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1.1 Background introduction and research significance Multi‐robot systems (MRSs) have important advantages over single robotsystems, such as flexibility, robustness, efficiency and redundancy. In severalapplications, a group of robots are required to accomplish the desired taskscooperatively, maintaining a specific pattern called a formation. The formationcontrol (FC) of a MRS is a technology for keeping the robots in the scheduledformation and adapting to the environment while moving to the target position.The formation control of multiple robots is very important in a number of areas,such as: (a) personal robotics systems where small independent robots can carryout the task of moving an object, such as a table, in a cooperative manner inthose situations where a single robot cannot perform the task alone; (b) militaryrescue and reconnaissance operations, where vehicles are often required tomaintain a close formation; (c) the self‐reconfiguring of metamorphic roboticsystems; (d) controlling the formation of satellites for scientific and planetaryexploration; and (e) autonomous vehicle highway systems where it is necessaryto control a platoon of cars in formation while allowing them to perform suchmaneuvers as lane changes, merger, or obstacle avoidance. Formation control isan important research field for MRS. Formation control is viewed as a kind of information consensus in which robots or agents interact with each other usingvarious sensors and communication techniques. The main goal is to coordinate aswarm of mobile agents or robots so as to achieve a desired formation pattern,avoiding inter‐agent collisions at the same time.Motivated by the above analysis, in this research, the formation formingmaintain for the multi-robot/agent systems will be studied, in a crowdedenvironment with obstacles. Through the design of a special formation controllaw, from the initial position to the targeted position with an aim of avoiding anycollision with any obstacle founded in the path leading to the goal position andmaintain the predefined formation.1.2 Related workThere are several types of formation control that have been studied in the fieldof formation control, for instance, in [1], Dongyu Li, Lihua Xie, Shuzhi Sam Geand Guangfu Maa define a multilayer formation control problem, where theagents can receive and transmit information among the layers. This paper alsogives a clue on multilayer formation control design in the presence of practicalissues, such as model uncertainties and loss of velocity measurements. In [2] BoHe and Feng Gao analyze the influence of leader state on closed loop dynamicsof formation theoretically. For the first time, it is proved that the leaderinformation can mask out the effect of others and the closed loop dynamics offormation is equivalent to the leader follower topology if all followers canreceive the leader information and others. In [3], Cheng-Chew Lim, Yutong Liuand Peng Shi developed a formation control strategy is proposed for multipleelliptical agent systems. The collision-free algorithm is built based on directionand distance of avoidance group of each agent. In [4] Yang Fei and Peng Shi theproblem of achieving time-varying formation for second-order multi-agentsystems with actuator hysteresis, unknown system dynamics and externaldisturbances. In [5], Cassandra McCord1, Jorge Pena Queralta1, Tuan NguyenGia1 and Tomi Wasteland: Coordination of multiple robots in order tocooperatively perform a given task requires a certain distribution of the differentunits in space. In [6], Jiayan Wen, Peng Xu, Chen Wang, Guang ming Xie,Yuan Gao investigate event-triggered circle formation problem of multi-agentsystems (MASs) with limited communication bandwidth over such networksetup among agents, in which each agent can only perceive the angular distancefrom itself to the nearest neighbor in counterclockwise direction as well as thecounterpart in the clockwise direction be acquired through communication. In[7], Bo He FrancoGarofalo; Francesco Lo Iudice: Steering the dynamics of a multi-agent systemtowards a balanced circular