# Road-Feature-Based Multiparameter Road Complexity Calculation Model of Off-Road Environment

Authors: Yanan Zhao; Zhiwei Li; Li Gao; Jian Xiong
Journal: Mathematical Problems in Engineering
 (2018)

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## Abstract

To promote the development of unmanned ground vehicle technologies, it is necessary to design a scientific and reasonable test method. Road is an important part of test environmental elements, and different road conditions can examine the adaptability of unmanned ground vehicles to the environment. Therefore, the scientific calculation of road complexity is of great importance. Previous studies on road are mainly based on the concept of road roughness; however due to the unicity of road feature indicators, road complexity can only be reflected to a certain extent. This paper proposes a new road-feature-based multiparameter road complexity calculation model of off-road environment to show the complexity of road more comprehensively. First, a multi-sensor-based data acquisition mobile platform is established to obtain more complete road data. Then, based on the analysis of road feature, road indicators like three-dimensional scale, average slope, and adhesion characteristics of travelable area are obtained. According to the analysis methods of road roughness, the principle of analytic hierarchy process, and the data collected from off-road environment, the calculation model of road complexity is determined. Finally, by calculating complexities of several cross-country roads, the feasibility of this model is verified, which provides a theoretical support for the scientific calculation and quantitative analysis of different road complexities.


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## Body

## 1. Introduction

With the rapid development of unmanned ground vehicle (UGV), more and more competitions and tests have been carried out at home and abroad to evaluate the level of UGV [1, 2], but no unified evaluation system has been formed yet. The level of UGV is usually determined by three aspects [3]: environment complexity (EC), mission complexity (MC), and human intervention (HI), wherein EC is the most basic aspect.As an important part of test environmental elements [4], road has a major impact on test and evaluation for UGV [5]. By setting different road conditions, the ability of UGV to adapt to different environments can be examined. For example, in DARPA Grand Challenge 2004, road conditions included well-paved roads, zigzags, hills, swamps, sharp turns, and steep slopes [6], where the performance for UGV to drive autonomously and avoid obstacles in off-road environment was examined; but no vehicle completed the game. In DARPA Grand Challenge 2005 and also in off-road environment, five teams completed the whole process [7] and the ability for vehicles to adapt to off-road environment improved significantly. DARPA Urban Challenge was held at a now-closed air force base to simulate urban traffic environment, focusing on the autonomous driving capacity of UGV in structured environment [8]. “Future Challenge” has been hosted since 2009 [9], where the venues were designed in urban road environment and rural road environment to assess the 4S performance (i.e., safety, smartness, smoothness, and speed) of UGV [10], respectively. The Unmanned Ground System (UGS) Challenge conducted by Chinese Army has been carried out in off-road environment since 2014 [11], where the testing environments included muddy uneven roads and part of hardened roads, so that the comprehensive adaptability of UGV in off-road environment can be assessed. It is due to changes in the road environment, in other words, changes in the complexity of road, that higher performance requirements have been put forward for UGV. UGV needs to improve its performance to comply with traffic rules on structured roads [12] and to ride smoothly on unstructured roads.In order to analyze the road elements quantitatively, “road complexity” is introduced to characterize the complexity of road environment. So far, few studies on road complexity have been carried out at home and abroad, and the research on road complexity in off-road environment is a huge gap. The research on roads till now is mainly based on the concept of road roughness: ASTM E867 standard defines roughness as “the deviation of a surface from a true planar surface with characteristic dimensions affecting vehicle dynamics and ride qualities” [13]. Researchers and organizations usually use international roughness index (IRI), flatness standard deviation, power spectral density (PSD) of profile elevations, and other statistical indicators to analyze road roughness [14]. IRI defined as the integral of the absolute rare difference between the simulated sprung and unsprung mass motion per unit of distance travelled [15] is essentially a computer-based virtual response-type system based on the response of a quarter-car vehicle model as it traverses a tested pavement section at a constant speed of 80 km/h [16]. PSD, a mathematical representation of the spatial wavelength composition of road profiles rather than a summary index of roughness [17], is calculated by the equation provided by ISO 8608 standard [18]; according to PSD, road roughness is divided into eight different classes. Dynamic load index (DLI), representing truck dynamic loads transmitted to road pavements due to the presence of irregularities on pavements surface [19], is calculated as a weighted index of variances of the profile elevations in the frequency ranges of 1.5-4 and 8-15 Hz, where the first frequency range corresponds to truck body bounce, the second frequency range to axle bounce [20]. However, whether it is IRI, PSD, or DLI, it can only reflect the road complexity to a certain extent. Therefore, it is necessary to propose a calculation method that reflects road complexity comprehensively.This paper concentrates on proposing a road-feature-based multiparameter road complexity calculation model of off-road environment. This model takes the longitudinal complexity, lateral complexity, and the travelable width of road into account, thus overcoming the drawbacks of a single indicator. With the multi-sensor-based data acquisition mobile platform, the road feature indicators like three-dimensional scale, average slope, and adhesion characteristics of the travelable area are obtained. By using the improved AHP (Analytic Hierarchy Process) [21], the weights of indicators are determined. Finally, the proposed road complexity calculation model is verified by calculating complexities of several cross-country roads, and the quantitative analysis of the road complexity is realized. By testing on roads with different complexities, it is possible to assess the level of UGV and to facilitate quantitative evaluation of UGV.


