# A Multi-Robot Formation Platform based on an Indoor Global Positioning System
## 1 Introduction  
Multi-robot formation control is one of the most important areas of research in Multi-Robot Systems [1, 2], due to general practical applications such as joint handing [3], cooperative rescue [4], group stalking, and exploration [5]. The goal of multi-robot formation control is to maintain a specified geometrical shape of a group of robots by adjusting the pose (positions and orientations) of robots [6], which generally follows the process of forming, maintaining, and switching of formation. The current research on the multi-robot formation mainly focuses on formation control theory [7, 8, 9], while some research lacks physical experimental realization to validate their theories and algorithms for having no available experimental testbed, especially a general and low-cost indoor multi-robot formation experimental platform. The positioning system is the basis of a multi-robot formation experimental platform, which determines the position and orientation of robots in real time. Currently, the indoor positioning systems used in multi-robot formation can be roughly classified into two main categories [10]--relative and absolute positioning systems [11]. For the relative positioning systems, the robots' pose is obtained from onboard sensors or other robots. For example, the pose information has been obtained by theencoders equipped with the robots [12], or a laser scanner mounted on the robot has been used to estimate the relative position of other robots [13]. However, considering formation scalability, the overall cost of the system will increase with the addition of robot number, as new cameras or laser range finders would be required. In addition, relative positioning based on onboard sensors will produce an accumulative error, which will cause distortion of the formation. In the absolute positioning systems, the pose of a robot is determined via measuring and recognizing the landmarks in indoor environments. In some research [6; 14; 15], cameras were mounted on the ceiling or overhead place to estimate the position and orientation of robots via measuring the positions of robots' marks. For example, [PERSON] [16] designed a positioning system with a single camera on the ceiling and each robot was distinguished thanks to three high-brightness LEDs. However, since the camera is susceptible to light and dynamic environment, the image processing including landmark recognition and feature extraction is not robust enough for positioning. To improve the precision of positioning, more cameras need to be equipped. In view of this, [PERSON] [17] proposed a vision system including 24 OptiTrack cameras to obtain each robot's position information, but this will also significantly increase the overall cost. To reduce the cost, choosing some economical positioning technologies to replace vision systems is urgently required. In addition, technologies such as Radio-Frequency Identification (RFID) [18], Ultra-Wideband (UWB) [19], and Bluetooth [10] are not suitable to be employed for multi-robot formation due to low precision. Recently, the ultrasonic system has been verified that it can reach a better trade-off between cost and precision, which absorbs the sight of many researchers and practitioners [20; 21]. Some formation experiments hve been implemented in the existing robot platforms, such as Koala from K-team [22] or TurtleBot3 from TurtleBot [23], which are often relatively complex and expensive. On the contrary, some commercially available off-the-shelf solutions, like the Create2 robot from iRobot [24] and the LEGO robot used in Reference [17], often lack onboard processing and networking [25]. In more recent work, Kilobots are designed for testing collective algorithms on large groups [26], which mainly serviced for swarm robots. Few of the existing platforms are uniquely designed for multi-robot formation control. For this reason, it is reasonable to design and manufacture our custom robot.