Adaptive Sliding Mode Control Design based on Disturbance Compensator for Controlling Multi-Agent Robots
الموضوعات : Majlesi Journal of Telecommunication Devices
Samira Zalaghi
1
,
amirhossein zaeri
2
1 - Department of Electrical and Electronic Engineering, Islamic Azad University, Tehran, North Branch, Iran
2 - Department of Electrical and Electronic Engineering, Shahinshahr Branch, Islamic Azad University, Shahinshahr, Isfahan, Iran.
الکلمات المفتاحية: Multi-agent System, Arrangement Control, Sliding Mode Control, Adaptive Disturbance Observer.,
ملخص المقالة :
In this research, the goal is to develop a sliding mode control strategy based on the disturbance compensator to control the arrangement of a multi-agent system. For this purpose, the exponential access law is used to derive chattering-independent sliding mode control laws. In this design method, the sliding level information and its sign are used simultaneously, and by properly adjusting the sliding gain so that it is relatively larger than the switching gain, chattering effects can be removed significantly. On the other hand, since the adjustment of the switching gain is closely related to the changes of uncertainty and external disturbances, an adaptive approach is used to determine it. This is done using the Lyapunov stability theory and it is expected that the switching gain matching law is directly dependent on the instantaneous information of the sliding surface. In addition, to improve the consistency of the closed loop and adaptability to the environmental conditions and parameter changes of the system, a perturbation observer such as the developed mode observer is used.
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Samira Zalaghi1
, Amir Hossein Zaeri2
1- Department of Electrical and Electronic Engineering, Islamic Azad University, Tehran, North Branch, Iran.
Email: Zalaghi.matpa@gmail.com (Corresponding author)
2- Department of Electrical and Electronic Engineering, Shahinshahr Branch, Islamic Azad University,
Shahinshahr, Isfahan, Iran.
Email: amzaeri@gmail.com
ABSTRACT: In this research, the goal is to develop a sliding mode control strategy based on the disturbance compensator to control the arrangement of a multi-agent system. For this purpose, the exponential access law is used to derive chattering-independent sliding mode control laws. In this design method, the sliding level information and its sign are used simultaneously, and by properly adjusting the sliding gain so that it is relatively larger than the switching gain, chattering effects can be removed significantly. On the other hand, since the adjustment of the switching gain is closely related to the changes of uncertainty and external disturbances, an adaptive approach is used to determine it. This is done using the Lyapunov stability theory and it is expected that the switching gain matching law is directly dependent on the instantaneous information of the sliding surface. In addition, to improve the consistency of the closed loop and adaptability to the environmental conditions and parameter changes of the system, a perturbation observer such as the developed mode observer is used.
KEYWORDS: Multi-agent System, Arrangement Control, Sliding Mode Control, Adaptive Disturbance Observer.
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1. Introduction
The problem of controlling the arrangement of multi-agent systems has attracted a lot of attention due to its wide applications in many fields such as unmanned vehicles and so on. The purpose of arrangement control is to design control rules to move the agents towards their desired state and thus achieve the target arrangement. Arrangement approaches can be divided into leaderless, single-leader and multi-leader. In the multi-leadership challenge, the goal is to direct followers to some desired space surrounded by leaders. This improves flexibility and maneuverability; Because the configuration can be easily controlled by controlling a small part of it. To realize the arrangement problem in multi-agent systems, the dynamics of the agents and the leader must be determined first. In these models, state variables, control signals and their descriptive parameters such as dynamic coupling coefficients between factors should be specified.
In addition, various performance objectives can be explored in this field, among which can be mentioned the arrangement in the presence of model uncertainties, external disturbances, fault of stimuli and delay in received data. In addition, another important issue is to avoid the collision of agents in different operating environments, which, of course, is related to the nature of the arrangement control algorithm. In other words, the control method should be able to properly by designing a suitable guidance and tracking program for the followers so that the agents always have a suitable relative distance from their neighbors. Therefore, the structure of a control algorithm in this field depends on the nature of predetermined performance goals, the type of agents and leaders used, and the conditions of the agents' functional environment.
In practical applications, individual equipment cannot achieve high efficiency and low cost target control. To improve efficiency, increase execution accuracy, reduce costs and reduce maintenance cost, several small devices with low cost, simple structure and easy assembly and maintenance are employed to work together to achieve the desired goals. The control objective is to replace a single-factor complex agent. Compared to single-agent systems, multi-agent systems have advantages:
1) Cooperation between agents can greatly increase the ability to perform the work of the automation device. Based on the extension of task performance capability, multi-agent systems can perform many complex tasks that are difficult to achieve by a single agent.
2) Multi-agent systems have lower energy costs and are easier to construct and maintain, which lead to better economic returns.
3) Multi-agent systems have better performance and higher efficiency.
A multi-agent system is a system that consists of a group of agents and can solve problems that are difficult for an individual agent through communication, consultation and cooperation between agents and the environment. Multiple agents cooperating with each other can complete work beyond the capacity range of an individual agent and manage the capacity of the entire system better than a single agent. Applications of multi-agent systems have increased in recent years, and control models and theories related to multi-agent systems have been used in engineering fields day by day. In aerospace technology, spacecraft can be considered as an agent. Tasks such as system cost reduction, system stability improvement, and performance scalability can be achieved by developing coordinated attitude control and multiple spacecraft formation control [1]-[2]. Using multi-agent technologies, multiple spacecraft systems, where spacecraft have simple structures and processes, can deal with collective targets that are difficult for a single spacecraft to process[3]. In the application of military technology, the use of multiple unmanned aerial vehicles (UAVs) [4] -[5] to perform reconnaissance and combat, the use of multiple robots for search, rescue, patrolling, mine clearance, etc., or the use of autonomous underwater vehicles to cruise under the sea can greatly improve overall combat capability, increase task completion and accuracy, and reduce casualties [6]-[7]. In industrial manufacturing processes, using multiple robotic arms to perform complex tasks on a production line can often improve assembly accuracy and production efficiency [8]-[9]. Research on multi-agent systems, as a new and comprehensive topic, has a wide range of applications and enormous potential value, attracting researchers in various fields and promoting the rapid development of related theories[10]-[11].
