Cloud Model Approach for Lateral Control of Intelligent Vehicle Systems

Studies on intelligent vehicles, among which the controlling method of intelligent vehicles is a key technique, have drawn the attention of industry and the academe.This study focuses on designing an intelligent lateral control algorithm for vehicles at various speeds, formulating a strategy, introducing the Gauss cloud model and the cloud reasoning algorithm, and proposing a cloud control algorithm for calculating intelligent vehicle lateral offsets. A real vehicle test is applied to explain the implementation of the algorithm. Empirical results show that if the Gauss cloud model and the cloud reasoning algorithm are applied to calculate the lateral control offset and the vehicles drive at different speeds within a direction control area of ±7, a stable control effect is achieved.


Introduction
In academic and industrial circles, studies on intelligent vehicles have drawn considerable attention.Such studies play an important role in the research on vehicles and intelligent transportation.Control methods are the key in the study of intelligent vehicles.Vehicle model parameters are extremely complex.The system model equation is nonlinear, and its system parameters constantly change over time.Research on vehicle control theory includes lateral tracking control and longitudinal tracking control.Lateral tracking control includes the support vector machine (SVM) method, the sublevel control method [1], the traditional PID (Proportional-Integral-Derivative) method [2], and the intelligent method.The latter includes the fuzzy control [3,4] and neural network control methods [5,6].Longitudinal tracking control includes the coordination of the brake and the accelerator as well as the antijamming capability of the control accuracy.One important study on intelligent vehicle control is the Urban Challenge, which was organized by DARPA (Defense Advanced Research Projects Agency) in 2007.The champion, "BOSS," used a road navigation and regional navigation control strategy [7].The third placer, the "Odin" team, used a control model [8] based on driver behavior.The "Talos" team applied the output path of the navigator and the speed commands of the low-level controller output, using the method based on a RRT (Rapidly-exploring-Random-Tree) [9], and generated a dynamic trajectory feasible tree through countless random samples, thereby expanding the typical RRT [10].Current self-adaptive control methods of intelligent vehicles modify parameters of PID on the basis of changes in intelligent vehicle states and object properties, thereby improving control.They mainly include adaptive control reference models [11], adaptive control fuzzy models [12,13], adaptive control neural networks models [14,15], and adaptive control evolutionary models [16].
The current study aims to improve the accuracy, robustness, and adaptability to various road conditions of the vehicle control algorithm.First, the convergence of vehicles toward trajectory tracking errors is investigated from the perspective of nonlinear system stability, which is the premise of vehicle tracking trajectory.Subsequently, the robustness and control algorithm that can adapt to the environment is also considered, thereby ensuring control performance when 2 Scientific Programming the running conditions of a vehicle are drastically changed.Finally, the function of vehicle motion control is expanded, which enables vehicles to complete automatic overtaking task, adaptive cruise task, automatic parking task, flowing into traffic task, and so on.
In most of the studies cited above, some researches only focused on lateral tracking control and some researches only focused on longitudinal tracking control, without considering driving speed and driving direction as input values.When intelligent driving tasks increase in complexity, the control systems cited earlier are unable to adapt to complex tasks.In addition, the control system should be able to guarantee stability.The main contributions of our study are as follows.
(1) A new uncertainty control system according to the Gauss cloud model (GCM) and cloud reasoning is illustrated.(2) The new model considers both speed and direction, whereas velocity and direction are mutually constrained.(3) The speed control rules for intelligent driving vehicles are constructed, with reference to human driving experience.
This paper is organized as follows.Section 1 presents the lateral control of intelligent vehicle.Section 2 presents the GCM, the GCM algorithm, and cloud reasoning, including a preconditioned Gauss cloud generator (PGCG), a postconditioned Gauss cloud generator (PCGCG), and a rule generator.Section 3 describes the lateral control algorithm for intelligent vehicle systems and cloud controller rules.Section 4 provides the results of the experiment and analysis performed using the cloud control algorithm.Finally, the results of experiment are illustrated in Section 5.

