Abstractions and controllers for groups of robots in environments with obstacles

We address the problem of controlling a formation of robots in a cluttered environment. Instead of explicitly controlling the relative positions between the robots and the environment, we construct a lower-dimensional abstraction of the group that establishes a boundary for the group. We then synthesize feedback controllers that allow the abstracted group to navigate a two-dimensional environment to a desired goal position, while automatically adapting the shape of the boundary as well as the position and orientation of the group to avoid collisions between the virtual boundary and the environment. In contrast to previous approaches, we address the planning and control problems concurrently and are naturally able to establish bounds on the positions of the robots through the abstraction. The complexity of the method is independent of the number of robots which promises scalability to large teams.