This thesis focuses on localizing and maintaining a robot formation in an unknown environment. Particularly, by combing the local measurements and the communication information from the other robots, each mobile robot is able to construct a map of the whole environment and localize the robot formation in a distributed manner. Furthermore, relying on the distributed map and the available local measurements, each agent can maintain robust geometric constrains with its neighboring agents. We investigate our research problem from the following aspects. First, we deal with the problem of localizing and maintaining a robot formation in an unknown static environment. we design a distributed estimation algorithm, which can be utilized to construct a map of the environment in a distributed fashion, and combine it with distributed control law to solve the formation maintaining issue. Second, we focus on localizing and maintaining a robot formation in an unknown dynamic environment, where the moving targets are assumed to follow periodic trajectories. By utilizing the distributed observer, each agent can estimate the position of other robots and the periodic trajectories of moving targets based only on its own local measurements. Furthermore, we propose an architecture of the local and distributed observer for each agent that allows for robust self-localization and for reaching a consensus global map.