## 2. Complexity-Calculation-Based Off-Road Environmental Data Acquisition System

### 2.1. Overall Architecture

In order to calculate the road complexity better, it is vital to have an accurate and comprehensive data acquisition of the road and its surface. The methods to acquire road environmental data can be divided into two major classes: the direct acquisition and the indirect acquisition. The direct acquisition method focuses on collecting the vertical road elevation data, while the indirect acquisition method obtains vibration response of vehicle to calculate TRI (truck ride index) [22], IRI, DLI, etc. Comparatively speaking, the indirect method can not obtain the real road surface data, while the direct acquisition method can obtain more complete road data, thus reflecting the road quality better.In the past few decades, a number of methods have been proposed and experimented to obtain road data directly. Studies have shown that satellite images, aerial photographs, and point cloud data are main data sources for road information [23]. Satellite images and aerial photographs can provide road pixels and its two-dimensional (2D) location information [24], while accurate three-dimensional (3D) road information can only be obtained from point cloud data captured with mobile lidar system (MLS) [25]. MLS is gaining popularity in 3D mapping applications along various road corridors [26, 27]. The precision and accuracy of road information obtained by MLS have been verified [28–30]. A few attempts have been made to compute the road geometry parameters from the MLS dataset. For the characterization of the vertical profiles and cross-sections of roads, a four-step method was devised using MLS data [31]. This method used a hierarchical strategy that includes segmentation, principal component analysis- (PCA-) based orthogonal regression, filtering, and parameter extraction procedures to process the MLS data and computed the best-fit geometric parameters of vertical and cross-sections. Aiming at the determination of road slopes, González-Jorge et al. used the different echoes of the lidar to perform automatic vegetation filtering and georeferenced points to avoid the GPS drift between different surveying [32]. In order to obtain high-precision road terrain, Yadav et al. proposed an automatic method to process MLS data [33]. This method used specific characteristics of a road to identify road surface points and refine road boundary [23]. Further road boundary was approximated to piecewise connected linear segments by using a best-fit polynomial. Road center points were computed by selecting collinear road boundary points at transverse direction. Finally the road width and road slope were computed by road center points and road boundary points.In this paper, a complexity-calculation-based off-road environmental data acquisition system is established to obtain road data directly. The basic architecture of off-road environmental data acquisition system is a stage achievement, which combines the studies of UGS’s environmental design based on complexity and the evaluation of UGS’s autonomous capability. As shown in Figure1, the basic architecture regards the calculation of complexity as the main line, collects local environmental data through cameras, lidars, and other sensors installed on the data acquisition equipment system, and then uses the vehicle-mounted and off-site test environmental data processing software system to extract parameters for complexity calculation. According to the combination method of test environmental elements and the complexity calculation method, along with the design of dynamic and static elements as well as task design in battlefield environment, the full complexity map of roads is formed, which provides a scientific basis to further improve the rules and evaluation method of UGV’s test.Figure 1
Basic architecture of off-road environmental data acquisition system.


### 2.2. Data Acquisition Mobile Platform

Data acquisition equipment system takes a Ford car as platform where the software and hardware system of the multisensor information collection is established. Data acquisition platform R&D (research and development) framework shown in Figure2 includes overall design of platform, selection and installation of sensors, calibration of sensors, and development of data acquisition software. A brief introduction is as follows.Figure 2
Data acquisition platform R&D framework.The overall design of the platform is based on a Ford platform. The Ford car has larger interior space, so the necessary sensors, power supply systems (providing power for sensors and data acquisition system), and data storage systems are installed. The platform also has the synchronous acquisition software to achieve multisensor information synchronization acquisition.Data acquisition sensors mainly include single-layer lidar, multilayer lidar, binocular camera, camera, GPS navigation equipment, gradiometer, and meteorological collection devices. Some sensors are installed on a platform fixed outside the roof; the others are installed inside the vehicle. The arrangement of sensors is shown in Figure3. In this paper, sensor model of single-layer lidar is UTM-30LX-EW 2D laser scanner, and its sampling period is 0.10s. GPS navigation equipment uses a Simpak982 GNSS (Global Navigation Satellite System) receiver to obtain location information of the path, and its sampling period is 0.05s. The resolution of the camera is 800∗600, and the sensor model of gradiometer is DP23850. Binocular camera is used to aid in ranging, and its data are not used in the experiment.Figure 3
Arrangement of sensors.In order to ensure the sensors installed in different locations have a unified coordinate system, it is necessary to establish the corresponding relationships between different sensors. By setting calibration objects and manually selecting the corresponding points, the rotation matrixes and the translation vectors among different coordinate systems of sensors are solved. Based on the difference of sensors, the calibrations are divided into lidar calibration, camera calibration, GPS system calibration, wheel encoder calibration, and the joint calibration. For example, the lidar’s installation parameters are pitch angle and roll angle, which are calibrated by using isosceles right triangle calibration plate and square calibration plate, respectively [34].


## 2.1. Overall Architecture

In order to calculate the road complexity better, it is vital to have an accurate and comprehensive data acquisition of the road and its surface. The methods to acquire road environmental data can be divided into two major classes: the direct acquisition and the indirect acquisition. The direct acquisition method focuses on collecting the vertical road elevation data, while the indirect acquisition method obtains vibration response of vehicle to calculate TRI (truck ride index) [22], IRI, DLI, etc. Comparatively speaking, the indirect method can not obtain the real road surface data, while the direct acquisition method can obtain more complete road data, thus reflecting the road quality better.In the past few decades, a number of methods have been proposed and experimented to obtain road data directly. Studies have shown that satellite images, aerial photographs, and point cloud data are main data sources for road information [23]. Satellite images and aerial photographs can provide road pixels and its two-dimensional (2D) location information [24], while accurate three-dimensional (3D) road information can only be obtained from point cloud data captured with mobile lidar system (MLS) [25]. MLS is gaining popularity in 3D mapping applications along various road corridors [26, 27]. The precision and accuracy of road information obtained by MLS have been verified [28–30]. A few attempts have been made to compute the road geometry parameters from the MLS dataset. For the characterization of the vertical profiles and cross-sections of roads, a four-step method was devised using MLS data [31]. This method used a hierarchical strategy that includes segmentation, principal component analysis- (PCA-) based orthogonal regression, filtering, and parameter extraction procedures to process the MLS data and computed the best-fit geometric parameters of vertical and cross-sections. Aiming at the determination of road slopes, González-Jorge et al. used the different echoes of the lidar to perform automatic vegetation filtering and georeferenced points to avoid the GPS drift between different surveying [32]. In order to obtain high-precision road terrain, Yadav et al. proposed an automatic method to process MLS data [33]. This method used specific characteristics of a road to identify road surface points and refine road boundary [23]. Further road boundary was approximated to piecewise connected linear segments by using a best-fit polynomial. Road center points were computed by selecting collinear road boundary points at transverse direction. Finally the road width and road slope were computed by road center points and road boundary points.In this paper, a complexity-calculation-based off-road environmental data acquisition system is established to obtain road data directly. The basic architecture of off-road environmental data acquisition system is a stage achievement, which combines the studies of UGS’s environmental design based on complexity and the evaluation of UGS’s autonomous capability. As shown in Figure1, the basic architecture regards the calculation of complexity as the main line, collects local environmental data through cameras, lidars, and other sensors installed on the data acquisition equipment system, and then uses the vehicle-mounted and off-site test environmental data processing software system to extract parameters for complexity calculation. According to the combination method of test environmental elements and the complexity calculation method, along with the design of dynamic and static elements as well as task design in battlefield environment, the full complexity map of roads is formed, which provides a scientific basis to further improve the rules and evaluation method of UGV’s test.Figure 1
Basic architecture of off-road environmental data acquisition system.


