Autonomous Tracking Control for Four-Wheel Independent Steering Robot Based on Improved Pure Pursuit

Jing Li， Qingbin Wu， Junzheng Wang， Hui Qin and Jiehao Li

（1. Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation,Beijing Institute of Technology, Beijing 100081, China；2. Key Laboratory of Servo Motion Sys?tem Drive and Control, Ministry of Industry and Information Technology, School of Automation,Beijing Institute of Technology, Beijing 100081, China）

Abstract: Autonomous tracking control is one of the fundamental challenges in the field of robotic autonomous navigation, especially for future intelligent robots. In this paper, an improved pure pur?suit control method is proposed for the path tracking control problem of a four?wheel independent steering robot. Based on the analysis of the four?wheel independent steering model, the kinematic model and the steering geometry model of the robot are established. Then the path tracking con?trol is realized by considering the correlation between the look?ahead distance and the velocity, as well as the lateral error between the robot and the reference path. The experimental results demon?strate that the improved pure pursuit control method has the advantages of small steady?state er?ror, fast response and strong robustness, which can effectively improve the accuracy of path track?ing.

Key words: autonomous tracking control；four?wheel independent steering robot；pure pursuit；lateral error

In recent years, with the development of ar?tificial intelligence and market demand, the re?search and application of intelligent mobile ro?bots are becoming increasingly popular[1]. Com?mon mobile robots can be categorized into whee?led type, footed type, crawler type, etc., and dif?ferent robots have their own advantages and dis?advantages. Among them, the wheeled robot has the advantages such as simple structure, fast moving speed and simple control, but the ability to overcome obstacles and the ability to adapt to the environment are poor. Footed robots have the advantages of strong environmental adaptab?ility, ability to cross obstacles, and flexible move?ment, but the disadvantages are low speed and low efficiency. The crawler robot has the advant?ages of strong terrain adaptability and strong stability. The four?wheel independent steering ro?bot studied in this paper is a novel four wheel?legged robot. Due to its unique steering mode and wheel leg structure, it has been favored in the development and research of robots[2].

The autonomous tracking control problem of the robot is to make the robot travel on a given reference path by controlling the speed and steer?ing of the robot. The reference path is generally given by the planning layer of the robot, and the reference path is composed of a series of path points, which need to contain information such as the position and direction of the robot. The autonomous tracking control of the robot is gen?erally divided into two types: one is path track?ing control[3], and the other is trajectory tracking control[4]. Path tracking control is independent of time. In path tracking control, it can be assumed that the robot travels at a constant speed, and the driving robot approaches the reference tra?jectory with some control law. Trajectory track?ing control is related to both time and space, re?quiring the robot to reach a predetermined refer?ence path point within a specified time. Although many scholars have studied path tracking con?trol and trajectory tracking control based on two?wheel steering, and have achieved many re?search results. However, there are few studies on path tracking control based on four?wheel steer?ing[5]. Compared with a traditional two?wheel steering robot, the four wheels of the four?wheel independent steering robot can be independently driven and work independently, which greatly improves the maneuverability and flexibility of the robot. Therefore, relying on the developed four?wheel independent steering robot, this pa?per mainly studies the path tracking autonomous control of four?wheel steering.

With the development of modern control theory and intelligent control methods, robot autonomous tracking control methods show a trend of diversification. At present, the autonom?ous tracking control methods mainly include:PID control, fuzzy control, sliding mode control,model predictive control, and pure pursuit con?trol. Among them, PID control is a relatively mature, stable and commonly used control meth?od. However, because its control parameters are generally obtained by the trial and error method,it is difficult to achieve intelligent optimal con?trol of lateral motion[6?7]. Fuzzy control fuzzy con?trol membership function and control rule para?meters need to be optimized and can not achieve the best performance of the control system[8?9].Sliding mode control may cause oscillation or in?stability of the control system due to the discon?tinuity of its control gain[10?11]. Model predictive control relies on accurate mathematical models,while the method has a large amount of compu?tation, and real?time problems affect its practic?al application[12?13]. Pure pursuit control has a long history of development for robot path track?ing. It has the advantages of easy implementa?tion, good real?time performance and mature ap?plication[14?15].

