  Formation control with the flocking approach is an efficient method that can
reach the formation without determining the agent's position. This paper
focuses on reaching the circular formation around the leader or target with a
specific geometric pattern for the second-order multi-agent system. This means
that the polygon formation is formed with arbitrary initial conditions. To
create the circular formation, two potential function terms have been used for
agent-agent and leader-agent interaction. In our approach, if some faults occur
during the circular formation and some agents fail, the regular polygon
formation will still form with fewer agents. Obstacle avoidance for a
single-circle formation and collision-free motion is guaranteed. A circular
formation with size scaling is proposed to better maneuver and pass through
obstacles. Also, several circles with the desired radius can be reached with
changes in the agent-leader potential function. In this work, optimization
algorithms with different scenarios are compared to calculate the parameters of
our algorithm.
