Kinematic and dynamic performances of artificial swarm systems: Aggregation, collision avoidance and compact formation

A novel control method for the artificial swarm system is proposed in this paper. To reflect the biological swarm performance (aggregation), a kinematic model of the artificial swarm system is established by introducing a special potential function. Then, the dynamic model is further obtained to satisfy more accurate dynamic swarm performances - collision avoidance and compact formation. The former can be realized by diffeomorphism transformation approach and a safety zone is guaranteed accordingly. As for the compact formation, we creatively convert it into a constraint-following problem between leader and followers. Based on the dynamic model, a novel control consisting of two parts is designed, including the model-based control and the adaptive robust control. On one hand, the trajectory tracking problem of the artificial swarm system is solved. On the other hand, the uncertainties in the artificial swarm system can be compensated perfectly. The deterministic performance, uniform boundedness and uniform ultimate boundedness, is guaranteed. The effectiveness of the collaborative control is verified by the proof based on Lyapunov approach and simulations of the artificial swarm system.