Distributed formation for robotic swarms considering their crossing motion

This paper discusses formation problem for robotic swarms when multiple robotic swarms cross one another's path. To realize the crossing motion, collision avoidance between agents is an important issue, with the potential to cause a general mix-up of formation during the crossing motion. To realize an orderly and well-organized crossing motion with the least mix-up, as well as collision avoidance, we propose a distributed controller. This well-organized crossing motion can realize visually appealing and highly entertaining robotic mass games. This paper proposes a distributed controller using the gradient of the cost functions about the formation maintenance, collision avoidance, and tracking to the desired trajectory. We then prove that we can achieve a well-organized crossing motion of multiple robotic swarms under several assumptions. Finally, experimental and numerical simulations are carried out to investigate whether the well-organized crossing motion can be achieved.