Collision avoidance cooperative attack with multiple pursuers based on bearing-only measurements

https://doi.org/10.1016/j.jfranklin.2019.11.061Get rights and content

Abstract

This paper provides a novel collisions avoidance cooperative attack method for multiple pursuers system based on bearing-only measurements. In the cooperative attack problem, the control algorithm must drive all of the attackers to converge to the desired position (target). However, the traditional consensus protocol based on the relative position information may cause the intervehicle collisions before the attackers can hit the target. To solve this issue, a distributed cooperative consensus control algorithm is proposed. Under this algorithm the potential collisions are proved to be avoided while the pursuers can achieve the final attack. Further more, considering the relative distance information is unavailable for some types of the pursuers to get, a control algorithm based on bearing-only measurements is proposed by referencing the distributed localization algorithm used in the sensors network. The advantages of this method are summed up as fully distributed, collisions avoidance, and bearing-only measurements. Finally, the effectiveness of the results is illustrated by numerical simulation.

Introduction

In modern military operation, the cooperative attack problem is one of the interesting and significant issues. As we know, when organized as a coordinated group, missiles system will provide more capabilities than the individual missile system in detecting the targets and penetrating the formidable defensive systems. Considering it is difficult to defend a group of attackers bursting into sight, multiple missiles against a single target can greatly enhance the target’s damage effect and decrease the target’s evasive possibilities [1]. The problem of the cooperative attack is essentially a problem that the multiple agents converge to a certain position through information exchange.

The cooperative control of a multi-agent system is a method that has attracted much attention, due to its potential applications in such areas as satellite formation flying, cooperative control of unmanned air vehicles, and sensor networks [2], [3], [4], [5]. From the perspective of the control structure, the cooperative control can be classified into the centralized method [6] and the distributed method [7], [8], [9]. Compared with the centralized method, the distributed control is more ideal when dealing with the system with a large number of agents. According to the distributed method, each agent can generate its own control independently based on the local information. Consequently, the requirements for the computational capacity and the communication bandwidth are decreased. Also, we notice that in the distributed algorithm, the consensus of the multi-agents system can be achieved when each agent only knows the information of its neighbours. Therefore, if the distributed algorithm is used to solve the cooperative attack problem, the cooperative attack can be achieved, even though there are only a few attackers know the position of the target.

In the formation flight of unmanned air vehicles, the consensus-based approaches convert the formation control problem into the consensus problem of relative positions and velocities of multi-agents [10], [11]. The formation control is achieved by using the relative positions to ensure global asymptotic convergence to the desired formation. In the formation problem, the collision avoidance has been widely considered, such as [12], [13]. In [12], the author solved the collision avoidance problem by using an optimization method. And in [13], the stochastic sampling method is considered. However, even though the formation control algorithm can partly solve the cooperative control problem of the formation flight [14], [15], [16], [17], the cooperative attack problem is different from the traditional formation flight. In the formation flight, there is an offset in the control algorithm to keep the formation, so that the collision is avoided even though the virtual positions of the vehicles achieve consensus. While in the cooperative attack problem, the offset is canceled in order to make the agents converge to the desired position. Therefore, the consensus protocol based on the positions of the missiles may cause a situation in which the missiles collide with the other before they achieve the final attack (Fig. 1).

The cooperative attack problem can be restated as a consensus tracking problem [18], [19], [20], [21]. The target can be viewed as a leader agent, and there exists at least one follower to be able to sense the target and other agents should be able to connect to the leader via the first follower. When considering the cooperative attack problem with collision avoidance, an interesting result is given in [22]. In this article, the author proposes a cyclic pursuit algorithm, according to which the pursuers will move toward the target in cyclic order, and thus, the collision is avoided. The articles [23], [24], [25] also consider the same problem by using similar methods. However, considering the actual applications, it is difficult to drive a missile to circle around the target. Therefore, these results cannot be used in multiple missile systems. Meanwhile, we should also notice that the relative position information includes the relative distance information and the bearing information. In practical, the relative distance measurement error can be very large if the agents are widely separated. And for some types of the missiles, the relative distance information is even unavailable to get, such as the infrared imaging guidance missile. To obtain the relative position information, more equipments are needed and the cost of the system is increased. The control algorithm based on bearing-only measurements is quite practical, because most of the missiles and vehicles are vision-based systems and the bearing measurement is more cost effective compared with the relative position information measurement when considering the cost of the measuring equipment [26], [27]. In [28], [29], [30], the bearing measurements are proposed for the location of a 2-D network, and Zhao and Zelazo [31] extends this problem to d-dimensional spaces. In [32], the author considers the measurements problem with a switching topology, so that the communication topologies in the localization process can switch over time. By using the distributed localization algorithm, each agent holds a local coordinate system with no knowledge about the global coordinate system and measures the bearing angle information about its neighbors in its local coordinate system [33]. All of the agents will cooperatively find the true location of themselves according to the distributed localization algorithm.