## 2.2. Data Acquisition Mobile Platform

Data acquisition equipment system takes a Ford car as platform where the software and hardware system of the multisensor information collection is established. Data acquisition platform R&D (research and development) framework shown in Figure2 includes overall design of platform, selection and installation of sensors, calibration of sensors, and development of data acquisition software. A brief introduction is as follows.Figure 2
Data acquisition platform R&D framework.The overall design of the platform is based on a Ford platform. The Ford car has larger interior space, so the necessary sensors, power supply systems (providing power for sensors and data acquisition system), and data storage systems are installed. The platform also has the synchronous acquisition software to achieve multisensor information synchronization acquisition.Data acquisition sensors mainly include single-layer lidar, multilayer lidar, binocular camera, camera, GPS navigation equipment, gradiometer, and meteorological collection devices. Some sensors are installed on a platform fixed outside the roof; the others are installed inside the vehicle. The arrangement of sensors is shown in Figure3. In this paper, sensor model of single-layer lidar is UTM-30LX-EW 2D laser scanner, and its sampling period is 0.10s. GPS navigation equipment uses a Simpak982 GNSS (Global Navigation Satellite System) receiver to obtain location information of the path, and its sampling period is 0.05s. The resolution of the camera is 800∗600, and the sensor model of gradiometer is DP23850. Binocular camera is used to aid in ranging, and its data are not used in the experiment.Figure 3
Arrangement of sensors.In order to ensure the sensors installed in different locations have a unified coordinate system, it is necessary to establish the corresponding relationships between different sensors. By setting calibration objects and manually selecting the corresponding points, the rotation matrixes and the translation vectors among different coordinate systems of sensors are solved. Based on the difference of sensors, the calibrations are divided into lidar calibration, camera calibration, GPS system calibration, wheel encoder calibration, and the joint calibration. For example, the lidar’s installation parameters are pitch angle and roll angle, which are calibrated by using isosceles right triangle calibration plate and square calibration plate, respectively [34].


## 3. Road-Feature-Based Road Complexity Calculation Model

### 3.1. Establishment of Complexity Calculation Model

Road data can be obtained through data acquisition mobile platform. As shown in Figure4, the road features can be divided into longitudinal features, lateral features, and travelable width features, wherein the longitudinal road features affect the longitudinal stability of vehicles and lateral road features affect vehicle lateral stability, while the travelable width affects vehicle passability directly. Compared with urban roads, the surface of cross-country roads has many gullies, and the existence of these gullies reduces the ride performance of vehicles. In this paper, we characterize cross-country roads by wave height difference, wave distance, slope, and adhesion characteristics, along with travelable width, and divide road complexity into longitudinal road complexity, lateral road complexity, and road width complexity. The road complexity Wd can be calculated as(1)Wd=Wx·p1+Wy·p2+Wk·p3The longitudinal road complexity Wx, lateral road complexity Wy, and road width complexity Wk can be calculated as(2)Wx=Wxhd·q1+Wxα·q2+Wxφ·q3(3)Wy=Wyhd·r1+Wyβ·r2+Wyφ·r3(4)Wk=exp⁡-K-B⁡where the road width limit B normally is set to 2, which characterizes the wheel track of the vehicle. K is travelable width. q1,q2,q3,p1,p2,p3,r1,r2,r3 are indicator weights.Figure 4
Off-road environment.The longitudinal road roughnessWxhd includes longitudinal wave height difference complexity Wxh and longitudinal wave distance complexity Wxd. Wxhd can be solved as(5)Wxhd=∑i=04miWxhi+Wxdi2,i=0,1⋯4where(6)Wxhi=HxiH(7)Wxdi=sech⁡Dxi-L,i=1,2,3,4Wxd0=Wxd1It is to be noted that H is a set value (the default value is 0.5 m), which can be seen as the maximum depth of the gully which the vehicle can pass through. mi is an indicator weight. Hxi is the longitudinal wave height. Dxi is the longitudinal wave distance between the peak position and the maximum peak position in a sampling interval. L is a constant with 3, which characterizes the wheelbase of the vehicle.The longitudinal slope complexityWxα and longitudinal adhesion characteristics complexity Wxφ are calculated by the following equations:(8)Wxα=tan⁡α(9)Wxφ=C·sech⁡2·φwhere C is an influencing factor: when the wheels are on the road with different adhesion characteristics at the same time, the value of C is 1.05; otherwise the value of C is 1.0. α is the longitudinal slope and the unit is degree. φ is the adhesion coefficient, and sech is a hyperbolic function.By substituting (5)–(9) into (2), the longitudinal road complexity Wx can be obtained. With the same method, the equations to calculate Wy are(10)Wyhd=∑j=04njWyhj+Wydj2,j=0,1⋯4(11)Wyhj=HyjH(12)Wydj=sech⁡Dyj-B,j=1,2,3,4Wyd0=Wyd1(13)Wyβ=tan⁡β(14)Wyφ=C·sech⁡2·φwhere Wyhd is the lateral road roughness. Wyh is the lateral wave height difference complexity. Wyd is the lateral wave distance complexity. ni is an indicator weight. Hyj is the lateral wave height. Dyj is the lateral wave distance between the peak position and the maximum peak position in a sampling interval. Wyβ is the lateral slope complexity. Wyφ is the lateral adhesion characteristics complexity. β is the lateral slope. By substituting (10)–(14) into (3), the lateral road complexity Wy can be obtained. Finally the road complexity Wd is calculated by substituting (2)–(4) into (1). The overall complexity calculation model can be expressed by the following block diagram (see Figure 5).Figure 5
Complexity calculation model.


