Leader-Following Formation Tracking of Multiagent Systems Using Adaptive Scaling Mechanism under Spatial Constraints

Multiagent formation tracking tasks in constrained space commonly require the formation to transform its pattern adaptively. Thus, the multiagent systems can effectively avoid spatial constraints and safely pass through the constrained region. Aiming to achieve such control objectives, a formation tracking control strategy based on the leader-following framework is designed in this article. An adaptive formation scaling mechanism called orientational scaling is first designed. A time-varying matrix introduces real-time information about the formation shape and obstacles into the formation tracking controller. With the action of the controller, the formation can perform an orientational scaling action on its pattern according to the constraints of the external space during the tracking of a given trajectory. Besides, a spatial receding control mechanism is also designed to handle possible collisions in scaling transformations in multiagent systems, reducing the collision risk and improving movement efficiency. The stability conditions of the system are given by adopting the Lyapunov stability theory. Finally, the effectiveness of the designed control strategy is illustrated by simulation results.