2. Dynamics of the second order multi agent system
In general, graph theory is used as an effective mathematical tool to describe coordinates and relationships between agents in a multi-agent system. Suppose 
that represents a directed graph where 
, represents the set of nodes, node i for the i-th agent, and represents the set of edges. An edge in the 
set is an ordered pair 
, which means that agent i can transmit information directly to agent j, but not necessarily the other way around. In contrast to the direct graph, the pairs of nodes in an indirect graph are not ordered, which means that the edge describes the paired information transfer between agent i and agent j. Hence, an undirected graph can be considered as a special case of a directed graph[6]. The matrix 
is a weighted adjacency matrix of the set with non-negative elements. Based on this, if there is an edge between the i-th factor and the j-th factor,
and otherwise 
. in other words:
(1) |
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The weight of communication between the i-th agent and the leader is denoted by 
. If here is an edge between the i-th agent and the leader, 
and zero otherwise. in other words:
(2) |
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The adjacency matrix can be rewritten as follows:
Based on the direct topology, the following points should be considered:
• Only some factors are directly related to the leader.
• Some agents must be coordinated with the leader's behavior only by following the behavior of other agents.
• Finally, all agents must be able to follow the leader's direction.
The communication between the agents or the agent with the leader is considered one-way.
The general multi-agent system used in this article includes the dynamic equation of the active leader as follows:
in which, 
and , 
represent the momentary position and speed of the leader, respectively. 
is a time-varying control input with condition 
and 
inertial leader. The point that should be remembered is that in the general dynamic state of the leader, it keeps its changes in the whole movement process and its behavior is independent of the followers. The dynamic equation of forces is described as follows:
Where
and 
represent the instantaneous position and speed of follower i, respectively.
represents the time-varying control input and 
is the follower's inertia. Also,
represents the uncertainty of the system caused by modeling errors and represents external disturbances, so that the condition 
is always assumed. This means that the instantaneous value of the uncertainty is not known, but the maximum range of its changes must be predetermined. N also represents the number of followers. Therefore, in the general state, the second-order general multifactorial system has 
state variables, and the dynamic behavior of the leader is somehow considered as a reference model, and the control rules of the followers are calculated from the momentary difference between the leader and the followers at the position level.
3. Adaptive sliding mode control based on disturbance compensator
In this section, the following exponential access condition is used to define the control rules[12]:
In fact, considering relation (6) for each follower, the control system is designed with two parameters. By considering the parameters, a stable dynamic can be achieved for the slip surface derivative. This problem means that the derivative of the slip surface becomes zero with the passage of time. Similarly, with high-order sliding mode controllers, in this situation, we can expect to reduce or eliminate chattering in the control signal by increasing the sliding mode gain. In other words, the section containing the slip surface has a great influence in dealing with the switching effects caused by the section containing the sign of the slip surface. As we know, the principles of sliding mode control are based on establishing the sliding condition. In the following, we show that using the above condition, Lyapunov stability is also established. For this purpose, we consider the Lyapanov function similar to the first design equal to the square of the slip surface:
(7) |
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By deriving it, we can write:
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(9) |
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Therefore, the derivative of the Lyapunov function in relation (8) is negative and the slip condition is established. The defined slip surface guarantees that in addition to the slip surface, its derivative also converges to zero. As a result, the exponential access condition can be expressed as follows:
(10) | |
By inserting the second derivative, we have the convergence error in the above relation:
(11)) | |
Therefore, the sliding mode control law is derived as follows:
where in:
(13) |
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4. Disturbance compensator design
As can be seen in relation (12), the vector function F includes nonlinear functions and the effects of external disturbances of follower dynamics. In this paper, a disturbance compensator is used to estimate these nonlinear effects including uncertainties and external disturbances. For this purpose, first consider the dynamics of the second-order multi agent system as follows:
(14) |
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Now, the nonlinear part including the uncertainty and the effects of external disturbances in the dynamics of each follower is considered as a state variable. In this case, the relation (14) can be rewritten as follows:
where in:
(16) |
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In this case, the dynamic equations of the disturbance estimator for the first follower are described as follows[13]:
(17) |
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And for the second follower, we can write:
(18) |
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And for follower N we will have:
(19) |
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In the above relationships, 
and 
are positive design parameters. Furthermore, the relationship is 
. The components of 
are positive and must be determined in such a way that the matrix 
is stable. In this case, the vector function F is rewritten as below:
(20) |
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5. Evaluation of AmbigoBot multi-robot arrangement control using the proposed method
In the rest of this section, a multi-agent system including a number of mobile robots is explained. As seen in Figure 1, each robot is an AmbigoBots type, the actual view of which is presented in Figure.2[14].
Fig. 1. Schematic view of AmbigoBots non-holonomic differential mobile robot[14].
According to Fig.1, the kinematic equations of each moving robot can be expressed as follows:
(21) | |
Fig. 2. A view of AmbigoBots mobile robot multimedia system.
In which, 
and 
represent the position of the center of mass of the mobile robot i and 
represent its momentary orientation. On the other hand, the position of each follower will be equal to:
By deriving equation (22) once, we can write:
(23) |
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In simple terms:
(25) |
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