Iterative Solution of Relative Localization for Cooperative Multi-robot Using IEKF

.


Introduction
The mobile robots can be used in various fields, and the mobile robots' technology and devices are classified according to the applied areas. The localization problem is one of the most important techniques and a fundamental for a mobile robot system. We can track the path of mobile robot if the robot knows its exact position continuously. When the robot uses only the dead-reckoning technique based on an odometry sensor, the accuracy of localization is limited by accumulation of positioning error, slip of a robot's wheel, kidnap problem, etc. [1]. The kidnap problem means that a well-localized robot is teleported to other position without any notification. The kidnapped robot is relocated in a different position manually and it has to relocalize itself based on the new sensors.
The multi-robot cooperation system has attracted a lot of interest recently. The multi-robot system has some benefits. Each robot in the multi-robot system can be more downsized than a single robot system, and it has more various applications [2]. The security robot system is one of the examples. If the security robot system uses a single robot, the system works within the limited functions. However, multi-robot system can prevent many dangers such as gas leaks, theft, fire accident, etc. Also, the multi-robot system is efficient when they are installed against the invaders. The robots can be grouped to surround the intruders. In case of the multi-robot system, the localization problem becomes more important. If each robot does not know its own position and other robot's local information, the robots can collide and their duties become tough to complete. Also, the multi-robot localization has another problem, i.e., each robot should know others' location in real time [3].
The formation matters in the multi-robot system in order to accomplish their goal. In every situation, each single robot has its own mission which finally becomes the multi-robot system's ultimate goal. However, the odometry sensor has some critical issues caused by an error accumulation, wheel's slip, kidnap, etc. [4].
There have been numerous approaches to single robot localization. Most studies to solve the localization problem utilize the proprioceptive sensors such as encoders in the wheel and exteroceptive sensors such as beacons. However, the multi-robot localization researches are not relatively common. As a simple approach, N-robots localization using N times independent position estimation is considered as a multi-robot localization method. As the advantages of using multi-robot system recently attract many researchers, the localization for multi-robot system has been studied actively. The multi-robot localization using relative observations was proposed by Martinelli [5]. The relative observation is made with relative bearing, distance and orientation. Also, Roumeliotis [6] proposed a distributed multi-robot localization. The distributed localization method uses multiple Kalman filters and each Kalman filter operates on each separate robot. Burgard [7] proposed collaborative multi-robot exploration which uses grid map to probe in unknown environments. Karazume [8] also proposed the cooperative positioning system principle. In this principle, one robot stays while the others are moving, and the moving Iterative Solution of Relative Localization for Cooperative Multi-robot Using IEKF robots' locations are calculated on the basis of the stationary robot's position.
We propose the localization of multi-robot system using the relative position in this paper. Each robot's location which is gained from the odometry sensor is used to obtain the relative position. In order to compensate the errors of odometry sensor, we use IR sensor as measurement values, then we apply the iterative extended Kalman filter to this process to track the accurate paths of multi-robot.
This paper is organized as follows. In section 2, we introduce the system modeling for mobile multi-robot. The multi-robot localization algorithm which uses the relative position and the iterative extended Kalman filter are described in section 3, and the simulation results show the improved localization performance of the proposed algorithm in section 4. Conclusions are drawn in section 5.

System Modeling of Multi-robot
In this section, we introduce a kinematic model of a single robot using odometry sensor and relative position among multi-robot.

Kinematic Model of a Mobile Robot
where X , Y and θ are the x, y position and the orientation of a robot using odometry in global coordinate, respectively. s T is the discrete sampling time, r is the wheel radius, b is the distance between wheel centers of the vehicle. ε is a Gaussian white noise.

Relative Position
In the multi-robot system, the local positioning system is required in order to prevent collision and to find the right path. Also, the formation can be performed from the local positioning results. The relative position is one of the famous local positioning skills. Therefore, the relative position is most frequently used as a multi-robot localization technique. However, there are various ways to obtain the relative position.
The relative position configuration is shown in figure 2 and table 1. R and each corresponding 2 R , 3 R and 4 R , respectively. In this configuration, the relative position consists of the distance and angles, and the robot 0 R is considered as a center robot. Also, the angle is defined from a base line which is 0 1 We stipulate a relative position for a set of the mobile robot which this paper covers. First, we assume the following states: 1) A set of independent robots move in same altitude. The motion of each robot is described by its own odometry sensor. These sensors observe the self-motion of the robot; 2) All robots are equipped with communication unit in order to exchange its own position and orientation within the group; 3) The master robot carries exteroceptive sensor which measures respective distant and bearing of satellite robots.   When a master robot and two satellite robots reach the sensible area, the relative position among the three robots can be described as following [9] ( ) where ϕ is the angle between the relative axis and the global axis, ( )

Iterative EKF Algorithm
In this section, we discuss the iterative EKF which improves the performance of the multi-robot localization system. The iterative EKF has the iterative measurement update process which differs from the normal EKF. The iterative measurement update process provides fast convergence rate by the linearization of measurement value iteratively. Therefore, the iterative EKF has the same time update process as the normal one. The update process of the proposed algorithm is shown below, 1) Time Update (Prediction)

Simulations
To verify the effectiveness of proposed position estimation algorithm, a simulation of the multi-robot localization system is implemented. In this simulation, a master robot and two satellite robots compose the system. The master robot contains a communication host to exchange position information and an IR sensor to measure distance to others. The others are slaves which contain only IR transmitter as in [10]. Figure 3 shows a simulation result of tracking path. In figure 3, two satellite robots move forward the master robot on collision free path which is represented as the dotted line and set a formation. The dashed line means a tracking result with odometry sensor only and the solid line represents the compensation result. The satellite robots can move toward the precise position of the master robot without a collision through our proposed algorithm based on IEKF even if the master robot is kidnapped. Figure 4 is a comparison of errors between dead-reckoning method and the proposed algorithm. The dotted line is an error of dead-reckoning, and the solid line represents an error of the proposed algorithm. The coordinate x and y are distinguished by adding point marks. Through figures 3 and 4, the performance of the proposed algorithm is much better than dead-reckoning method.

Conclusions
The localization problem becomes more significant issue in the multi-robot system. To reduce the influence of kidnap problem, we proposed a compensation method with a relative position model which is applicable for multi-robot system by applying the iterative extended-Kalman filter. With this algorithm, we improved the performance by reducing the tracking error. Also, our proposed algorithm overcame the issue of recovery from kidnap problem by using the computation of the current position adaptively. Through some simulations, it is demonstrated that the proposed algorithm can reduce the influence of kidnap problem and improve the tracking accuracy of multi-robot system.