### 3.2. Determination of the Indicator Weights

In order to apply the complexity calculation model proposed in this paper, it is of great importance to determine the weight of each indicator. Several feasible methods have been put forward so far, such as AHP, information entropy theory [35], and improved AHP. The improved AHP uses a three-demarcation method to construct judgment matrix, overcoming the subjectivity and blindness of traditional AHP. An optimal transfer matrix model is also used by improved AHP, so the consistency check of judgment matrix is avoided. According to our previous method [21], the specific steps of improved AHP to calculate indicator weight are as follows.Step 1 (establish the judgment matrix).
With the improved AHP, the 3-scale judgment matrix is constructed:(15)A=a11⋯a1n⋮⋱⋮an1⋯annwhere(16)aij=1,iis  more  important  thanj.0,iis  equally  important  thanj.-1,iis  not  as  important  asj.Step 2 (calculate the optimal transfer matrix).
The optimal transfer matrixR is(17)R=r11⋯r1n⋮⋱⋮rn1⋯rnnwhere rij=1/n∑k=1n(aik+akj); then the optimal transfer matrix R is turned into the consistency matrix D:(18)D=d11⋯d1n⋮⋱⋮dn1⋯dnnwhere dik=exp⁡(rik).Step 3 (calculate the relative indicator weights).
The relative indicator weights can be represented by the eigenvector corresponding to the maximum eigenvalue in matrix D. The eigenvector is calculated by product method:(19)ω=ω1,ω2,⋯ωnTωi=∏k=1ndik∑k=1n∏k=1ndik1/nwhere ω=ω1,ω2,⋯ωnT is the weight vector of all factors.


## 3.1. Establishment of Complexity Calculation Model

Road data can be obtained through data acquisition mobile platform. As shown in Figure4, the road features can be divided into longitudinal features, lateral features, and travelable width features, wherein the longitudinal road features affect the longitudinal stability of vehicles and lateral road features affect vehicle lateral stability, while the travelable width affects vehicle passability directly. Compared with urban roads, the surface of cross-country roads has many gullies, and the existence of these gullies reduces the ride performance of vehicles. In this paper, we characterize cross-country roads by wave height difference, wave distance, slope, and adhesion characteristics, along with travelable width, and divide road complexity into longitudinal road complexity, lateral road complexity, and road width complexity. The road complexity Wd can be calculated as(1)Wd=Wx·p1+Wy·p2+Wk·p3The longitudinal road complexity Wx, lateral road complexity Wy, and road width complexity Wk can be calculated as(2)Wx=Wxhd·q1+Wxα·q2+Wxφ·q3(3)Wy=Wyhd·r1+Wyβ·r2+Wyφ·r3(4)Wk=exp⁡-K-B⁡where the road width limit B normally is set to 2, which characterizes the wheel track of the vehicle. K is travelable width. q1,q2,q3,p1,p2,p3,r1,r2,r3 are indicator weights.Figure 4
Off-road environment.The longitudinal road roughnessWxhd includes longitudinal wave height difference complexity Wxh and longitudinal wave distance complexity Wxd. Wxhd can be solved as(5)Wxhd=∑i=04miWxhi+Wxdi2,i=0,1⋯4where(6)Wxhi=HxiH(7)Wxdi=sech⁡Dxi-L,i=1,2,3,4Wxd0=Wxd1It is to be noted that H is a set value (the default value is 0.5 m), which can be seen as the maximum depth of the gully which the vehicle can pass through. mi is an indicator weight. Hxi is the longitudinal wave height. Dxi is the longitudinal wave distance between the peak position and the maximum peak position in a sampling interval. L is a constant with 3, which characterizes the wheelbase of the vehicle.The longitudinal slope complexityWxα and longitudinal adhesion characteristics complexity Wxφ are calculated by the following equations:(8)Wxα=tan⁡α(9)Wxφ=C·sech⁡2·φwhere C is an influencing factor: when the wheels are on the road with different adhesion characteristics at the same time, the value of C is 1.05; otherwise the value of C is 1.0. α is the longitudinal slope and the unit is degree. φ is the adhesion coefficient, and sech is a hyperbolic function.By substituting (5)–(9) into (2), the longitudinal road complexity Wx can be obtained. With the same method, the equations to calculate Wy are(10)Wyhd=∑j=04njWyhj+Wydj2,j=0,1⋯4(11)Wyhj=HyjH(12)Wydj=sech⁡Dyj-B,j=1,2,3,4Wyd0=Wyd1(13)Wyβ=tan⁡β(14)Wyφ=C·sech⁡2·φwhere Wyhd is the lateral road roughness. Wyh is the lateral wave height difference complexity. Wyd is the lateral wave distance complexity. ni is an indicator weight. Hyj is the lateral wave height. Dyj is the lateral wave distance between the peak position and the maximum peak position in a sampling interval. Wyβ is the lateral slope complexity. Wyφ is the lateral adhesion characteristics complexity. β is the lateral slope. By substituting (10)–(14) into (3), the lateral road complexity Wy can be obtained. Finally the road complexity Wd is calculated by substituting (2)–(4) into (1). The overall complexity calculation model can be expressed by the following block diagram (see Figure 5).Figure 5
Complexity calculation model.


