Formation of geometric patterns in multi-robot systems with limited visibility

Multi-robots system has great advantages such as enhancing the system robustness in the situation where one member fall down or lost. They also can manipulate the environment in more efficient way since they distribute work among themselves especially in tasks where it is needed to cover large areas. Formation patterns problem is defined as the coordination between group of robots given their initial distribution to generate and maintain a specific geometric patterns like circle, line, square, etc. The research inspiration for the pattern formation came out from mimicking and observing animals' behaviors like bees, flocks of bird, colonies of ants and school of fish. Patterns formation for a group of robots has a strong dependency on the level of agreement they have about their local coordinates. If there is no agreement between robots on at least on one axis, the pattern formation problem is unsolvable. Many researches tackled the pattern formation problem assuming that the robots have agreement on one common coordinates system. The main models for pattern formation that were found in literature are classified under two categorizes; the first one assumes that the robots have unlimited visibility and can observe all members' positions even if they are far from each other. This assumption becomes unreasonable for large group of robots. The second category assumes that the robots have limited visibility. Under this assumption the robots need to maintain visible to each other all the time. In this work, we will be using the assumption of limited visibility but under the condition that at least one robot will always maintain the visibility with the other robots. The coordinates agreement approach for team of robots with limited visibility is highlighted as an essential step toward pattern formation. Moreover, this work focuses on the coordination between a group of robots to generate specific shape without any explicit communication among them to guarantee a decentralized system. This work proposes a detailed algorithm for circle formation as a simple and symmetric shape. Based on the circle formation algorithm, the circular wedge algorithm is devised which considers the direction of the designated shape and the uniform distribution of its robots.