Considering the practical requirements, how to design a controller to avoid the potential collision of the agents before they approach the target while reducing the cost of the measuring equipment becomes a significant and challenging issue. Motivated by the above observations, in this paper we propose a distributed control algorithm to avoid the potential intervehicle collision of the pursuers before the final attack. Moreover, this algorithm is a bearing-only based method for each vehicle should only know the bearing angle information about its neighbors, which is applicable for infrared measurement systems. The main contribution of this paper is concluded as following.

(1) Collision avoidance. A distributed cooperative consensus protocol is designed in this paper which prevents the potential collisions caused by the consensus protocol based on the relative position of the vehicle. And the intervehicle collisions are proved to be avoided before the final attack, while the vehicles can consensus to a certain point. Therefore, the cooperative attack problem can be well solved.

(2) Bearing-only measurement. By combining the design of the distributed control system with the distributed localization algorithm used in the sensors network, the new algorithm can fully take the advantage of the coordinate system in both of the consensus control and the information acquisition.

The rest of this paper is organized as follows. In Section 2, we provide some background of the graph theory. Section 3 shows the main results of this paper. In Section 4, some numerical examples are presented to show the effectiveness of the proposed control algorithms. Finally, concluding remarks are given in Section 5.

Section snippets

Mathematical preliminaries

Consider there exist N pursuant agents, labeled as agents 1 to N. The graph G=(V,E) is denoted to be a directed communication topology among N agents, where V={1,2,,N} and EV × V stand for the node set and the edge set, respectively. An edge (i, j) ∈ E indicts that agent j can obtain information from agent i, but not contrarily. The neighbors of agent i are represented as Ni={jV|(i,j)E}. The graph G is said to be connected if there exists a path among each pair of distinct nodes. The

Control algorithm design

To clarify the design of the control algorithm, this section can be divided into three parts. In the first part, an intervehicle collisions avoidance control algorithm is given by using a direct velocity control, and the collisions can be avoided if all of the agents move with the desired velocity. In the second part, an adaptive controller is designed so that the agents can track the velocity control signals given in the first part, and the consensus can be achieved without using the relative

Simulation

This section gives two numerical examples of six pursuant agents and a target agent to illustrate the theoretical results. In the first example, we apply the control algorithm (55) in the simulation, and all of the agents can only measure their neighbors’ bearing information. And the second example is in contrast to the first example to explain the effect of the collisions avoidance term, where the collisions avoidance term is set to be zero for all of the time.

Conclusion

This paper considers the potential intervehicle collisions problem caused by the consensus protocol based on the relative position of the vehicle. A distributed cooperative consensus control algorithm is designed under which the intervehicle collisions are proved to be avoided while the vehicles can consensus to a certain point. Moreover, by combining the design of the distributed control system with the distributed localization algorithm used in the sensors network, the control objective can

Acknowledgments

This research was supported by the National Natural Science Foundation of China under Grant no. 11332001, Research project fund 17-163-11-ZT-003-018-01, Joint fund of the Ministry of education of China 6141A020223. The author would like to thank the reviewers and the associate editor for the helpful comments on this paper.

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      The passive bearing-only sensor has been extensively implemented in relative navigation missions such as UAV formation flight, optical navigation for interplanetary missions and visual navigation due to its weight and cost constraints (Chu et al., 2020). For multiple pursuers, a novel collision avoidance cooperative attack method grounded on bearing-only measurements is presented in (Hu and Yang, 2020). To prevent inter-vehicle collisions, a distributed cooperative consensus control algorithm is proposed before the attackers can hit the target.

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