Practical Formation Control for Multiple Anonymous Robots System with Unknown Nonlinear Disturbances  
[PERSON]  
1 Marine Engineering College, Dalian Maritime University, Dalian 116026, China; [EMAIL_ADDRESS] (PX. ); [EMAIL_ADDRESS] (M.X. ); [EMAIL_ADDRESS] (G.X)  
[PERSON]  
2 College of Artificial Intelligence, Nankai University, Tianjin 300350, China  
constrained scenarios are investigated involving time-delayed [27], locomotion constraints of robots [30; 31; 32], collision/deadlock avoidance [33; 34; 35], finite-time control [36; 37], and input saturation [23]. According to the aforementioned existing literature, most of the results focused on equidistant circular formation control problems in the aspects of theory and application. However, when performing specific tasks, even distribution may not be the best configuration [38], forming arbitrary formations on a circle or plane has been studied by only a few recent works [25; 30; 36]. [PERSON] et al. [36] designed distributed control protocols to control multiple robots to form a predetermined circular formation. In order to make the strategies more practical, the sampled data control protocol and finite-time control protocol were further extended. [PERSON] et al. [30] handled the situation where the mobile robots are subject to motion constraints. To facilitate the establishment of a more general formative framework, [PERSON] et al. [25] studied the general formation control problem of multiple mobile robots on a plane, where the robots are expected to maintain a distribution formation, and rotate or remain stationary around a stationary or moving target. This paper aims to design a distributed control law that can ensure that multiple anonymous mobile robots form any non-uniform and non-circular formation with a moving target center on a plane. When the prescribed formation is set as an even distribution case, the non-uniform and non-circular formation thus reduces to the uniform circle formation. More specifically, the whole control objective can be divided into two sub-objectives. The first sub-objective is target circling, which indicates that all mobile robots must converge into a circular formation on a preset target as its center and rotate around the target with the same speed. At the same time, the second sub-objective is spacing adjustment, which means that all robots need to keep a desired distance from their neighboring robots without the requirement that all required distances between adjacent robots are the same. A networked system composed of multiple mobile robots under the models described by kinematic points is considered. Additionally, all robots move on a plane. Meanwhile, the robots are oblivious, anonymous, and unable to directly exchange information with each other. In other words, they can only perceive state information (including the relative position and relative speed) between the robot and its neighbors and the counterpart between the robot and the target. This study focuses on keeping order and avoiding collisions between anonymous mobile robots, which makes the strategy more attractive when applying to real robot systems. More specifically, a system composed of multiple mobile robots, modeled as kinematic points and moves on the plane, is considered. The robots can only perceive the relative position and speed of neighboring robots and that between robots and the target. The difference between this paper and Ref. [39] is listed as follows. (1) Different from Ref. [39], which only pays attention to circle formation, the main goal of this paper is to design a general formation control protocol with obstacle avoidance conditions. (2) From a practical perspective, the proposed control protocol considers the case of unknown nonlinear disturbance, which makes it easy to use in real robot systems. The main contributions are summarized as follows: firstly, we design a distributed control law to deal with the formation problem asymptotically using the information of relative position and speed.