Formation and obstacle avoidance in the unknown environment of multi-robot system

This paper presents formation and obstacle avoidance in the unknown environment of multi-robot system. With the leader-following algorithm, multi-robot system can form and keep various formations and realize formation transformation. Through artificial potential field algorithm, multi-robot system can successfully avoid obstacle in the unknown environment while keeping formation. The proposed method not only can realize obstacle avoidance of multi-robot system with formation in the unknown environment, but also can be adopted in real time and applicable to many different situations. By means of Pioneer3 mobile robot platform, the simulation and experimental works, which considering various formations and unknown environment, demonstrate the effectiveness of the proposed method.

input of sensor information.The selection of behaviors of robot is based on some rules and each behavior has its specific purpose or task.The behavior-based algorithm can obtain real time feedback and it has complete distributed control structure.The collaboration of robot is implemented by sharing the knowledge of relative position, status, etc., among robots.Therefore, the merits of behavior-based algorithm are parallel, distributed and in real time.The disadvantage of this method is that, it is lack of clear definition of group behavior.It is hard to design the local basic behavior and control rule to synthesize nominated formation, and so on.
Another type of methods is virtual structure method [4].This method assumes that there is a geometric shape among robots, which is called as virtual structure.During the movement of robots this structure is kept to fix.The merit of this method is that, it is easy to assign the group behavior of robot and it has feedback of formation.However, this method limits the scale of movement due to the virtual structure and the formation is therefore not so flexible.
The third type of method is leader-following algorithm [5].In this research, this algorithm is adopted to keep the formation due to its merits.This method will be briefly introduced in section II.
Concerning about obstacle avoidance, there are many algorithms.Artificial potential field algorithm is very suitable for real time control of robot due to its explicit physical implication and simple mathematical description.This method is adopted to realize obstacle avoidance in this research.The fundamental idea will be introduced in section III.
This paper presents formation and obstacle avoidance in the unknown environment of multi-robot system.With the leader-following algorithm, multi-robot system can form and keep various formations and realize formation transformation.Through artificial potential field algorithm, multi-robot system can successfully avoid obstacle in the unknown environment while keeping formation.The proposed method not only can realize obstacle avoidance of multi-robot system with formation in the unknown environment, but also can be adopted in real time and applicable to many different situations.By means of Pioneer3 mobile robot platform, the simulation and experimental works, which considering various formations and unknown environment, demonstrate the effectiveness of the proposed method.
The organization of the paper is as below.In section II, the multi-robot system formation by means of leader-following algorithm is introduced.Section III presents the obstacle avoidance of multi-robot system with formation in the unknown environment by means of artificial potential field method.Section IV shows the simulation and experimental results by use of Pioneer3 mobile robot platform.In the last section V the conclusion is drawn.

II. MULTI-ROBOT FORMATION BY MEANS OF LEADER-FOLLOWING ALGORITHM
A. Leader-Following Algorithm Leader-following algorithm is first proposed in [5], which is adopted for the formation control of mobile robot.The fundamental idea is that, in a group composed of multiple robots, one of robots is assigned as the leader and others are followers.The followers are keeping the position and direction with a certain distance to the leader.According to the relative position between leader and follower, it can form different network topology structures, i.e., different formations.In this algorithm, the collaboration of multi-robots is implemented based on the knowledge about the status of leader robot.The leader can control the motion trend of the system.Each follower is controlled with a formation through keeping the limitation of distance, direction angle, etc., with the leader.
The leader-following algorithm can be applicable to various situations.For example, either one leader or more leaders can be assigned.But the leader of the formation of group must be only one.Since the leader-following algorithm is based on the space geometric relation among robots, the merit of this algorithm is that, the behavior of the entire robot group can be controlled as long as the behavior or trajectory of the leader is given.It can simplify the control process of multi-robot system.However, this algorithm has two obvious disadvantages.One is that, there is no clear formation feedback because the leader does not consider other robots' movement during the course of motion.For example, if the leader moves too fast, or the follower is blocked by obstacle, the formation will be destroyed.Under the serious condition, the quality of fulfilling the task may be affected.The second disadvantage is that, if the leader is failed, the entire formation can not be kept and the consequence will be very serious.
The leader-following algorithm is mainly adopted for the flight of spacecrafts with formation, the collaboration of robot manipulators in the production line, as well as searching in a region by multiple robots, etc.

B. Behavior of Leader for Formation
The task of leader is to lead the entire formation to the destination.By means of the idea of behavior-based algorithm, the control of leader has three behaviors.One is destination-oriented forward walking behavior.The second is obstacle avoidance behavior, which will be introduced in the next section.The third is lock-prevent behavior.The highest priority of the above three behaviors is lock-prevent behavior.And the lowest priority of them is destination-oriented forward walking behavior.

I. Destination-oriented forward walking behavior
In the destination-oriented forward walking behavior, a robot can be regarded as particle.The destination position of leader is defined as ) , (

II. Lock-prevent behavior
In the process of robot movement to the destination in the environment with obstacles, robot may not continuously move and can not fulfill the task.At this moment, robot is staying at the status of locking.In order to assist robot escape from this status, it is better to define a lock-prevent behavior.
In this research, Pioneer3 mobile robot is adopted to test the proposed method.This kind of robot has defined a lock-prevent behavior, called ArActionStallRecover. When the wheel of the robot is locked, it can move by means of a series of pre-defined actions.Normally, this behavior is set with the highest priority.