Model and Problem Formulation
2.1.Gauss Cloud Model.The Gauss distribution (GD) is one of the most important distributions in probability theory, in which the general characteristics of random variables are represented as means of the mean and variance of two numbers.As a fuzzy membership function, the bell-shaped membership function is mostly used in sets, which is typically expressed through the analytical expressions of () = exp{−( − ) 2 /2 2 }.This study presents a cloud model based on the GD, called the Gauss cloud model (GCM), which is defined as follows [17,18].Definition 1.  is expressed in a precise numerical quantitative domain.(, , ) is a qualitative concept on .If the value of  ( ∈ ) is a random realization of the qualitative concepts of , then the "expectation" of the GD  ∼ (,  2 ) is denoted as Ex, and its "variance" is denoted as  2 .Meanwhile, the "expectation" of GD   ∼ (,  2 ) is denoted as , and its "variance" is denoted as  2 .  is the full form of GD   ∼ (,  2 ) and is a random realization [19].The certainty degree of  in  is satisfied via () = exp{−( − ) 2 /2(  ) 2 }.The distribution of  in the domain of  is called a Gauss cloud (GC) [20].The GC algorithm is presented as follows [17,20].
The algorithm causes distribution drops, called cloud distribution (CD).The algorithm of GCM can be obtained through a cloud generator (CG), which forms a forward Gauss cloud generator (GCG), as shown in Figure 1.The Gauss random number generation method is the foundation of the whole algorithm.It generates uniform random numbers in [0, 1] and uses them to calculate the Gauss random number.Random number sequences are determined through the uniform random function of a seed.The method of using uniform random numbers to generate a Gauss random number is described in detail in [21].GC distribution (GCD) is different from the GD because the GCD algorithm uses the Gauss random number twice, in which one random number is the basis of another random number.Among these, (1) when  = 0, the algorithm generates a precise value of  and the value of  is transformed into a GD, (2) when  = 0 and  = 0, the value of  of the algorithm generation is an exact value of , and  ≡ 1.
From (1) and ( 2), certainty can be concluded as a special case of uncertainty, and the GD is a special case of the GCD.
For a qualitative concept of a steering angle of positive and negative 40 ∘ , given that  = 80 ∘ ,  = 1, and  = 0.1, 1000 cloud drops are generated.The distribution of drops and its certainty degree of  (, ) are shown in Figure 2.

Preconditioned Gauss Cloud Generators and Postcondi-
tioned Gauss Cloud Generators.Knowledge forms a concept and its relationship with communicating and abstracting.The relationship among concepts forms certain rules, from which rules library and rules generator can be established through knowledge reasoning based on GC.Rules include preconditioned and postconditioned rules.Preconditioned rules include one or several rules, whereas postconditioned rules express the results and specific control actions generated by the preconditioned rules.In the control field, "perceptionaction" can establish the rule library based on the relationship among concepts, thereby realizing control of uncertainty.A preconditioned Gauss cloud generator (PGCG) and a postconditioned Gauss cloud generator (PCGCG) are composed of the GCG, which is defined as follows.
Definition 2. Assume the following rule: where  corresponds to concepts  1 in universal sets  1 and  corresponds to concepts  2 in universal sets  2 . is a specific value in universal sets  1 , where the GCG generates a specific value of  based on the concept  1 of the certainty degree of  distribution, and  ∈ [0, 1], which is called a PGCG [22], as shown in Figure 3.
The PGCG algorithm is presented as follows [23].

The PGCG Algorithm
Input.Three figures (, , ) and a specific value .
(2) Calculate the certainty: (3) Generate the distribution of drops (, ).As shown in Figure 4, the distribution of drops (, ) of the specific value of  and the certainty degree of  is on the line of  = .Definition 3. Assume the following rule: where  corresponds to concepts  1 in universal sets  1 and  corresponds to concepts  2 in universal sets  2 .The certainty degree of  belongs to [0, 1].The GCG generates the certainty degree of  drop distribution, which is satisfied by applying concepts  2 in universal sets  2 , called PCGCG [24], as shown in Figure 5.
As shown in Figure 6, the drop distribution (, ) of the cloud drop specific value of  and the certainty degree of  is on the line of  = .

