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This paper focuses on the problem of an adaptive neural network dynamic surface control (DSC) based on disturbance observer for the wheeled mobile robot with uncertain parameters and unknown disturbances. The nonlinear observer is used to compensate for the external disturbance, and the neural network is employed to approximate the uncertain and nonlinear items of system. Then, the Lyapunov theory is introduced to demonstrate the stabilization of the proposed control algorithm. Finally, the simulation results illustrate that the proposed algorithm not only is superior to conventional DSC in trajectory tracking and external friction disturbance compensation but also has better response, adaptive ability, and robustness.

Wheeled mobile robot is an intelligent object. It can collect the surrounding environmental information from the constant feedback of sensors and allodial makes decisions. Then, it outputs motion instructions and guides itself to move to the destination quickly with high precision of trajectory tracking [

Nowadays various intelligence control algorithms for mobile robot have been represented in the literature, such as genetic algorithm [

On the other hand, the output of the disturbance observer can be extensively used in feed-forward compensation of external disturbances. The disturbance observers can give fast, excellent tracking performance and smooth control actions without the use of large feedback gains [

To the best of our knowledge, the DSC method and disturbance observer have been seldom used in the control of wheeled mobile robot so far. The first main contribution of this paper is the compensation of external friction by using the nonlinear disturbance observer. The second contribution is the design of the dynamic surface control method combined with neural network. During the design process, neural networks are employed to approximate the nonlinearities, and adaptive method and DSC are used to construct neural network controller. It means that uncertain parameters are taken into account and explosion of complexity is solved. Finally, to testify to the superiority of the proposed control algorithm, a comparison between DSC, neural network dynamic surface controller (NNDSC) and NNDSC with nonlinear observer is studied. The simulation results are provided to demonstrate the effectiveness and robustness objectively against the parameter uncertainties and external disturbances.

The schematic diagram of wheeled mobile robot is shown in Figure

The wheeled mobile robot.

The dynamics of wheeled mobile robot with uncertain parameters and nonlinearity in Figure

For simplicity, the following notations are introduced:

Outdoor wheeled mobile robot suffers more unknown and uncertain disturbance than indoor one. In the real control system it is unavoidable for some implicit, prior unknown modeling and external disturbance to exist. Suppose the sum of all external uncertainty items to describe with function

By using these notations, the dynamic model of wheeled mobile robot can be described by the following differential equations:

System dynamic equations of wheeled mobile robot are a coupled system. Firstly it is to decouple the system mentioned and then to convert to parametric strict-feedback forms. It is defined as follows:

The reference signals

Figure

A general architecture of RBF neural network.

For the Gaussian neural network,

Define state variable

By equation transformation, (

On the basis of the difference between real output and evaluated output of system, the evaluator can be adjusted to design disturbance observer.

Suppose that nonlinear disturbance observer owns the following form:

Define the auxiliary variable:

By obtaining the output of neural network dynamic surface controller, the disturbance of wheeled mobile robot existing is compensated well. The control law is designed as

Furthermore, (

Define

To aim at the wheeled mobile robot represented in (

For the reference signal

According to (

The adaptive laws are chosen as

For the reference signal

Construct the virtual control law

According to the known

Define the dynamic surface as

Combining (

The adaptive laws are chosen as

From the analysis mentioned above, the control schematic of wheeled mobile robot neural network dynamic surface control based on nonlinear disturbance observer is shown clearly in Figure

Control schematic of wheeled mobile robot.

To verify the proposed controller, we make a comparison between neural network dynamic surface control and traditional dynamic surface control.

From (

According to the definition, the virtual control function is equal to (

From (

Define the filter error

In the same way, the following can be deduced:

According to

In the same way, it can be deduced that

For any given

To aim at the wheeled mobile robot expressed in (

Choose the

Consider that

Then it can be verified easily that

If

Taking those into account, there exists

In the condition of

In this section, in order to illustrate the effectiveness of wheeled mobile robot neural network dynamic surface control method which was based on nonlinear disturbance observer, the simulation will be conducted under the initial condition of

The reference signals are taken as

The proposed neural network dynamic surface controllers are used to control the wheeled mobile robot. The center of neural network

The control parameters of traditional dynamic surface controllers are chosen as follows:

In comparison with traditional dynamic surface control, the neural network dynamic surface control is run under the assumption that the system parameters and the nonlinear functions are unknown.

Figures

Linear velocity trajectory tracking.

Orientation angle trajectory tracking.

Linear velocity tracking error.

Orientation angle tracking error.

As explained in the previous sections, to obtain a precise mathematical model of robot is very difficult and sometimes impossible because of the existence of gear clearance, friction coefficient variation of roadbed, and motor parameter change coming from outside. In such cases, to verify the robustness of system, the drive gain

Robustness analysis.

To take into account Coulomb friction and viscous friction, the external friction of system is given below:

The nonlinear disturbance observer parameters are taken as

External friction is applied to determine the antidisturbance performance of robot. Figure

Comparison between real friction and observed friction with nonlinear observer.

Orientation angle tracking error comparison.

This paper presents an adaptive neural network DSC algorithm based on disturbance observer for uncertain nonlinear wheeled mobile robot system. The presented controller which surmounts the shortages of the conventional DSC guarantees the convergence of tracking error and the boundedness of all the closed-loop signals. In addition, the simulation results are obtained to prove the effectiveness and robustness against the parameter uncertainties and external friction disturbances. Therefore, these characteristics of NNDSC with nonlinear observer show great advantages over the other two methods and make it a competitive control choice for the wheeled mobile robot application.

The authors declare that there is no conflict of interests regarding the publication of this paper.