# Event-triggered consensus control method with communication faults for multi-UAV

*Intell Robot*2023;3(4):596-613.

## Abstract

This paper investigates the event-triggered consensus for a group of unmanned aerial vehicles (UAVs) with communication faults under the assumption that the position sensors of some individuals are damaged. The objective is to make the UAV group reach consensus in urgent tasks such as obstacle avoidance or evasion. Using the Lyapunov stability theory, sufficient conditions to achieve system consensus are given based on different velocity and position interaction topologies. Considering the limited capabilities of sensors and processors, an event-triggered consensus protocol is adopted to reduce the sampling frequency. Finally, simulation results illustrate the effectiveness of our approach.

## Keywords

*,*communication faults

*,*consensus

*,*event-triggered control

*,*interaction topology

## 1. INTRODUCTION

The multi-agent systems (MAS) abstracted from complex systems, such as unmanned aerial vehicle (UAV) groups, are regarded as significant research objects for studying group intelligent behavior in recent years^{[1]}. With excellent performance in simplifying the analysis process, it is applied to various fields of UAVs, such as formation control^{[2]}, collaborative investigations^{[3]}, and many other fields. Through the consensus control of MAS, intelligent emergence phenomena can be achieved by self-organization and internal interactions^{[4,5]}. As a focus of international research in related fields, the realization of consensus has profound significance in practical applications^{[6–9]}.

The extensive and complex application scenarios of unmanned systems make fault-tolerant control crucial. One of the important factors contributing to the failure of unmanned systems is the damage to some individual sensor components. Huang *et al*. addressed the problem of IMU sensor failure by training and designing a controller based on long short-term memory (LSTM) neural networks and datasets and proposed an AI-based fault-tolerant control method. Furthermore, simulation verification further tested the recovery ability and effectiveness of the design method in the above scenarios^{[10]}. Similarly, GPS fault detection and exclusion were solved by Chang and Tsai through an approach based on the moving average (MA)^{[11]}. Compared with traditional least-squares residual methods, their approach exhibits higher performance in detecting small faults and similar performance levels in detecting large faults. This method has a lower incorrect exclusion rate (IER) than traditional parity space methods and has been verified through simulation. In addition, the complex communication environment of unmanned systems also poses a great challenge for consensus research, which involves time-delay networks, random networks, asynchronous networks, *etc.*^{[12]} proved the condition for consensus in time-delay networks by introducing disagreement functions abstracted from the Lyapunov function for the disagreement network dynamics. Based on this, Xiao *et al*. extended the result to variable topology^{[13]}. The concept of consensus in random networks was proposed by Hatano, referring to the system converging to consensus with a probability close to 1^{[14]}. Asynchronous networks have been extensively studied in order to be closer to the actual situation. It is difficult to update the system state synchronously due to the complex communication environment. The proof of the consistency of a single integral system in this situation is given by Cao *et al*.^{[15]}. Recently, Yan *et al*. presented a distributed control protocol and a distributed adaptive controller based on fault compensation to achieve consensus against link failures and actual/sensor faults^{[16]}. Moreover, Chen *et al*. developed an adaptive compensation protocol and an ^{[17]}. Based on the radial basis function neural network (RBFNN), A data-driven distributed formation control algorithm is proposed for MAS with sensor faults by Xiong and Hou^{[18]}.

Heterogeneous systems have also been a hot research topic in this field in recent years. Lee *et al*. first studied inertial systems and analyzed the impact of individual inertia indices on system consensus^{[19]}. Using the decomposition approach, Li and Spong investigated the stability of multiple inertial systems with non-balanced velocity/position coupling^{[20]}. By applying the graph theory and the Lyapunov direct method, the consensus problem of heterogeneous systems composed of first-order and second-order individuals was solved by Zheng^{[21,22]}. studied the consensus problem of a heterogeneous MAS consisting of quadrotors and two-wheeled mobile robots and proposed two linear quadratic regulations (LQR)-based consensus protocols to control the heterogeneous system, which showed good performance in practical systems. Based on the state observers, Ma *et al*. solved the output consensus problem of heterogeneous MAS, which is applicable when system states are not available^{[23]}. By designing distributed fixed-time observers and fixed-time tracking controllers, Du *et al*. investigated the fixed-time consensus problem for nonlinear heterogeneous systems^{[24]}. Li *et al*. further explored their research field to group consensus with input constraints^{[25]}.