## 3.2. Determination of the Indicator Weights

In order to apply the complexity calculation model proposed in this paper, it is of great importance to determine the weight of each indicator. Several feasible methods have been put forward so far, such as AHP, information entropy theory [35], and improved AHP. The improved AHP uses a three-demarcation method to construct judgment matrix, overcoming the subjectivity and blindness of traditional AHP. An optimal transfer matrix model is also used by improved AHP, so the consistency check of judgment matrix is avoided. According to our previous method [21], the specific steps of improved AHP to calculate indicator weight are as follows.Step 1 (establish the judgment matrix).
With the improved AHP, the 3-scale judgment matrix is constructed:(15)A=a11⋯a1n⋮⋱⋮an1⋯annwhere(16)aij=1,iis  more  important  thanj.0,iis  equally  important  thanj.-1,iis  not  as  important  asj.Step 2 (calculate the optimal transfer matrix).
The optimal transfer matrixR is(17)R=r11⋯r1n⋮⋱⋮rn1⋯rnnwhere rij=1/n∑k=1n(aik+akj); then the optimal transfer matrix R is turned into the consistency matrix D:(18)D=d11⋯d1n⋮⋱⋮dn1⋯dnnwhere dik=exp⁡(rik).Step 3 (calculate the relative indicator weights).
The relative indicator weights can be represented by the eigenvector corresponding to the maximum eigenvalue in matrix D. The eigenvector is calculated by product method:(19)ω=ω1,ω2,⋯ωnTωi=∏k=1ndik∑k=1n∏k=1ndik1/nwhere ω=ω1,ω2,⋯ωnT is the weight vector of all factors.


## 4. Experiments

### 4.1. Test Sites

Off-road environment is complex and diverse and due to the limitation of test conditions, only a few cross-country roads (see Figure6) have been chosen, including muddy road, gully road, sand road, and hardened road, to calculate the road complexities. Test sites are in TaHe of China (52.2188N, 124.4124E), where the Unmanned Ground System Challenge (code-named Conquer Obstacle-2016) was held by the Chinese Army [11]. The total length is about 8 kilometers. Figure 7 shows part of the test route. See supplementary materials (available here) for a complete map.Figure 6
Cross-country roads: (a) dry unpaved road, (b) dry unpaved road with small gully, (c) dry unpaved road with larger gully, and (d) wet unpaved road with larger gully.
(a) (b) (c) (d)Figure 7
Test sites. The pink line is test route, and next to the route is road information displayed by the image.


### 4.2. Processing of Dataset

Off-road environmental data are obtained through data acquisition mobile platform. Simpak982 GNSS receiver obtains location information of the path, and the original data format is shown in Figure8. Then GPS data are filtered to obtain latitude, longitude, altitude, and velocity. The angular resolution of UTM-30LX-EW 2D laser scanner is 0.25 degrees, and the scanning range is 120 degrees ahead. So there are 481 data points in each sampling period. The original data format of lidar is shown in Figure 9. It is to be noted that that there are many “1” in the data. During processing, these data will be replaced by their neighboring values. Then the data of lidar are processed with the following equation [34]:(20)z=dlk·cos⁡b0+k·A⁡·sin⁡δ-z0where z is the road roughness, dlk is the scanning distance between lidar and road surface, k is the sequence number of lidar rays, A is the lidar resolution, b0 is the scanning starting angle, δ is the pitch angle, and z0 is the road clearance of lidar. In transverse section of road, Y coordinate value is road roughness, and X coordinate value is calculated by the following formula:(21)x=z0·tan⁡b0+k·Asin⁡δThe parameters like road wave height difference, wave distance, and travelable width are calculated with MATLAB. In order to filter out small height changes, the MATLAB functionsmooth() is used to smooth data. The identification of peak positions is achieved by calling the differential functiondiff() twice. Then the wave height difference and wave distance can be calculated. Lateral road roughness is calculated directly from the lidar data collected in each sampling period, while longitudinal road roughness is calculated by combining GPS data and lidar data. In longitudinal section of road, Y coordinate value is the 241st value of lidar data in each sampling period, and X coordinate value is calculated by multiplying velocity by time. Velocity is extracted from GPS data, and time is the sampling period of UTM-30LX-EW 2D laser scanner. The X coordinate value in longitudinal section of road is accumulated. The first coordinate value X1 is zero, Xi=Xi-1+V·T (V is velocity, T is time, andi =2,3,⋯N). When XN≥L, calculate longitudinal road complexity and zero the X coordinate value. At this point, N lateral road complexity has been calculated and the average is calculated to bring in (1). L is a set value, referring to the classification of pavement structure in PIARC (Permanent International Association of Road Congresses). PIARC sets the construction wavelength of the uneven road to 0.5-50 meters. In this paper, L = 25 meters is chosen as a sampling length.Figure 8
Original data format of GPS.Figure 9
Original data format of lidar. The data are distances between lidar and road surface.The calculation of the road width is achieved by comparing the height difference between two adjacent waves, and if the height difference is greater than threshold, the road boundary is considered to be reached. In this paper, the threshold is 0.5 meters. For detailed codes, see supplementary material. Figure10 shows the process to identify the peak positions, and the largest five crest positions as well as the travelable width are marked in Figure 11.Figure 10
Identification of peak positions.Figure 11
Largest five crest positions and travelable width.In this paper, the slope measured on vehicle is approximately the slope of road. The slope data are obtained by gradiometer. Two gradiometers are installed on the floor of the copilot to measure longitudinal and lateral road slope, wherein one gradiometer is mounted along the direction of travel, and the other is mounted perpendicular to the direction of travel. Quantitative analysis of the adhesion coefficient is very difficult, so the adhesion coefficient of road surface is artificially set by comparing the real road conditions with the experience value. The real road condition is obtained by observing the video, and the experience value is selected by Table1.Table 1
Average adhesion coefficient on various road surfaces.
Road surfaces Peak adhesion coefficient Sliding adhesion coefficient Asphalt or concrete road (dry) 0.8~0.9 0.75 Asphalt road (wet) 0.5~0.7 0.45~0.60 Concrete road (wet) 0.8 0.7 Gravel road 0.6 0.55 Dirt road (dry) 0.68 0.65 Dirt road (wet) 0.55 0.4~0.5 Snowy road 0.2 0.15 Ice road 0.1 0.07


