A formation control approach to adaptation of contour-shaped robotic formations

Much research has been done in the area of robot formations. Most of them consider rigid formations where the robot aggregate forms a rigid virtual body. Relatively little has been done on deformable formations composed of rigid links as well as flexible ones. In this paper, we will examine and design controllers for a special type of robotic formations, i.e., those resembling contours. These type of formations have numerous applications in the underwater world, including adaptation to plume boundaries and isoclines of concentration fields, flock shepherding, and shape formation. We adopt general curve evolution theory as a suitable abstraction to describe the motion of such formations. We will first design controllers using simple geometrical reasoning, based on basic requirements on connectivity and mission accomplishment, and will later show that they lead to the same controller structure.