The system of our four?wheel independent steering robot is strongly coupled, time?varying and multivariate nonlinear[16?18]. Although vari?ous autonomous path tracking control methods have been well developed, their methods have certain limitations when applied to actual robot systems. In the pure pursuit, the fixed look?ahead has a great impact on path tracking, and the method does not consider the influence of the lat?eral error on the steering control[19?20]. In this pa?per, we propose a strategy to overcome at least some of these issues. The basic idea is to regard the look?ahead distance as a function of speed,and to add lateral error as input in the pure pur?suit, so as to obtain more reasonable steering control. The specific implementation is first to determine the look?ahead distance according to the speed, and then calculate the steering angle by steering geometric model. At the same time, it is necessary to monitor the distance from the ro?bot center to the reference path in real time, and further adjust the size of the steering angle ac?cording to the distance. The results show that the proposed method has good characteristics of real?time and robustness and has small path tracking error. Although pure pursuit is not a new control method, the work of dealing with pure pursuit of four?wheel steering is limited.

The remainder of this paper is organized as follows. Section 1 describes the four?wheel steer?ing model. Section 2 introduces the pure pursuit based on the robot kinematics model. The im?proved pure pursuit is then described in Section 3. The experimental results and analysis are provided in Section 4. Finally, some concluding remarks and future work directions are given in Section 5.

1 Four-Wheel Steering Model

In the current research, most steering mod?els are vehicle steering models, that is, only two front wheels are turned, and the steering center is on the straight line of the rear axle. As shown in Fig. 1, the steering model we studied is a four?wheel steering model. The corners of the inner wheels are the same, the corners of the outer wheels are the same, and the steering center is at the center of the robot body.

Fig. 1 Four?wheel steering model

From geometric relations, it can be con?cluded that:wheels; L is the distance between the robot’s front wheels and the rear wheels.

The velocity relationship is presented as fol?lows

2 Pure Pursuit

2.1 Kinematic model

Fig. 2 Kinematic model

Robot kinematics is modeled as follows. At the center of the robot A (xA,yA), the speed along the X axis is

2.2 Steering geometry model

Under the assumption of the above?described robot kinematics model. Fig. 3 shows the defini?tion of the variables that define the pure pursuit control when driving forwards. R is the radius of curvature, “ref path” is the reference path, point A is the center of the robot, point B is the look?ahead point, Lfwis the look?ahead distance, L is the wheel spacing of the robot, δ is the steering angle of the robot, and η is the robot’s heading angle.

Fig. 3 Steering geometry model

According to the sine theorem, the following curvature conversion formula can be derived

Substituting Eq.(11) into Eq.(9), the follow?ing equation can be obtained

Eq. (12) reflects the relationship between the steering angle of the robot and the heading angle of the robot, which lays a theoretical foundation for pure tracking control. The determ?ination of the appropriate look?ahead distance becomes a key factor affecting the steering angle of the wheel.

3 Improved Pure Pursuit

3.1 Determination of look-ahead distance

The look?ahead distance is an important para?meter for the robot to implement path tracking.It is especially important to adjust the look?ahead distance reasonably. A smaller look?ahead distance will make the robot track the path more accurately, while a too small look?ahead distance will cause the robot to be unstable or even oscil?late. A longer look?ahead distance will make the trajectory of the robot forward more smooth,while an excessive look?ahead distance will cause the robot’s steering control to fail. Based on the above analysis, too long or too short distance is not conducive to the path tracking of the robot.It is very important to determine the appropri?ate look?ahead distance selection rules.

First, consider our wheeled robot experi?ment platform, the look?ahead distance should not be greater than the distance that the envir?onment sensing system can detect and plan, oth?erwise the path tracking will fail. Second, the look?ahead distance should be a value that dy?namically changes according to the actual speed of the robot. According to a large number of ro?bot path tracking tests, the final design of the re?lationship between forward distance and speed is shown in Fig. 4. The formula is described as

Fig. 4 Look?ahead distance as a function of the speed

3.2 Lateral error based control

Fig. 5 Robot path tracking diagram

The core of pure pursuit is to calculate the steering angle of wheel by Eq. (12), and its in?put variables are only heading angle and look?ahead distance. In order to improve the accuracy of path tracking, we take the lateral error into account, and let it affect the change of angle. We can now monitor the lateral error as a measure?ment in real time. Segmentation control is per?formed according to the magnitude of the lateral error. When the lateral error is in different threshold ranges, multiply the front wheel steer?ing angle δ by a coefficient k to adjust the steer?ing angle of the robot wheel reasonably, so that the robot can realize path tracking faster and more stably.

