Boundary following by robot formations without GPS

We design sensing algorithms and a control law for a group of mobile robots to follow a boundary curve without utilizing a Global Positioning System (GPS). The sensing algorithms allow each robot to estimate the shape and the orientation of the entire formation from readings of range sensors and a speedometer. The usage of GPS is avoided because each robot is able to estimate the relative position of the entire formation with respect to the boundary curve. Based on these estimates, we present a control law that allows the robot formation to achieve desired non-singular shape while following the boundary curve. We control the distance between the center of mass of the formation and the boundary curve so that it converges to desired value. Our control law also guarantees that there will be no collision between any pair of robots and no collision between any robot and the boundary curve.