### 4.3. Results and Discussions

Table2 shows the parameters of Figure 6, where the units of height and length are millimeters, and the units of slope are degrees. As mentioned in the previous section, road complexity calculation model includes longitudinal adhesion characteristics complexity, longitudinal road roughness, longitudinal slope complexity, lateral adhesion characteristics complexity, lateral road roughness, lateral slope complexity, and road width complexity. So the road indicators are longitudinal adhesion characteristics, longitudinal road roughness, longitudinal slope, lateral adhesion characteristics, lateral road roughness, lateral slope, and travelable width. According to (15), (17), (18), and (19), matrix A, optimal transfer matrix R, matrix D, and the indicator weights ω are as follows:(22)A=011-1111-101-1-111-1-10-1-1-111110111-111-1011-1-11-1-101-1-1-1-1-1-10R=17048-22610-404-6-226-8-40-10-6-22261004812-226-4048-6-22-8-404-10-6-2-12-8-40D=11.773.140.751.332.364.170.5611.770.420.751.332.360.320.5610.240.420.751.331.332.364.1711.773.145.550.751.332.360.5611.773.140.420.751.330.320.5611.770.240.420.750.180.320.561ω=0.2160.1220.0690.2880.1620.0920.052TThe final weights used in road complexity calculation model are shown in Table 3 and the complexity calculation results are shown in Table 4.Table 2
Parameters of Figure6.
Features Parameters of road feature Figure6(a) Figure6(b) Figure6(c) Figure6(d) H y 0 133.91 109.97 379.22 496.87 H y 1 29.387 106.72 327.03 340.62 H y 2 24.813 94.947 139.56 340.06 H y 3 22.686 77.712 121.41 254.11 H y 4 22.067 62.637 109.57 163.80 H x 0 24.791 76.431 126.59 13.856 H x 1 24.783 50.215 117.59 10.416 H x 2 19.426 40.663 112.83 10.319 H x 3 16.336 38.407 98.155 10.205 H x 4 15.913 31.081 63.261 8.8541 D y 0 237.00 1251.0 233.22 1067.7 D y 1 237.00 1251.0 233.22 1067.7 D y 2 3605.7 3191.7 1720.7 5823.9 D y 3 5438.7 3998.6 8059.6 1704.9 D y 4 2313.3 5775.1 587.14 616.60 D x 0 7900 1120 7960 10195 D x 1 7900 1120 7960 10195 D x 2 3900 4090 2010 10903 D x 3 5130 3270 3370 4200.6 D x 4 2770 1790 4300 1510.3 α 1.25 1.23 2.45 1.95 β 0.30 0.75 1.05 1.25 φ 0.60 0.60 0.60 0.40 K 6576 6103 8899 8229Table 3
Weights.
Symbols m 0 m 1 m 2 m 3 m 4  values 0.3 0.3 0.2 0.1 0.1  Symbols n 0 n 1 n 2 n 3 n 4  values 0.3 0.3 0.2 0.1 0.1  Symbols p 1 p 2 p 3 q 1 q 2  values 0.407 0.542 0.052 0.300 0.169  Symbols q 3 r 1 r 2 r 3 C  values 0.531 0.299 0.170 0.531 1.0Table 4
Results.
Symbols Complexity calculation results Figure6(a) Figure6(b) Figure6(c) Figure6(d) W y h d 0.248 0.401 0.482 0.641 W x h d 0.022 0.279 0.253 0.061 W y β 0.005 0.013 0.018 0.022 W x α 0.022 0.022 0.043 0.034 W y φ 0.552 0.552 0.552 0.748 W x φ 0.552 0.552 0.552 0.748 W x 0.304 0.381 0.377 0.421 W y 0.358 0.406 0.431 0.579 W k 0.010 0.017 0.001 0.002 W d 0.318 0.376 0.387 0.485As can be seen from Table2, the lateral wave height difference is bigger than the longitudinal wave height difference, so the lateral complexity is also larger than the longitudinal complexity. Table 4 shows that the complexities of cross-country roads (Figure 6) increase in turn, and it is in line with the reality. The main influence factor of road complexity is the lateral complexity, which has impacts on lateral stability of the vehicle. The influence of road width on complexity is not obvious, since the travelable width obviously allows vehicle to pass smoothly. When travelable width becomes smaller, the complexity increases exponentially. The relation curve between road complexity and travelable width is shown in Figure 12. The influence of the adhesion coefficient can be seen from the parameters of Figures 6(c) and 6(d). The main difference between Figures 6(c) and 6(d) is that the adhesion coefficient is different. The adhesion coefficient of Figure 6(c) is 0.6, while the adhesion coefficient of Figure 6(d) is 0.4. So the road complexity values are 0.387 and 0.485, respectively, with a difference of about 0.1. By setting different adhesion coefficients for Figure 6(d), the relation curve between the road complexity and adhesion coefficient can be obtained. As it can be seen from Figure 13, for the same road, with the decrease of adhesion coefficient, road complexity increases linearly.Figure 12
Relation curve between complexity and travelable width.Figure 13
Relation curve between complexity and adhesion coefficient.From the results and analysis above, it is shown that the complexity of the road can be quantitatively characterized by road complexity. Road complexity reflects road accessibility. In fact, the test sites of this paper is set for the Unmanned Ground System Challenge. By setting road environment with different complexity, the level of the unmanned vehicle can be checked. During the competition, the road environment is set to dry unpaved road, wet unpaved road, gully road, and paved road, and the road adhesion coefficient is in the range of 0.4-0.8. Only the UGV with excellent off-road capability can successfully pass all the test sections. By setting up snow and ice roads or muddy roads, it is possible to set up a more complex road environment to test the adaptability of UGV in harsh environments.


