Hybrid control of a tricycle wheeled AGV for path following using advanced fuzzy-PID

1. Introduction

Automated Guided Vehicle (AGV) is a transportation vehicle automatically traveling on unknown path traced in working environment. AGV is most often used to deliver materials around a manufacturing facility or a warehouse. With lots advantages such as reduction in the number of worker, improvement of productivity and quality, improvement of working environment and safety, less damage on transporting goods, real- time control of material flow and improved management on product, AGV has become more and more popular and useful in modern industrial production.

Control of AGV for path following has received a great of interest to many researchers because of its nonlinear characteristics caused by nonholonomic constraints of the wheels. Most controllers are designed based on nonlinear techniques [1]-[4] including the backstepping approach, the sliding mode control, the Lyapunov function approach, the dynamic feedback linearization technique, etc.. Designing controllers using these approaches is rather complex. Furthermore, it requires some detailed information related to system parameters, working environment and complete knowledge of the dynamics that are usually infeasible in practical.

To overcome the above problems, Fuzzy controller is a suitable solution. Fuzzy controller doesn’t require accuracy mathematical modeling of the system. Fuzzy logic controller can control the system with various situations of practical fields. Applying a fuzzy controller is simple, rapid and inexpensive because the rules can be linguistically interpreted by a human expert. Over the latest decade, fuzzy logic has been widely used for mobile robot control [5]-[17]. Precup et al. introduced fuzzy control solution for a class of tricycle mobile robots [11]. The control system structure contained two control loops to control the forward velocity and the direction of the robot. Antonelli et al. proposed a path following approach for mobile robot using fuzzy-logic set of rules which imitated the human driving behavior [12]. Baturone et al. introduced a design of embedded DSP-based fuzzy controllers for autonomous mobile robots [16]. In previous papers addressing path tracking control, the fuzzy controller used very simple rules and was usually single input single output controller [11], while a tricycle WMR needs a multi-input multi-output controller because it has two degree of freedom.

Among 5 types of WMR introduced by Campion et al. [18], a tricycle WMR is most widely used for industrial AGV [19]-[20]. However, a detailed report about kinematic and dynamic modeling of tricycle WMR has not been reported in literature.

From the above reasons, the purpose of this paper is as follows: First, kinematic and dynamic modeling using the well known Lagrange equation of the AGV is presented. Second, a hybrid controller that integrates two control loops, kinematic control loop and dynamic control loop, is designed for AGV to follow an unknown path. The kinematic control loop is based on fuzzy logic framework and the dynamic control loop is based on two PID controllers. For path following, a tracking error vector is defined. The fuzzy controller uses the tracking error vector as its inputs including position error, angle error and derivative of angle error. From the fuzzy output, velocity control vector at the tracking point is achieved. Because the AGV is driven by a steering driving wheel, steering angle and angular velocity of steering wheel should be calculated. Finally, in dynamic control loop, two PID controllers are used to control two DC motors for tracking the desired steering angle and the desired angular velocity of the steering wheel. Simulation and experimental results are presented to show the effectiveness of the proposed controllers.

2. System Modeling

This chapter presents the kinematic and dynamic modeling for the proposed AGV system. This AGV model is based on the model for tricycle wheeled mobile robot introduced by Campion et al. [18].

The AGV has two fixed passive wheels and one steering driving wheel. r_f is the radius of two fixed passive wheel and r_s is the radius of the steering driving wheel. Figure 1 shows the coordinate of AGV. XOY is the global coordinate frame and X_QQY_Q is the moving coordinate frame. Q is the tracking point that is placed in the middle of two fixed passive wheels. θ is the heading angle of AGV. B₁ denotes a steering driving wheel.

Figure 1:

Coordinate for AGV’s modeling

B₂ and B₃ denote two fixed passive wheels. X_Q axis of moving coordinate frame is passed through the centers of wheels. C is the center of mass of the AGV. ϕ_i (i = 1,2,3) is the rotational angle of the i^th wheel. β is the steering angle of the steering wheel.

The posture vector of the tracking point Q on the AGV is specified as follows:

where (x, y) are global coordinate of tracking point and θ is the heading angle of the AGV. Velocity control vector at the tracking point Q is defined as follows:

where ν and ω are linear velocity and angular velocity at the tracking point Q.

The posture vector for total AGV is specified as follows:

where Φ = [ϕ₁ϕ₂ϕ₃]^Τ. Because the AGV is driven by steering driving wheel, kinematic control vector u_k is defined as follows:

3. Measurement of Tracking Errors using Camera Sensor

Figure 2 shows schematic for the tracking errors of AGV. e_pos is the position error between the position of the tracking point Q on the AGV and the reference point on the reference path. e_θ is the angle error between the Y_Q axis and the tangent line of the path at the reference point.

Figure 2:

Schematic for the tracking errors of AGV

Figure 3 shows the schematic of camera window for measuring the tracking errors using camera sensor. The camera sensor is a Logitech webcam C600. The webcam specification is up to 30 frames per second, 2.0-megapixel sensor and hi-speed USB 2.0 communication. The camera has a resolution of 640pixel × 480pixel

Figure 3:

Schematic for measuring the tracking errors using camera sensor

The camera window is fixed on camera and captures the images of 15cm × 15cm. The image size is small in comparison with curvature radius of the reference path. Therefore, it is assumed that the image of reference path is straight line as shown in Figure 3.