Considering the limited capabilities of sensors and processors compared to traditional communication devices that rely on data interaction, event-triggered protocols are necessary for systems that rely on data interaction, as they can significantly reduce the sampling frequency. Drof *et al*. first introduced the concept of event-triggered and dynamically changed the system sampling frequency by measuring the state variables, which inspired ways to reduce the system load^{[26]}. The event-triggered threshold was correlated with the system state by Fan *et al*. Their research results show that this approach has superior dynamics compared to constant thresholds^{[27]}. These efforts have also been gradually extended to complex systems, including heterogeneous systems^{[28]} and time-delayed systems^{[29,30]}. Designed and implemented an event-triggered formation control for second-order MAS under communication faults based on linear matrix inequalities conditions on a real platform of UAVs^{[31]}. Investigates the secure consensus control of multirobot systems with an event-triggered communication strategy under aperiodic energy-limited denial-of-service (DoS) attacks. Each robot exchanges the local positioning information with other robots through the unreliable communication network and determines its consensus control based on transmitted position estimates. The paper proposes a secure control scheme such that the robots can move to the desired secure consensus position in the presence of attacks. Simulation and experimental results demonstrate the effectiveness of the event-triggered consensus in practical applications.

In this paper, we investigate the consensus problem for a group of multi-UAVs with communication faults under the assumption that the position sensor of some individuals is damaged. An event-triggered consensus protocol is designed for the UAV group based on a centralized triggering mechanism such that the UAV group can eventually converge to the same speed and position by sensor measurements, even if a sudden change in speed occurs in one individual.

The main contributions of this paper are as follows. First, we consider the scenario that the states of UAVs are sensed by their neighbors with communication faults and the position sensor of some individuals is damaged, which means that their interaction topologies of speed and position are not necessarily the same and the same topology can be considered as a special case in this paper. Furthermore, we consider the impact of the inertia index on system consensus and provide quantitative analysis results, similar to the research result in^{[19]}, but we do not limit the graph to be balanced. Moreover, an event-triggered consensus protocol is adopted to adapt to the case of this paper.

The rest of the paper is organized as follows. Section 2 formulates the consensus control problem and reviews the required lemmas. The main results and proof process are arranged in Section 3. Section 4 shows the simulation results of an illustrative example, and finally, Section 5 concludes this paper.

* Notations*: Given two matrices

## 2. PROBLEM FORMULATION AND PRELIMINARIES

### 2.1. Problem formulation

Consider a group of UAVs

where

* Remark 1*. Referring to hierarchical interaction mechanisms, the decision weight is influenced by individual attribute, which is determined by social relationships and interaction patterns. Higher decision weight means that an individual is less susceptible to the influence of neighbors. Therefore, the conclusion of this paper can be extended to the heterogeneous system. In addition, this paper focuses on the consistency proof of large-scale network topology based on the graph theory. Using traditional drone models will make the proof process obscure and cumbersome. The control input in this paper can be considered as the expected acceleration. Therefore, the dynamic model of UAVs has been simplified during the proof process.