Rule Generator
Definition 4. Assume the following rule: where  is the PGCG that generates the drop distribution (, ) with a specific value of  and a certainty degree of . is the PCGCG that generates the drop distribution (, ) of the cloud with a specific value of  and a certainty degree of , which is called the single-condition single-rule GCG (SCSRGCG) [27,28].The composition diagrams of PGCG and PCGCG are shown in Figure 7.
The SCSRGCG algorithm is presented as follows.
The SCSRGCG implies an uncertainty transfer in the conceptual reasoning process.In the universal sets  1 of the PGCG, the distribution of the certainty degree of  belongs to the specific value of , whereas the certainty degree of  is the input of the PCGCG that generates the drop distribution (, ) of the cloud specific value of  and the certainty degree of .The processing of the certainty value of  to the certainty value of  is uncertain.Definition 5. Assume the following rule: where  1 is the PGCG that generates the drop distribution ( 1 ,  1 ) of the specific value of  1 and the certainty degree of  1 ,  2 is the PGCG that generates the drop distribution ( 2 ,  2 ) of the specific value of  2 and the certainty degree of  2 , and  is the PCGCG that generates the drop distribution (, ) of the cloud drop specific value of  and the certainty degree of .The certainty degree  is obtained from the "soft and" of  1 and  2 , which is called a double-condition singlerule GCG (DCSRGCG).The composition diagrams of two PGCGs and one PCGCG are shown in Figure 8.
The "soft and" is expressed via 2D GCM (1,   ,   , 1,   ,   ), which expresses the uncertainty of "and" of  1 and  2 ; the result of "and" is expressed by the certainty degree of  [29].The degree of "soft and" can be realized by adjusting the values of   ,   ,   , and   when   =   = 0 and   =   = 0.Then, "soft and" becomes an "and" operation.The "soft and" output is presented in Figure 9, which shows the distribution of the drops and their certainty degree The DCSRGCG can establish numerous conditions of single-rule GCG (MCSRGCG) based on its composition principle.The SCSRGCG and the MCSRGCG are stored in the rule library and applied in qualitative knowledge reasoning and intelligent control field.