Figure 4:

Image processing procedure

Form Figure 3, the tracking errors can be obtained as follows:

Images captured from web camera are processed by using AForge, NET framework, C# framework designed for developers and researchers in the fields of computer vision and artificial intelligence. To calculate the position error and the angle error from the image captured by camera, image processing procedure includes steps a shown as follows:

4. Controller Design

To control the AGV for path following, a control algorithm is designed as in Figure 5. The controller integrates two control loops, kinematic control loop based on fuzzy logic framework and dynamic control loop based on two conventional PID controllers.

Figure 5:

Structure of the proposed path-following controller for AGV

The fuzzy controller uses the tracking error vector as its inputs including the position error, the angle error and the derivative of angle error. The fuzzy outputs are derivative of the linear velocity, and the angular velocity at the tracking point, Q.

From the fuzzy output, the velocity control vector at the tracking point is achieved. Because the AGV is driven by the steering driving wheel, the steering angle and the angular velocity of the steering wheel should be calculated. Finally, in dynamic control loop, two PID controllers are used to control two DC motors for tracking the desired steering angle and angular velocity of the steering wheel.

4.1 Fuzzy controller Design

Fuzzy rules are normally created based on human experience and logic. Therefore, it is necessary to analyze the desired outputs based on available inputs. From two inputs, the position error and the angle error, AGV posture is defined in 9 different situations as shown in Figure 6. From 9 situations, 9 rules are generated, respectively. In addition, two other rules are proposed when derivative of angle error are large, especially while the robot moves away the path with high velocity.

Figure 6:

Structure of a fuzzy controller

Table 1 shows the fuzzy rules designed for AGV for path following and the membership functions are given in Figure 7.

Table 1:

Fuzzy rules

Figure 7:

Membership functions

4.2 PID controller Design

The dynamic control loop includes two PID controllers in Figure 8. The first one is used for tracking the desired steering angle, β_d.

Figure 8:

Dynamic control loop

The second one is used for tracking the desired rotation angular velocity of steering wheel, η_d.

A PID controller 1 is designed based on steering angle error of the steering wheel as follows:

where k_p1, k_i1 and k_d1 are the coefficients of the PID controller 1.

A PID controller 2 is designed based on rotational angular velocity error as follows:

where k_p2, k_i2 and k_d2 are the coefficients of the PID controller 2.

5. Simulation and Experimental Results

To verify the effectiveness of the proposed controllers, simulations and experiments have been done for the AGV to follow an unknown path. In the simulation, the initial values and the numerical parameter values are given in Table 2 and Table 3.

Table 2:

Initial values for simulation

Table 3:

Numerical parameter values of AGV

The reference path has five segments with three straight line segments and two curved line segments. The radius of the first curve is 6 m and the radius of the second curve is 4 m. Figure 9 shows the reference path in simulations and experiments.

Figure 9:

Reference path

The coefficients in two PID controllers are obtained by trial and error method in simulations and experiments. Their numerical values are given as follows: k_p1 = 300, k_i1 = 0.5, k_d1 = 25, k_p2 = 200, k_i2 = 5, k_d2 =5. Figure 10 shows the position error that becomes zero when the path is a straight line and is bounded within ± 0.1m in both simulation and experimental results when the path is a curved line. Figure 11 shows angle error that is bounded within ± 0.8^o in both simulation and experimental results. Figure 12 shows steering angle of steering wheel in experiment and the steering wheel angle is bounded within 90^o ± 40^o in both simulation and experimental results. Figure 13 shows the linear velocity of AGV at tracking point Q

The linear velocity is limited within 0.5m/s and 2m/s in both simulation and experimental results. Figure 14 shows the path following result of the AGV in experiment.

Figure 10:

Position error

Figure 11:

Angle error

Figure 12:

Steering angle of steering wheel

Figure 13:

Linear velocity of tracking point on AGV

Figure 14:

Path following result of the AGV in experiment

6. Conclusions

This paper developed an industrial AGV, a tricycle wheeled mobile robot. First, kinematic model and dynamic model of the AGV were presented. Second, schematic of tracking errors using camera sensor were defined. After that, control algorithm for path-following of AGV was proposed based on integration of two control loops, kinematic control loop and dynamic control loop. The kinematic control loop based on fuzzy logic framework and the dynamic control loop based on two PID controllers were designed. The effectiveness of the proposed system was shown through simulation and experimental results. The AGV could follow the desired path with a large enough curvature radius smoothly. So the system could be applied and implemented to the industrial field in practical.

Acknowledgments

This research was supported by a grant of preparatory association from Pukyong National University.

This paper is extended and updated from the short version that appeared in the Proceedings of the International symposium on Marine Engineering and Technology (ISMT 2014), held at Paradise Hotel, Busan, Korea on September 17-19, 2014.

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