# Leader-Follower Formation Control of Wheeled Mobile Robots without Attitude Measurements
## 1 Introduction  
In recent years, autonomous mobile vehicles have attracted interest from the scientific community, mainly due to the wide range of applications in which they can be implemented; ranging from searching, surveillance and exploration applications to cargo transportation and cooperative manipulation [1, 2]. Cooperative formation control focuses more on the efficiency and fault tolerance that a single mobile robot could not provide [3]. A particular problem of multi-robot coordination that has received much attention in the last decades is formation control. The objective of formation control of multiple mobile robots is to achieve a desired formation pattern while guaranteeing that the multiple robots as a group accomplish a given task cooperatively [4]. The formation control approach has been implemented in different types of vehicles, this in order to perform the tasks, with greater ease and robustness. For example, in [5] this approach was used for underwater vehicles, where the follower tracks a reference trajectory based on the leader position and predetermined formation without the need for leader's velocity and dynamics. This is desirable in marine robotics due to weak underwater communication and low bandwidth. In order to tackle the harsh conditions of underwater environment, in [6] the authors drive unmanned underwater vehicle using a deterministic artificial intelligence approach. This technique is based on self-awareness of the robot and relies on the dynamic of the vehicle and linear regression instead of stochastic or traditional control theory methods. Another application of this technique is presented in [7], where the authors address formation control for a team of quadrotor UAVs in which the robots follow a specified group trajectory while safely changing the shape of the formation according to the specifications of the task. On the other hand, in [8] the formation control of a group of unicycle-type wheeled mobile robots at the dynamicslevel with a little amount of inter-robot communication is investigated. Another interesting approach arises from bio-inspired control techniques. The robotic swarm control is a new paradigm of multi-robot control system aiming to achieve task in collective way using low level interactions between the members of the swarm. For instance, in [9] the authors proposed to employ a variation of the particle swarm optimization (PSO) algorithm to achieve formation in a swarm of agents while tracking a dynamic target. This techniques is inspired on the pheromone based communication of the ant colonies. Several formation control approaches have been proposed in the literature, and they are mainly divided in three categories: behavior-based methods, leader-follower and virtual structure methods [10; 11]. The behavior-based approach is inspired by the emerging behaviors in nature such as flock of birds, random walks of ants and school of fish [12]. In this case, a group behavior (or mission) comprises some low-level actions (or sub-tasks) and is constructed to achieve the global objective, where the individual robot needs to perform low-level actions to accomplish the group behavior [13]. In the leader-follower formation [14; 15], one robot is chosen as the leader which decides the whole formation group's moving trajectory, the other ones are the followers which are tasked to follow the leader, and the desired relative separations and bearings are expected to be maintained [16]. This strategy is easily implemented by using two controllers only and is suitable to describe the formation of robots, but it is hard to take into account the functioning capabilities of different robots, i.e., ability gap of a robot [17]. Finally, in the virtual structure formation, robots behave like particles embedded in a rigid virtual structure [18].