Lateral Control Approach of an Intelligent Vehicle System
The control of an intelligent vehicle mainly comprises the control for speed and angle under conditions of car-following driving, lane-changing driving, and intersection driving, with car-following driving being the most common.Using Under the condition of car-following driving, an intelligent vehicle should constantly adjust its speed according to obstacles, such as vehicles and pedestrians, while driving efficiently and avoiding collisions.The angle control of an intelligent vehicle aims to keep the car in the middle of the road, with an equal distance between the left/right lane line and the center of the vehicle while driving.Furthermore, the heading direction should remain in accordance with the lane line.
The speed and angle controls of intelligent vehicles are both typical double-conditional and single-rule controllers.In Figure 10, the solid line represents the real lane line, whereas the thick dotted line represents the central axis of the lane calculated according to two lane markings.The black dots represent the geometric center of an intelligent vehicle, which is represented by a rectangle.Vehicles achieve angle control by calculating the distance  between the geometric center of an intelligent vehicle and the central axis of the lane, as well as the included angle  between heading direction and the central axis.
The input of the cloud controller is the distance  (in meters) between the geometric center of an intelligent vehicle and the direction of the central axis of the lane and the included angle  (in degrees) between heading directions and lane line.The output is the steering wheel angle  (in degrees).On the basis of a brief summary of an actual driving experience, several qualitative conclusions are drawn: (1) If the intelligent vehicle does not veer off the middle of the lane and the heading direction of that vehicle remains in accordance with the axis of the lane, then the steering wheel should be returned to the zero position to keep the car moving straight forward.That is, if  and  are near 0,  should be 0, thereby enabling the vehicle to proceed normally.
(2) If the vehicle offsets to the right, then turn the wheel to the left to try and return the vehicle to the center of the lane.For a higher offset value, a greater adjustment angle of the steering wheel is necessary.That is, if  is more than 0, then  is less than 0. A positive correlation exists between  and 's absolute value.
(3) If the vehicle offsets to the left, then turn the wheel to the right and try to return the vehicle to the center of the lane.For a greater offset value, a greater adjustment angle of the steering wheel is necessary.That is, if  is less than 0, then  is more than 0. A positive correlation exists between  and 's absolute value.
(4) If the included angle between the heading direction and the central axis of the lane is greater than 0, which indicates that the vehicle is drifting toward the right front of the axis, then turn the wheel to the left and try to return the vehicle to the center of the lane.For a higher offset value, a larger adjustment angle of the steering wheel is necessary.If  is more than 0, then  is less than 0. A positive correlation exists between  and 's absolute value.
(5) If the included angle between the heading direction and the central axis of the lane is less than 0, which indicates that the vehicle is drifting toward the left front of the axis, then turn the wheel to the right and try to return the vehicle to the center of the lane.For a higher offset value, a larger adjustment angle of the steering wheel is necessary.If  is less than 0, then  is more than 0. A positive correlation exists between  and 's absolute value.
In the next section, we will describe the linguistic value sets of the input and the output, define the range of different linguistic values, and establish the cloud controller and its control rules based on the aforementioned five qualitative rules.

Cloud Controller Rules.
The variables , , and  can be described using five qualitative concepts, namely, "positive more," "positive less," "near-zero," "negative less," and "negative more."The input and output variables define the five qualitative concepts and construct a corresponding cloud regulation generator.
The detailed car-following state and the speed control rules for intelligent vehicles are shown in Table 1.The rule set RS() of distance  between the geometric center of an intelligent vehicle and the central axis of the lane is shown in Table 1(a).The rule set RS() of the included angle  between heading direction and the central axis of the lane is shown in Table 1(b).The parameter settings of the qualitative concepts in the rules are shown in Table 2.

Lateral Control Algorithm.
The GCM and cloud reasoning can express human inference and decision and both exhibit strong robustness in solving the control problems of complicated systems.This study applies the GCM and the steering behavior imposed by cloud reasoning on drivers to build models.The model is shown in Figure 11.
The flowchart of the steering control algorithm shown in Figure 11 consists of two modules: steering wheel adjustment angle decision and steering wheel adjustment speed decision.The former comprises double-condition single-input and single cloud controllers, which are used to independently estimate the preview drift angle and the preview cornering distance.These controllers are called controller  and controller , where   refers to the output of controller  and   refers to the output controller .  ,   ∈ [−1, 1] denotes adapting the expectation direction of the adjustment angle of the steering wheel.The left represents the negative values, whereas the right represents the positive values.A value stands for an expectation degree.When the value is closer to 1, the expectation degree is higher, and vice versa.The adjustment angle decision will constantly determine the adjustment of the steering wheel in terms of controller output.The module of the steering wheel adjustment speed decision, which consists of double-condition single-input and single-cloud controllers, adopts the waterfall structure connection.It inputs the variables for the controller, which outputs the longitudinal velocity of the vehicle, and obtains the information of the adaptation speed of the wheel after adjusting speed.Negative values indicate adjusting the wheel to the left, whereas positive values indicate adjusting the wheel to the right.When the absolute value is closer to 1, the steering speed is faster.Conversely, the steering speed is lower when the absolute value is farther from 1.

