Stabilization of Balanced Circular Motion About a Desired Center

In this paper, we study the collective motion of a group of N(⩾ 2) identical agents trying to achieve a circular formation centered at a desired location, which is fixed. A circular formation is characterized by the motion of all agents around the same circle in the same direction. To solve this problem, we propose a planar motion model that incorporates two control inputs. One of the control inputs is chosen independently and the other control input is decided by using the composite Lyapunov function. We show that the desired location of the center of this circular formation, which is fixed, is obtained by directing the centroid of the group of agents to that desired location. This leads to a collective formation of all the agents, known as balanced circular formation. The theoretical findings are supported by simulations.