* Definition 1*. The heterogeneous multi-UAV system (1) is said to reach consensus for any initial conditions, when and only when we have

To achieve urgent task objectives, an event-triggered consensus protocol will be proposed based on the following second-order consensus protocol:

where

* Remark 2*. The communication and sensor faults assumed in this paper refer to the inability of individuals to obtain information sent by neighbors through wireless data transmission or other means. Therefore, in order to cope with situations where wireless data transmission cannot be utilized due to strong interference, the method of individuals acquiring information through sensors, such as position and velocity, is widely adopted. We further assume that position sensors of some individuals are damaged, and they are unable to obtain the position information of surrounding individuals (in fact, the processing methods for damaged position sensors and speed sensors are generally similar, and this article only discusses the former), which is reflected in the Laplacian matrix that contains all-zero rows.

### 2.2. Preliminaries

* Lemma 1*. Communication topology can be represented as a weighted directed (undirected) graph

**Lemma 2**^{[25]}. If graph

(a)

(b) 0 is an eigenvalue of matrix

(c)

(d) Laplacian matrix

Laplacian matrix

The mass matrix of the system is recorded as

* Remark 3*. Actual physical meaning in the formula denoted by

Due to the limited refresh rate and sampling frequency of sensors and processors, the event triggering mechanism is proposed to reduce the pressure on sensors and save processor resources while ensuring that they can still react quickly in the face of unexpected situations.

State error is an important decision factor in event-triggered consensus control. Define

We define

And we have

Therefore, system (5) can be converted to the form in continuous time gives

Different from the previous consensus control methods [Similar to the form of System (5)] for the UAV system (1), the individuals are supposed to guarantee the interaction of velocity through independent information collection of position and velocity [the form of System (4)] when extreme cases, such as partial damage to position sensors, are considered, which is also the difficulty and focus of this study.

## 3. METHODS AND RESULTS

### 3.1. Linear transformation of the system

First, System (4) can be transformed into the form of system (5) based on the lemma as follows:

**Lemma 3**^{[26]}. For Laplacian matrix related to the directed graph, there exists a non-singular matrix

so that

where

where

Therefore, non-singular linear transformations are built as

Thus,

* Lemma 4*. For Laplacian matrix

Proof: Define

where

Since

then

Since

On the other hand, since matrix

The proof is, thus, completed.

According to Lemma 4, the positive vector

Furthermore, system (13) is equivalent to the system as follows:

Therefore:

Similarly, one has that

Define

From system (26), together with (5), one has that

where

According to (6), (7), and (8), Converting system (27) to the form in continuous time gives:

where

Thus, the proof of consensus in system (1) is transformed into the proof of stability of system (27).

* Remark 4*. The stability of system (27) implies that the state errors between the UAVs are zero. According to Definition 1, these two propositions are equivalent.

### 3.2. Analysis of stability

Now, the main result of this paper can be given as follows.

* Theorem 1*. Consider system (27) and event-triggered consensus protocol (28), sufficient conditions for the stability of the system are given as follows:

where

*Proof*: Choose the Lyapunov function as

in which

Define

The contract transformation does not change the positivity of the matrix, and

Since condition (31) implies that

Differentiate

in which

And

where

According to conditions (31) and (32), matrix is a positive definite matrix. One has that

in which

From condition (33), one has that

Define an event-triggered function as follows:

At an event time

which denotes that condition (33) can always be satisfied.

Therefore, based on Lyapunov stability principles, for an arbitrary initial state

which are equivalent to that

where

The proof is thus completed.

* Remark 5*. According to the event-triggered function (50), the event-triggered condition is met when the error

* Theorem 2*. Consider system (27) and event-triggered consensus protocol (28), the system will not exhibit the Zeno behavior, which means that the time interval between any two events will not be less than

in which

*Proof*: Similar to the proof in^{[32]}, we define

And one has that

and

in which

From (33), the solution of the equation above also satisfies that

so that

The proof is, thus, completed.