## 4.1. Test Sites

Off-road environment is complex and diverse and due to the limitation of test conditions, only a few cross-country roads (see Figure6) have been chosen, including muddy road, gully road, sand road, and hardened road, to calculate the road complexities. Test sites are in TaHe of China (52.2188N, 124.4124E), where the Unmanned Ground System Challenge (code-named Conquer Obstacle-2016) was held by the Chinese Army [11]. The total length is about 8 kilometers. Figure 7 shows part of the test route. See supplementary materials (available here) for a complete map.Figure 6
Cross-country roads: (a) dry unpaved road, (b) dry unpaved road with small gully, (c) dry unpaved road with larger gully, and (d) wet unpaved road with larger gully.
(a) (b) (c) (d)Figure 7
Test sites. The pink line is test route, and next to the route is road information displayed by the image.


## 4.2. Processing of Dataset

Off-road environmental data are obtained through data acquisition mobile platform. Simpak982 GNSS receiver obtains location information of the path, and the original data format is shown in Figure8. Then GPS data are filtered to obtain latitude, longitude, altitude, and velocity. The angular resolution of UTM-30LX-EW 2D laser scanner is 0.25 degrees, and the scanning range is 120 degrees ahead. So there are 481 data points in each sampling period. The original data format of lidar is shown in Figure 9. It is to be noted that that there are many “1” in the data. During processing, these data will be replaced by their neighboring values. Then the data of lidar are processed with the following equation [34]:(20)z=dlk·cos⁡b0+k·A⁡·sin⁡δ-z0where z is the road roughness, dlk is the scanning distance between lidar and road surface, k is the sequence number of lidar rays, A is the lidar resolution, b0 is the scanning starting angle, δ is the pitch angle, and z0 is the road clearance of lidar. In transverse section of road, Y coordinate value is road roughness, and X coordinate value is calculated by the following formula:(21)x=z0·tan⁡b0+k·Asin⁡δThe parameters like road wave height difference, wave distance, and travelable width are calculated with MATLAB. In order to filter out small height changes, the MATLAB functionsmooth() is used to smooth data. The identification of peak positions is achieved by calling the differential functiondiff() twice. Then the wave height difference and wave distance can be calculated. Lateral road roughness is calculated directly from the lidar data collected in each sampling period, while longitudinal road roughness is calculated by combining GPS data and lidar data. In longitudinal section of road, Y coordinate value is the 241st value of lidar data in each sampling period, and X coordinate value is calculated by multiplying velocity by time. Velocity is extracted from GPS data, and time is the sampling period of UTM-30LX-EW 2D laser scanner. The X coordinate value in longitudinal section of road is accumulated. The first coordinate value X1 is zero, Xi=Xi-1+V·T (V is velocity, T is time, andi =2,3,⋯N). When XN≥L, calculate longitudinal road complexity and zero the X coordinate value. At this point, N lateral road complexity has been calculated and the average is calculated to bring in (1). L is a set value, referring to the classification of pavement structure in PIARC (Permanent International Association of Road Congresses). PIARC sets the construction wavelength of the uneven road to 0.5-50 meters. In this paper, L = 25 meters is chosen as a sampling length.Figure 8
Original data format of GPS.Figure 9
Original data format of lidar. The data are distances between lidar and road surface.The calculation of the road width is achieved by comparing the height difference between two adjacent waves, and if the height difference is greater than threshold, the road boundary is considered to be reached. In this paper, the threshold is 0.5 meters. For detailed codes, see supplementary material. Figure10 shows the process to identify the peak positions, and the largest five crest positions as well as the travelable width are marked in Figure 11.Figure 10
Identification of peak positions.Figure 11
Largest five crest positions and travelable width.In this paper, the slope measured on vehicle is approximately the slope of road. The slope data are obtained by gradiometer. Two gradiometers are installed on the floor of the copilot to measure longitudinal and lateral road slope, wherein one gradiometer is mounted along the direction of travel, and the other is mounted perpendicular to the direction of travel. Quantitative analysis of the adhesion coefficient is very difficult, so the adhesion coefficient of road surface is artificially set by comparing the real road conditions with the experience value. The real road condition is obtained by observing the video, and the experience value is selected by Table1.Table 1
Average adhesion coefficient on various road surfaces.
Road surfaces Peak adhesion coefficient Sliding adhesion coefficient Asphalt or concrete road (dry) 0.8~0.9 0.75 Asphalt road (wet) 0.5~0.7 0.45~0.60 Concrete road (wet) 0.8 0.7 Gravel road 0.6 0.55 Dirt road (dry) 0.68 0.65 Dirt road (wet) 0.55 0.4~0.5 Snowy road 0.2 0.15 Ice road 0.1 0.07