C. Behavior of Follower for Formation
The task of follower is to reach the destination following the leader.It only needs to follow the leader and be able to avoid the obstacle, without knowing the position of destination and the route of formation.Therefore, one of important behaviors of follower is to keep the formation.
According to [6], the motion function of single mobile robot is as below.
where ( , , ) x y φ denotes the robot position and motion direction in a certain inertial coordinate system.
) , ( ω v denotes the linear velocity and angular velocity of moving object.A certain point h at the place which has the distance L from the axis line of robot to the center of the object is considered as below.The reason to consider this point is that, this point is always the central position of the sensor of moving object in the experimental platform.The offset point of this axis center is defined as, sin cos It can be obtained as below after equation transformation.
Based on the above model, a simple leader-following system, illustrated by Fig. 1, can be considered, where L R denotes leader, F R follower.
Therefore, the tracking error between F R and V R is where The next step is to choose a control law to reduce the tracking error.The control law is selected as below.(7) [6] has proved the convergence of this algorithm.

A. Behavior of Leader for Obstacle Avoidance
The behavior of leader for obstacle avoidance is based on artificial potential field (APF) algorithm.The APF algorithm is proposed by Khatib in 1986 [7].Originally, this method is to solve the problem that manipulator can not bumps into working table when it moves to grasp the object.Later it is found that this method has good effect for mobile robot.It can generate very smooth moving trajectory.The basic idea of this method is to simplify the robot, obstacle and target to be a point respectively.Therefore, the moving space of robot becomes a two-dimensional space.If robot wants to reach the destination, it needs to continuously move to the destination.This movement process can be regarded as a motion in a virtual artificial field of force.The obstacle can generate repulsion to robot and the target point can generate attraction.The resultant of attraction and repulsion can control the moving direction of robot.Any moving direction of any position of robot in the space is determined by the total strengthen of field composed by repulsion field of obstacle and attraction field of target point.The attraction position field function is defined as, ) X (X, k = (X) U The repulsion potential field function is as, η is positive ratio gain coefficient of position.
) , ( 0 X X ρ is the shortest distance between robot and obstacle in the moving space. 0ρ is the biggest distance of obstacle affecting the robot.Its value is determined based on the specific situation between obstacle and target point.Normally, this value is smaller than the half of the distance among each obstacle and the smallest distance between target point and each obstacle.When robot does not reach the target point, the repulsion of obstacle to the target point is as, The resultant force of robot is as, This resultant force determines the moving direction.The graph of force is illustrated as below.

B. Behavior of Follower for Obstacle Avoidance
Concerning about obstacle avoidance, assume that each robot has one virtual outer covering.The radius of this outer covering is determined by the maximal velocity of robot as well as braking ability.It is therefore called as protected shell.Any object and other robots should be avoided to enter into the region of this protected shell.
If follower detects out one obstacle in this protected shell, illustrated by Fig. 3, it will turn a small angle to avoid the direction of this obstacle.And then it will turn an angle which is necessary to keep the formation.These two angles are combined to calculate the new expected angle  where l denotes the shortest distance between the center of follower and obstacle.γ denotes the relative angle of the nearest point between the center of robot and obstacle.According to this strategy, follower can not be collided with the nearest obstacle while keeping the expected formation.

B. Simulation and experimental results
Pioneer3 mobile robot platform provides a simulation system MobileSim.In this system, a map can be installed and In order to verify the proposed method, the following simulation and experimental works have been carried out by use of MobileSim.
Fig. 5 is the simulation results about the obstacle avoidance of leader robot individually.

V. CONCLUSIONS
This paper introduces formation and obstacle avoidance in the unknown environment of multi-robot system.With the leader-following algorithm, multi-robot system can form and keep various formations and realize formation transformation.Through artificial potential field algorithm, multi-robot system can successfully avoid obstacle in the unknown environment while keeping formation.The proposed method not only can realize obstacle avoidance of multi-robot system with formation in the unknown environment, but also can be adopted in real time and applicable to many different situations.By means of Pioneer3 mobile robot platform, the simulation and experimental works, which considering various formations and unknown environment, demonstrate the effectiveness of the proposed method.In the future research, we will further consider more complicated environment with various types of obstacles.In addition, we will propose new method to optimize the movement of multiple robots with formation in order to improve autonomous and adaptive features of multi-robot system.
of the leader is as below.

Fig. 1
Fig.1 Simple model of leader-following system

k
is positive ratio gain coefficient of position.g X X , respectively denote the position of robot and target point at the moving space.
between robot and target point.The attraction force att F of target point is the negative gradient of attraction potential field.It is as below.

Fig. 2
Fig.2 Force of robot in the artificial potential field

Fig. 4
Fig.4 Sonar distribution and its identity coordinate of Pioneer3 be obtained.User can run the developed program in MobileSim before running on Pioneer3 mobile robot.Actually, it has same effect of running in MobileSim and Pioneer3 mobile robot.