formation is a paradigmatic ex-ample of formationcontrol that attracted extensive research interest from the engineering community. The traditional estimation and control strategies typically relied onboth accurate directional measurements and a thorough knowledge of theenvironment, which are seldom available in applications. In [15], Amir Amini;Amir Asif; Arash Mohammedi: studies formation control in general linearmulti-agent systems where communication between the neighboring agents isbased on the fulfillment of dynamic event-triggering (DET) conditions. A novelco-design optimization is proposed to simultaneously design all required controland DET parameters. In [16], H TRNG NGHA, TRN THANH KT,NGUYN TN LU propose a distributed control method for multi-mobilerobots to avoid obstacles. Firstly, the Limit Cycle (LC) method is exploited toset the reference trajectory for robots to avoid obstacles. Secondly, the controlrule that control a leading robot following the reference path is introduced. References【1】 Li D, Ge SS, He W, Ma G, Xie L. Multilayer formation control of multi-agentsystems. Automatica. 2019 Nov 1;109:108558.【2】 He, B. and Gao, F., 2020. Influence analysis of leader information with application toformation control of multi-agent systems. International Journal of Control,Automation and Systems, 18(12), pp.3062-3072.【3】 Liu Y, Shi P, Lim CC. Collision-free formation control for multi-agent systems withdynamic mapping. IEEE Transactions on Circuits and Systems II: Express Briefs.2019 Sep 5;67(10):1984-8.【4】 Fei, Yang, Peng Shi, and Cheng-Chew Lim. "Neural network adaptive dynamicsliding mode formation control of multi-agent systems." International Journal ofSystems Science 51.11 (2020): 2025-2040.【5】 McCord, C., Queralta, J.P., Gia, T.N. and Westerlund, T., 2019, September.Distributed progressive formation control for multi-agent systems: 2d and 3ddeployment of uavs in ros/gazebo with rotors. In 2019 European Conference onMobile Robots (ECMR) (pp. 1-6). IEEE.【6】 Wen, J., Xu, P., Wang, C., Xie, G. and Gao, Y., 2019. Distributed event-triggeredcircle formation control for multi-agent systems with limited communicationbandwidth. Neurocomputing, 358, pp.211-221.【7】 He, B. and Gao, F., 2020. Influence analysis of leader information with application toformation control of multi-agent systems. International Journal of Control,Automation and Systems, 18(12), pp.3062-3072.【8】 Mehdifar, F., Bechlioulis, C.P., Hashemzadeh, F. and Baradarannia, M., 2019.Prescribed Performance Distance-Based Formation Control of Multi-Agent Systems(Extended Version). arXiv preprint arXiv:1911.07266.【9】 Yang, Z., Zhang, Q. and Chen, Z., 2019. Formation control of multi-agent systemswith region constraint. Complexity, 2019.【10】 Chen, F. and Ren, W., 2019. On the control of multi-agent systems: A survey.Foundations and Trends in Systems and Control, 6(4), pp.339-499.【11】 Li, Xiaoduo, Xiwang Dong, Qingdong Li, and Zhang Ren. "Event-triggeredtime-varying formation control for general linear multi-agent systems." Journal ofthe Franklin Institute 356, no. 17 (2019): 10179-10195.【12】 Shi, Q., Li, T., Li, J., Chen, C.P., Xiao, Y. and Shan, Q., 2019. Adaptiveleader-following formation control with collision avoidance for a class ofsecond-order nonlinear multi-agent systems. Neurocomputing, 350, pp.282-290.【13】 Sakurama, K., 2020, December. Formation Control of Multi-Agent SystemsWith Generalized Relative Measurements. In 2020 59th IEEE Conference onDecision and Control (CDC) (pp. 2799-2804). IEEE.【14】 DeLellis, P., Garofalo, F. and Iudice, F.L., 2020, May. Formation Control ofMulti-agent Systems in an Uncertain Environment. In 2020 European ControlConference (ECC) (pp. 454-458). IEEE.【15】 Amini, A., Asif, A. and Mohammadi, A., 2020, July. Dynamic event-triggeredformation control for multi-agent systems: A co-design optimization approach. In2020 American Control Conference (ACC) (pp. 707-712). IEEE.【16】 NGHA, H.T., KT, T.T. and LU, N.T., 2019. Distributed formation controland obstacle avoidance of MULTI-ROBOT system. Journal of Science andTechnology-IUH, 40(04).
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