Stable Schooling Formations Emerge from the Combined Effect of the Active Control and Passive Self-Organization

Abstract

This work presents a numerical study of the collective motion of two freely-swimming swimmers by a hybrid method of the deep reinforcement learning method (DRL) and the immersed boundary-lattice Boltzmann method (IB-LBM). An active control policy is developed by training a fish-like swimmer to swim at an average speed of 0.4 L/T and an average orientation angle of 0∘. After training, the swimmer is able to restore the desired swimming speed and orientation from moderate external perturbation. Then the control policy is adopted by two identical swimmers in the collective swimming. Stable side-by-side, in-line and staggered formations are achieved according to the initial positions. The stable side-by-side swimming area of the follower is concentrated to a small area left or right to the leader with an average distance of 1.35 L. The stable in-line area is concentrated to a small area about 0.25 L behind the leader. A detailed analysis shows that both the active control and passive self-organization play an important role in the emergence of the stable schooling formations, while the active control works for maintaining the speed and orientation in case the swimmers collide or depart from each other and the passive self-organization works for emerging a stable schooling configuration. The result supports the Lighthill conjecture and also highlights the importance of the active control.

Keywords

• immersed boundary-lattice Boltzmann method
• deep reinforcement learning
• fish schooling
• collective motion
• side-by-side swimming
• in-line swimming