* Theorem 3*. Consider system (27) and event-triggered consensus protocol (28), for any positive definite matrix

* Theorem 4*. For the multi-UAV system, appropriate distance should be maintained between individuals. Consensus protocol (2) can be transformed into

in which

Therefore, offset

## 4. SIMULATION

According to the scenario described in Remark 2, we consider a UAV group consisting of five individuals whose dynamics are described by (1). The information interaction topologies of their velocity and position are described in Figure 1A and B, respectively. The position information of other UAVs cannot be sensed by individual 1 due to the damage of its position sensor.

One can obtain a Laplacian matrix of interaction topologies of velocity and position, respectively, as follows:

Consider

Through available sensors, UAV groups reach consensus within 10 s. Suppose that the UAV group encounters an emergency at 10 s that causes a sudden change of velocity in an individual.The overall task flow of UAV groups is shown in Figure 3.

Simulation results show that the system can reach consensus under the event-triggered protocol proposed in this paper. The variation curve of

The evolution of

Figure 5,Figure 6, and Figure 7 show the simulation results of the UAV group encounter the emergency situation.

The simulation results above demonstrate the effectiveness of the proposed protocol in this paper with communication faults, even in case of unexpected situations. The protocol proposed in this paper has a broader application scenario and is further promoted compared to traditional consensus proof. In order to cope with communication faults, wireless detection, and other tasks, an event-triggered protocol has been introduced due to the lower frequency and effectiveness of obtaining neighbor information through sensors compared to traditional information exchange based on wireless data transmission, which provides a theoretical basis for further physical verification. At the same time, the protocol allows for damage to some sensors, further improving the fault tolerance range of the system.

## 5. DISCUSSION

In this paper, an event-triggered consensus protocol of multi-UAVs has been proposed, which is used to solve the consensus problem of systems in normal or emergency situations with communication faults. Compared to traditional protocols, differences in the interaction topologies of speed and location information are allowed. With the help of Lyapunov stability principles, sufficient conditions to achieve system consensus are given. We have also presented simulation results to illustrate the effectiveness of our approach.

In future work, how to obtain more generalized and sufficient consensus conditions will be considered. Further, we will extend the results presented in this paper to complex inertial systems and topological networks, including random and time-delay networks.

## DECLARATIONS

### Authors' contributions

Made significant contributions to the research direction and design and conducted theoretical analysis, proof, and explanation: Guo Z, Wei C, Shen Y

Providing administrative, technical, and material support: Yuan W

### Availability of data and materials

Not applicable.

### Financial support and sponsorship

This work was supported by the Science and Technology Innovation 2030-Key Project of "New Generation Artificial Intelligence" (No. 2018AAA0102403) and the National Natural Science Foundation of China under grants (No. T2121003, No. U20B2071, No. 91948204, and No. U19B2033).

### Conflicts of interest

All authors declared that there are no conflicts of interest.

### Ethical approval and consent to participate

Not applicable.

### Consent for publication

Not applicable.

### Copyright

© The Author(s) 2023.

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## Cite This Article

**OAE Style**

Guo Z, Wei C, Shen Y, Yuan W. Event-triggered consensus control method with communication faults for multi-UAV. *Intell Robot* 2023;3(4):596-613. http://dx.doi.org/10.20517/ir.2023.32

**AMA Style**

Guo Z, Wei C, Shen Y, Yuan W. Event-triggered consensus control method with communication faults for multi-UAV. *Intelligence & Robotics*. 2023; 3(4): 596-613. http://dx.doi.org/10.20517/ir.2023.32

**Chicago/Turabian Style**

Guo, Zilong, Chen Wei, Yankai Shen, Wanmai Yuan. 2023. "Event-triggered consensus control method with communication faults for multi-UAV" *Intelligence & Robotics*. 3, no.4: 596-613. http://dx.doi.org/10.20517/ir.2023.32

**ACS Style**

Guo, Z.; Wei C.; Shen Y.; Yuan W. Event-triggered consensus control method with communication faults for multi-UAV. *Intell. Robot.* **2023**, *3*, 596-613. http://dx.doi.org/10.20517/ir.2023.32

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