Hardware Architecture of an Intelligent Vehicle System.
The on-board sensor configuration of an intelligent vehicle comprises a radar sensor, a vision sensor, and a positioning sensor.The radar sensor consists of two separate Universal Transverse Mercator (UTM) single laser radars on the left and right of the body, a forward SICK single laser radar, a forward four-layer laser radar, and a backward millimeter wave radar.The vision sensor comprises three front-facing cameras, two rear-facing cameras, and two lateral cameras set in both rearview mirrors.The positioning sensor consists of the Global Positioning System (GPS) and an inertial measurement unit (IMU), as is shown in Figure 12.This study is based on a "MengShi" intelligent vehicle, as is shown in Figure 13.All types of sensors are mainly applied to sense the surroundings of the vehicle for real-time acquisition of its location, posture, speed, and time.to the control layer.It simultaneously provides the driver with feedback information from the surroundings and other vehicles through sounds and images.
Sensor and Sensing Layer.This layer consists of a radar sensor, a vision sensor, a GPS sensor, and an IMU sensor.It focuses on completing the collection of sensor data.To realize the "plug and play" feature of the sensor, the standard data format of various sensors should be normative, which requires transforming the specific data format of the sensor to the standard format understood by an intelligent vehicle.The sensor data collected in this layer is delivered to the sensory module.The sensing layer focuses on sensor data analysis, road edge identification, obstacle detection, traffic sign detection, and body state estimation, which can facilitate the planning and decision of an intelligent vehicle.
Decision and Planning Layer.This layer focuses on path planning and navigation, which determine the driving pattern of an intelligent vehicle by analyzing environment data and vehicle data from the sensory module.This layer also determines the position of the vehicle in a detailed electronic map and generates the traveling track according to the coordinates of the target point.Human intervention and obstacles also influence the track.
Control Layer.This layer controls vehicles to enable them to proceed based on track data and current vehicle state.It also receives human instructions and performs acceleration/deceleration and steering operations.This layer directly outputs the control order to the accelerator, as well as the braking and steering controller, of the vehicle. marks the distance between the geometric center of the vehicle and the lane line.The instant velocity is obtained using GPS.The control angle of the steering wheel target is calculated through a decision algorithm and recorded.

Analysis of Maintenance Situations on
Lanes under Different Speeds (1) Vehicle Speed Lower Than 80 km/h.When speed is lower than 80 km/h, a section of real-time data (75 in total) is randomly selected for analysis.Figure 16 shows the variation curve of the included angle  between the vehicle body and the lane line.The -axis represents the number of sampling points (unit: amount).The -axis represents the included angle  (unit: degree).The value of the included angle  between the lane line and the heading direction of the vehicle body should range from −0.5 ∘ to 0.8 ∘ , with a fluctuation range within 1.3 ∘ .Figure 17 shows the variation curve of distance d between the vehicle body and the lane line.The -axis represents the number of sampling points (unit: amount).
The -axis represents the distance  (unit: m).The distance  should range from 0.2 m to 0.8 m, with a fluctuation range within 0.6 m.The data further demonstrate that the second half of the driving drifts toward the left side of the lane line by a wide margin, but the overall situation remains good.(2) Vehicle Speed between 80 km/h and 90 km/h.When speed is between 80 km/h and 90 km/h, a section of real-time data (192 in total) is randomly selected analysis.Figure 18 shows the variation curve of the included angle  between the vehicle body and the lane line.The -axis represents the number of sampling points (unit: amount), The -axis represents the included angle  (unit: degree).The value of the included angle  between the lane line and the heading direction of the vehicle body should range from −0.6 ∘ to 0.6 ∘ , with a fluctuation range within 1.2 ∘ .Figure 19 shows the variation curve of distance  between the vehicle body and the lane line.The -axis represents the number of sampling points (unit: amount).The -axis represents the distance  (unit: meter).The distance  should range from −0.1 m to 0.4 m, with a fluctuation range within 0.5 m.The data show that the situation of the lane remains good.(3) Vehicle Speed between 90 km/h and 100 km/h.When speed is between 90 km/h and 100 km/h, a section of real-time data (176 in total) is randomly selected for analysis.Figure 20 shows the variation curve of the included angle  between the vehicle body and the lane line.The -axis represents the number of sampling points (unit: amount).The -axis represents the included angle  (unit: degree).The value of the included angle  between the lane line and the heading direction of the vehicle body should range from −0.5 ∘ to 0.6 ∘ , a range of 1.1 ∘ .Figure 21 shows the variation curve of the distance  between the vehicle body and the lane line.The -axis represents the number of sampling points (unit: amount).The -axis represents the distance  (unit: meter).The distance  should range from −0.25 m to 0.05 m, with a fluctuation range of 0.3 m.The data show that the situation of the lane remains good.
(4) Vehicle Speed Greater Than 100 km/h.When speed is greater than 100 km/h, a section of real-time data (96 in total) is randomly selected for analysis.Figure 22 shows the variation curve of the included angle  between the vehicle body and the lane line.The -axis represents the number of sampling points (unit: amount).The -axis represents the included angle  (unit: degree).The value of the included angle  between the lane line and the heading direction of the vehicle body should range from −0.4 ∘ to 0.7 ∘ , a fluctuation range within 1.3 ∘ .Figure 23 shows the variation curve of the distance  between the vehicle body and lane line.The -axis represents the number of sampling points (unit: amount).The -axis represents the distance  (unit: meter).The distance  should range from −0.6 m to −0.2 m, with a fluctuation range within 0.4 m.The data show that the lane situation of the lane remains good.Steering to the right creates a negative value, whereas steering left creates a positive value.Approximately 81% of the angles of the steering wheel range from −3 ∘ to 3 ∘ , 3% range from −6 ∘ to 6 ∘ , and the maximum angle ranges from −7 ∘ to 7 ∘ .According to relevant laws, the floating range of a manually operated steering wheel ranges from −7.5 ∘ to 7.5 ∘ , which is a stable operation.