Finally, after considering the lateral error,the heading angle and the stability and safety of the robot itself, we designed the steering control?ler shown as

4 Experimental Results

4.1 Hardware system

Fig. 6 shows the four?wheel independent stee?ring robot. The hardware system of the four?wheel independent steering robot mainly in?cludes the energy system, the environment sens?ing system, the integrated navigation system, the actuator and the control system.

Fig. 6 Four?wheel independent steering robot

4.2 Straight path experiment

The straight path experiment is carried out in the campus road. The length of the straight path test is about 35 m. The experimental data acquisition process is shown in Fig. 7. Fig. 8 shows the reference path and actual path of the robot for path tracking. Fig. 9 shows the real?time variation of the lateral error and wheel steering angle of the robot under two different control methods.

Fig. 7 Data acquisition process for straight experiments

Fig. 8 Reference path and actual path comparison

Fig. 9 Lateral error and steering angle real?time change diagram

As shown in Fig. 8, the straight path track?ing effects of the two methods can be visually compared. With the improved pure pursuit, the robot can eliminate large lateral errors in a short period of time and quickly enter stable linear path tracking. When tracking the straight path,we can see that the robot can adjust in time after the robot deviates from the reference path due to the disturbance of the robot or the external, so that the robot keeps track of the reference path stably.

As shown in Fig. 9, the performances of the two methods on the lateral error and steering angle can be compared. From the real?time vari?ation of the lateral error, the improved pure pur?suit has a better performance than the pure pur?suit. First, the improved pursuit can eliminate lateral errors in less time. Second, after the ro?bot has eliminated the initial lateral error. Com?pared with the pure pursuit method, the im?proved pure pursuit method reduces the average lateral error from 6.43 cm to 5.46 cm, and the maximum lateral error from 14.1 cm to 11.5 cm.It can be observed from the real?time change curve of the steering angle that the improved pure pursuit performs better in the process of strai?ght path tracking, and the amplitude of the angle change is smaller than that of the pure pursuit.

4.3 Curve path experiment

The curve path experiment is also carried out in the campus road. The length of the curve path test is about 26 m. The experimental data acquisition process is shown in Fig. 10. The ex?perimental results are shown in Fig. 11 and Fig. 12.Fig. 11 shows the reference path and actual path of the robot for path tracking. Fig. 12 shows the real?time variation of the lateral error and wheel steering angle of the robot under two different control methods.

Fig. 10 Data acquisition process for curve experiments

Fig. 11 Reference path and actual path comparison

Fig. 12 Lateral error and steering angle real?time change diagram

As shown in Fig. 11, the curve path track?ing effects of the two methods can be visually compared. It can be observed that in a period of time, the two methods have the same effect. But when turning, the improved pure pursuit has a smoother turning track and a smaller lateral er?ror. When the robot has a large lateral error due to turning, the improved pure pursuit can re?duce the lateral error faster, so that the robot path tracking effect is better.

As shown in Fig. 12, we can compare the performance of the two methods on the lateral error and steering angle. From the comparison curve of the real?time change of the lateral error,we can see that the lateral error of the improved pure pursuit is reduced from 8.8 cm to 8.4 cm,and the maximum lateral error is reduced from 26.3 cm to 22.8 cm. It can be seen from the real?time curve of the steering angle that the im?proved pure pursuit has a better performance than the pure pursuit, so the trajectory of the ro?bot is smoother when tracking the curved path.

5 Conclusion

In this paper, a controller based on pure pursuit is designed to control the lateral motion of the four?wheel independent steering robot so that the robot can track the given path. Based on the pure pursuit controller, the lateral dis?tance between the robot and the reference path are monitored in real time as one of the factors that influence the steering angle of the wheel.When the improved pure pursuit is utilized, the robot will have a faster dynamic response, which can quickly reduce the lateral error and reach a steady state. Robots also have better steering characteristics for quick and smooth steering.The improved pure pursuit is suitable for path tracking research of four?wheel independent steering robots. At the same time, it has a bet?ter performance than the pure pursuit.

In future research, new methods to control the impact of lateral error on robot path track?ing should be considered.