Scientific Programming

Volume 2016 (2016), Article ID 6842891, 12 pages

http://dx.doi.org/10.1155/2016/6842891

## Cloud Model Approach for Lateral Control of Intelligent Vehicle Systems

^{1}State Key Laboratory of Software Development Environment, Beihang University, Beijing 100191, China^{2}State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100083, China^{3}Information Technology Center, Tsinghua University, Beijing 100083, China^{4}The Institute of Electronic System Engineering, Beijing 100039, China

Received 6 June 2016; Revised 9 September 2016; Accepted 28 September 2016

Academic Editor: Xiong Luo

Copyright © 2016 Hongbo Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. 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 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.

#### 2. 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 . 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 is denoted as* Ex*, and its “variance” is denoted as . Meanwhile, the “expectation” of GD is denoted as , and its “variance” is denoted as . is the full form of GD and is a random realization [19]. The certainty degree of in is satisfied via . The distribution of in the domain of is called a Gauss cloud (GC) [20]. The GC algorithm is presented as follows [17, 20].*The GC Algorithm**Input*. Three figures and the number of cloud drops . *Output*. A sample set that represents concept extension and its certainty , .(1)Generate Gauss random .(2)Generate Gauss random .(3)Calculate the certainty: .(4)Repeat (1)–(4) until the number of cloud drops is .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 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 , the algorithm generates a precise value of and the value of is transformed into a GD,(2)when and , the value of of the algorithm generation is an exact value of , and .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°, , and , 1000 cloud drops are generated. The distribution of drops and its certainty degree of () are shown in Figure 2.