Conclusion
This study proposes a novel type of lateral control migration algorithm for intelligent vehicles.On the basis of the GCM and cloud reasoning, it also presents the qualitative concept cloud parameterization of the speed control rule for a vehicle on an expressway, designs a lateral control algorithm for an intelligent vehicle, and provides the speed control rules for different car-following conditions.The lateral controller of the vehicle, which is based on the GCM and the cloud reasoning algorithm, can be adapted to various speeds.Therefore, 81% of the angles of the steering wheel range from −3 ∘ to 3 ∘ , 3% range from −6 ∘ to 6 ∘ , and the maximum angle, which can achieve stable control, is within the range of −7 ∘ to 7 ∘ .

Figure 6 :
Figure 6: Cloud drop distribution of the PCGCG.

4. 2 .
Experiment Result and Analysis.When the intelligent vehicle proceeds,  marks the included angle between the intelligent vehicle and the lane line.Negative and positive values refer to drifting to the left and right, respectively.

Figure 16 :Figure 17 :
Figure 16: Variation curve of the included angle  between the vehicle body and the lane line.

Figure 18 :Figure 19 :
Figure 18: Variation curve of the included angle  between the vehicle body and the lane line.

Figure 20 :Figure 21 :
Figure 20: Variation curve of the included angle  between the vehicle body and the lane line.

Figure 22 :Figure 23 :
Figure 22: Variation curve of the included angle  between the vehicle body and the lane line.
Control Angle of the Steering Wheel.The curve graph of the control angle of the steering wheel is shown in Figure24.The -axis represents the traveled mileage of the vehicle (unit: km).The data recording interval is 50 ms.The -axis represents the control angle of the steering wheel (unit: degree).

Figure 24 :
Figure 24: Curve graph of steering wheel control.

Table 1 :
(a) Rule sets RS() of distance  between the geometric center of an intelligent vehicle and the central axis of the lane.(b) Rule sets RS() of included angle  between heading direction and the central axis of the lane.

Table 2 :
Parameter setting of the qualitative concepts of the composition of the speed control rules of an intelligent vehicle.