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This paper focuses on the problem of target tracking using

The competition and cooperation behaviors of living beings, such as swarms of ants, shoals of fish, or even the troops in military, have certain advantages, including avoiding predators, increasing the chance of finding food, saving energy, and so on. For example, for a joint vigilance task in military, all soldiers should keep unmoved and the one who finds an invader should track the invader closely. Such a behavior can be deemed as a coordination based on the competition, where the soldier who finds the invader is the “winner” and wins the opportunity to do the tracking task while the rest ones are the “losers” and keep unmoved to do the vigilance.

Deemed as a modeling of cooperation, consensus algorithms estimate the related weights or states by mitigating differences among multiple agents in a group and have been applied to many computation problems depicted in distributed manner, such as multiagent systems [

Research in many fields observes and confirms the fact that the competition is equally important as the cooperation for complex systems [

Currently, robotics is playing an indispensable role in modern society as well as academic researches and industrial applications [

Although some achievements have been earned for the cooperative control of multiple mobile robots, there are still some unsatisfactory aspects with existing solutions. One of the unsatisfactory aspects in the existing achievements is that they can not select the fittest mobile robots in a group to execute the task with the rest ones unmoved. In this paper, we use multiple mobile robots for tracking target in a competition manner, which extends

The remainder of this paper is organized into five sections. The preliminary for tracking target via multiple mobile robots in a competition manner is presented in Section

This section presents the preliminary and the model of the robot.

In the ensuing sections, the coordination models for multiple mobile robots will be viewed as singularly perturbed systems. Therefore, for investigating the convergence speed and stability of these models, the following theoretical basis on a singularly perturbed system is presented as a preliminary, which will be utilized in the ensuing proofs of Theorems

Consider the following singularly perturbed system:

Assume that the following conditions are satisfied for all

The equation

The functions

The origin of the reduced system

The origin of the bounded-layer system

To lay a basis for further investigation, the mathematical symbols and their meanings used in this paper are listed as follows:

The differential-driven-wheeled mobile robot (Figure

Differential-driven-wheeled mobile robot model.

With the aid of feedback linearization technique presented in [

In this part, problem definitions are presented as follows.

With all-to-all communications, construct a model for

With limited communications, design a model to achieve the same goal as presented in Problem

This section presents a centralized competition control law for tracking the moving target with all-to-all communications.

The neural network model presented in [

Substituting (

As illustrated in Figure

Position

the moving target are all available to the

distance tolerant

The

target approach the latter and the rest ones keep unmoved

1: Initialize variable

2:

3: Get

4: Communicate with all the other mobile robots and get

5: Calculate

6: Drive the

7:

Control block diagram for the

In addition, we have the following theorem for the proposed centralized coordination model (

There exists

The proof involves two aspects.

For aspect

For aspect

Using the linear translation

Since all the five conditions are satisfied for all

Based on the above aspects

We have developed centralized model (

Equation (

Thus, by using consensus filter (

As illustrated in Figure

Position

velocity

robot, a preset distance tolerant

The

target approach the latter and the rest ones keep unmoved

1: Initialize variables

2:

3: Get

4: Communicate with mobile robot(s)

5: Calculate

6: Calculate

7: Drive the mobile robot using the generated

8:

Control block diagram for the

There exists

The proof involves two aspects.

For aspect

For aspect

Therefore, condition

Since all the five conditions are satisfied for all

Based on the above aspects

For the distributed coordination model (

In this section, computer simulations are provided based on ten differential-driven-wheeled mobile robots. In what follows, the parameters are set as

In this example, model (

(

(

Outputs of

Specifically, as shown in Figure

As the continuation of simulation results shown in Figure

To observe the target tracking task in a different perspective, outputs of the

In this example, the distributed coordination model (

(

(

Outputs of

Specifically, as shown in Figure

Simulation results on phase 2 of the target tracking are shown in Figure

Figure

Simulation results with zero-initial-velocity constraint, as well as bound limits on velocity of mobile robots are shown in Figure

Performance of

In this paper, we have proposed centralized and distributed coordination models with all-to-all and limited communications, respectively. Simulations based on differential-driven-wheeled mobile robots have been conducted to illustrate the efficacy of the proposed centralized and distributed coordination models for tracking moving target in a competition manner with all-to-all communications and limited communications.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work is supported by the National Natural Science Foundation of China (no. 61703189), by the Fund of Key Laboratory of IoT of Qinghai Province (no. 2017-ZJ-Y21), by the Natural Science Foundation of Gansu Province, China (no. 18JR3RA264), by the Guangdong Outstanding Young Teacher Training Program in Higher School (no. YQ2015104), by the Guangzhou Higher School Innovation and Entrepreneurship Education Project (2017153201), by the Opening Foundation of Key Laboratory of Opto-Technology and Intelligent Control, Ministry of Education (no. KFKT2018-1), by the National Natural Science Foundation of China (no. 11561029), by the Belt and Road Special Project of Lanzhou University (no. 2018ldbryb020), by the Fundamental Research Funds for the Central Universities (no. lzujbky-2017-37), by the Fund of Robot Technology Used for Special Environment Key Laboratory of Sichuan Province (no. 17kfkt03), by the Natural Science Foundation of Hunan Province (no. 2017JJ3257), by the Research Foundation of Education Bureau of Hunan Province, China (no. 17C1299), by Hong Kong Research Grants Council Early Career Scheme (with no. 25214015), by Hong Kong Polytechnic University (with nos. G-YBMU, G-UA7L, 4-ZZHD, F-PP2C, and 4-BCCS), and also by the outstanding Youth Foundation of Shandong Province (ZR2016JL024).