spatial scales. Given the limited single-day samples and result contingency, MERRA-2 serves only as a large-scale atmospheric reference to confirm the consistency of LiDAR results with regional background characteristics and exclude instrument anomalies and inversion deviations. By retrieving the MERRA-2 reanalysis data (Figs. 5 and 6). Figure 5 shows that Hefei experienced a distinct aerosol pollution episode from the 22nd to the 24th. Figure 6 shows the hourly averaged data on the 23rd. Figure 6a–c illustrate the northwest-to-southeast transport of the pollution plume from 11:30 to 14:30 UTC, with the Hefei area impacted by the pollution process. However, constrained by its relatively coarse spatial resolution, MERRA-2 struggles to capture the details of local, short-term, and vertical variations in aerosols. Through vertical detections and comparative analysis, we can obtain a more refined vertical distribution of aerosols from the LiDAR results. The comparison shows consistency in the main aerosol layer height and signal intensity variation trend, preliminarily verifying the physical rationality of the system observations. Restricted by the test period and site constraints, this study concentrates on the system integration and detection feasibility verification of the unmanned vehicle-borne aerosol LiDAR, and continuous observations under diverse conditions and over multiple periods are not performed in the current work. Future work will expand samples covering different pollution levels and meteorological conditions, and conduct systematic cross-validation and quantitative accuracy evaluation combining MERRA-2 data, ground monitoring data and synchronous fixed-point LiDAR observations.

Cone-scanning detection relies on the synchronous rotation of the LiDAR gimbal in both elevation and azimuth to realize three-dimensional spatial sampling. With a fixed elevation angle, the LiDAR rotates uniformly over the full 0–360° azimuth range to conduct stereoscopic tomographic sampling of the atmosphere within a 2.5 km detection radius. This mode can simultaneously capture the spatial distribution of aerosol and cloud masses at different azimuths and altitudes, compensating for the limitation of fixed-point vertical detection, which only provides single vertical profiles and lacks horizontal spatial coverage.

Owing to constraints imposed by the experimental environment, horizontal scanning is not feasible. We conducted cone-scanning detection experiments in Hefei (31.8593° N, 117.2160° E) on 28 February, 5 and 6 March 2025, respectively. To ensure reliable retrieval results, backscattering LiDAR signals from a sufficient number of independent laser pulses are accumulated at each azimuth angle. The parameters are set as follows: the 0° direction corresponds to due west, the elevation angle is 75°, the step angle is 1°, and the full scan takes approximately 1 h. The Range-corrected data were optioned for a range of 2.5 km. Figure 7 shows the Range-corrected signal of cloudy days (28 February), polluted days (5 March) and clean days (6 March). Cloudy condition on 28 February (Fig. 7a): Continuous cloud echoes are observed at 2 km altitude in the 0–100° southeast azimuth, with only sparse aerosol plumes at 2.1–2.3 km, indicating low overall aerosol loading; Polluted condition on 5 March (Fig. 7b): Thin clouds are widely distributed at 0.85–1.5 km near the ground. Aerosol plumes spread along the scanning circumference with a much larger coverage, and high near-ground backscattered LiDAR signals reflect elevated regional aerosol concentrations; Clean condition on 6 March (Fig. 7c): No concentrated cloud or aerosol signals are observed across the entire detection radius. The values of range-corrected signals stay at extremely low levels throughout the field of view, demonstrating clean atmospheric conditions. The system can achieve three-dimensional scanning and positioning tracking of atmospheric aerosols.

We did an unmanned intelligent cruise detection experiment in Hefei (31.8593° N, 117.2160° E) on 26 February. The location of the experiment was chosen near a laboratory building within the school. See Table 1 for unmanned vehicle parameters. The physical constraints are shown in Table 2. Figure 8 shows the validation and simulation analysis of the trajectory planning algorithm based on the Gaussian pseudo-spectral method. Through simulation and emulation, we can achieve obstacle avoidance during the cruising detection process, and ensure safe and normal cruising according to the planned path.

Before the experiment, enter the Mie-scattering LiDAR system to configure the relevant detection parameters. This is followed by turning on the wire control chassis module of the unmanned vehicle and the modules related to the environment sensing and positioning module. Finally, the planned path is selected and the vehicle switches to autopilot.

Figure 9 shows a plot of the Range-corrected signal from one unmanned cruise detection. We first clarify the background air pollution conditions on the test day: the air quality index (AQI) of Hefei reached 115,with synchronous ground monitoring values of PM_2.5 was 80 µg m⁻³, and PM₁₀ was 100 µg m⁻³ (Data from China Environmental Monitoring Station; https://air.cnemc.cn:18007/, last access: 18 October 2026). It can be seen from Fig. 9a that the near-surface pollution layer was confined within the altitude range of 0–0.3 km throughout the observation period. The range-corrected signal gradually decreased from 0.8 to 0.2 W × km² as the vehicle cruised forward, indicating a continuous reduction of aerosol concentration along the traveling path. In the later stage of the experiment, the aerosol layer rose to 0.5 km, which corresponds to the gradual uplifting of the local atmospheric boundary layer and the increased vertical diffusion height of aerosols over time.

This cruise measurement demonstrates the unique advantages of the vehicle-borne detection system over fixed-point LiDAR. Conventional fixed-site LiDAR can only acquire time-resolved vertical aerosol profiles at a single location. In contrast, this unmanned cruising observation system enables the acquisition of three-dimensional spatial aerosol distributions with geolocation and altitude information.