## 4.3. Results and Discussions

Table2 shows the parameters of Figure 6, where the units of height and length are millimeters, and the units of slope are degrees. As mentioned in the previous section, road complexity calculation model includes longitudinal adhesion characteristics complexity, longitudinal road roughness, longitudinal slope complexity, lateral adhesion characteristics complexity, lateral road roughness, lateral slope complexity, and road width complexity. So the road indicators are longitudinal adhesion characteristics, longitudinal road roughness, longitudinal slope, lateral adhesion characteristics, lateral road roughness, lateral slope, and travelable width. According to (15), (17), (18), and (19), matrix A, optimal transfer matrix R, matrix D, and the indicator weights ω are as follows:(22)A=011-1111-101-1-111-1-10-1-1-111110111-111-1011-1-11-1-101-1-1-1-1-1-10R=17048-22610-404-6-226-8-40-10-6-22261004812-226-4048-6-22-8-404-10-6-2-12-8-40D=11.773.140.751.332.364.170.5611.770.420.751.332.360.320.5610.240.420.751.331.332.364.1711.773.145.550.751.332.360.5611.773.140.420.751.330.320.5611.770.240.420.750.180.320.561ω=0.2160.1220.0690.2880.1620.0920.052TThe final weights used in road complexity calculation model are shown in Table 3 and the complexity calculation results are shown in Table 4.Table 2
Parameters of Figure6.
Features Parameters of road feature Figure6(a) Figure6(b) Figure6(c) Figure6(d) H y 0 133.91 109.97 379.22 496.87 H y 1 29.387 106.72 327.03 340.62 H y 2 24.813 94.947 139.56 340.06 H y 3 22.686 77.712 121.41 254.11 H y 4 22.067 62.637 109.57 163.80 H x 0 24.791 76.431 126.59 13.856 H x 1 24.783 50.215 117.59 10.416 H x 2 19.426 40.663 112.83 10.319 H x 3 16.336 38.407 98.155 10.205 H x 4 15.913 31.081 63.261 8.8541 D y 0 237.00 1251.0 233.22 1067.7 D y 1 237.00 1251.0 233.22 1067.7 D y 2 3605.7 3191.7 1720.7 5823.9 D y 3 5438.7 3998.6 8059.6 1704.9 D y 4 2313.3 5775.1 587.14 616.60 D x 0 7900 1120 7960 10195 D x 1 7900 1120 7960 10195 D x 2 3900 4090 2010 10903 D x 3 5130 3270 3370 4200.6 D x 4 2770 1790 4300 1510.3 α 1.25 1.23 2.45 1.95 β 0.30 0.75 1.05 1.25 φ 0.60 0.60 0.60 0.40 K 6576 6103 8899 8229Table 3
Weights.
Symbols m 0 m 1 m 2 m 3 m 4  values 0.3 0.3 0.2 0.1 0.1  Symbols n 0 n 1 n 2 n 3 n 4  values 0.3 0.3 0.2 0.1 0.1  Symbols p 1 p 2 p 3 q 1 q 2  values 0.407 0.542 0.052 0.300 0.169  Symbols q 3 r 1 r 2 r 3 C  values 0.531 0.299 0.170 0.531 1.0Table 4
Results.
Symbols Complexity calculation results Figure6(a) Figure6(b) Figure6(c) Figure6(d) W y h d 0.248 0.401 0.482 0.641 W x h d 0.022 0.279 0.253 0.061 W y β 0.005 0.013 0.018 0.022 W x α 0.022 0.022 0.043 0.034 W y φ 0.552 0.552 0.552 0.748 W x φ 0.552 0.552 0.552 0.748 W x 0.304 0.381 0.377 0.421 W y 0.358 0.406 0.431 0.579 W k 0.010 0.017 0.001 0.002 W d 0.318 0.376 0.387 0.485As can be seen from Table2, the lateral wave height difference is bigger than the longitudinal wave height difference, so the lateral complexity is also larger than the longitudinal complexity. Table 4 shows that the complexities of cross-country roads (Figure 6) increase in turn, and it is in line with the reality. The main influence factor of road complexity is the lateral complexity, which has impacts on lateral stability of the vehicle. The influence of road width on complexity is not obvious, since the travelable width obviously allows vehicle to pass smoothly. When travelable width becomes smaller, the complexity increases exponentially. The relation curve between road complexity and travelable width is shown in Figure 12. The influence of the adhesion coefficient can be seen from the parameters of Figures 6(c) and 6(d). The main difference between Figures 6(c) and 6(d) is that the adhesion coefficient is different. The adhesion coefficient of Figure 6(c) is 0.6, while the adhesion coefficient of Figure 6(d) is 0.4. So the road complexity values are 0.387 and 0.485, respectively, with a difference of about 0.1. By setting different adhesion coefficients for Figure 6(d), the relation curve between the road complexity and adhesion coefficient can be obtained. As it can be seen from Figure 13, for the same road, with the decrease of adhesion coefficient, road complexity increases linearly.Figure 12
Relation curve between complexity and travelable width.Figure 13
Relation curve between complexity and adhesion coefficient.From the results and analysis above, it is shown that the complexity of the road can be quantitatively characterized by road complexity. Road complexity reflects road accessibility. In fact, the test sites of this paper is set for the Unmanned Ground System Challenge. By setting road environment with different complexity, the level of the unmanned vehicle can be checked. During the competition, the road environment is set to dry unpaved road, wet unpaved road, gully road, and paved road, and the road adhesion coefficient is in the range of 0.4-0.8. Only the UGV with excellent off-road capability can successfully pass all the test sections. By setting up snow and ice roads or muddy roads, it is possible to set up a more complex road environment to test the adaptability of UGV in harsh environments.


## 5. Conclusions

In this paper, a road-feature-based multiparameter road complexity calculation model of off-road environment is presented. This model uses wave height difference, wave distance, slope, adhesion characteristics, and travelable width as road feature indicators and takes the longitudinal road complexity, lateral road complexity, and the travelable width into account, thus overcoming the drawbacks of single indicator of other methods, reflecting the complexities of different roads more comprehensively. Through the calculation of road complexities in cross-country roads, the feasibility of this model is verified. Experiments show that this model can quantitatively analyze road complexity in off-road environment and provide a theoretical support for the scientific calculation of different road complexities.In addition, an overall architecture of data acquisition system is also presented, which provides an effective method for environmental data acquisition. The indicator weights are calculated by using improved AHP, which makes the determination of indicator weights more scientific.Due to the limited test samples, only some road complexities are calculated. In future work, more tests are expected to be conducted to obtain more road environmental data, and a road complexity database is expected to be established to provide data support for environment design of unmanned vehicle testing.



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*Source: 1952792-2018-10-25.xml*