Dynamic multi-target fully distributed control for specified-time-area surrounding formation

The objective of this study is to address the surrounding formation problem in MAS (multi-agent systems), which holds significant potential for applications in agricultural herding, fire rescue, and national defense. The primary focus is to develop a control strategy that enables a group of agents to spatially track a target and form a surrounding formation with a predefined radius using distributed methods, followed by the execution of task-specific operations. The research particularly emphasizes the surrounding of dynamic multiple targets, which presents a more realistic and complex challenge due to the evolving configuration of moving targets. This necessitates real-time adjustments to the surrounding radius by the agents based on the target configuration. Additionally, achieving surrounding formation at precise time points is critical for practical implementation. The study aims to propose a fully distributed algorithm capable of dynamically acquiring time-varying surrounding radii and achieving specified-time-area surrounding formation for dynamic multiple targets.

This study first proposed a surrounding formation algorithm based on a center position estimator and a surrounding radius estimator. The center position estimator employed a dynamic average consensus algorithm, enabling each agent to estimate the centroid of all target positions. The surrounding radius estimator utilized a dynamic max-consensus algorithm, allowing each agent to estimate the minimum distance required to surround all targets, which was then incorporated into the corresponding formation vector. The outputs of both estimators served as inputs to the surrounding formation algorithm. By employing a time-domain mapping method, all estimators and controllers were discretized using specific sampling sequences to achieve timed control. Finally, the concept of "holistic planning, segmented control" was introduced, coupling the temporal and spatial dimensions through the Pontryagin’s maximum principle to realize specified-time-area surrounding formation.

The designed center position estimator effectively addresses the conflicts caused by the mutual influence of multiple targets on the formation center, accurately estimating the centroid of the target cluster. The surrounding radius estimator allows each agent to obtain the surrounding radius in a fully distributed manner, with the radius dynamically adjusted based on the target configuration. The controller drives the agents to their designated positions for the surrounding formation, achieving the desired formation. Both the estimators and the controller are designed to converge at a specified time, with the convergence speed dependent on the predefined time, demonstrating significant flexibility. Additionally, the steady-state error at the specified time is guaranteed to be zero, indicating superior precision compared to most existing methods.

With the continuous advancement of technology, swarm operations have gradually become a crucial aspect of modern warfare. Against this backdrop, this paper addresses the problem of specified-time-area surrounding formation for dynamic multi-targets. A specified-time-area control method based on a center position estimator and a surrounding radius estimator is proposed. The main contributions are as follows:

1. Firstly, a center position estimator is designed based on the dynamic average consensus algorithm, achieving precise estimation of the centroid of multiple dynamic targets and resolving conflicts caused by the mutual influence of different targets on the center position

2. Secondly, a surrounding radius estimator is designed based on the dynamic max-consensus algorithm, enabling real-time updates of the surrounding radius to ensure that no target escapes before the formation is completed. Additionally, the formation vector containing the optimal surrounding radius is estimated by each agent in a fully distributed manner, realizing truly autonomous surrounding formation.

3. The concept of "holistic planning, segmented control" is introduced, and the two estimators along with the controller are designed. By coupling spatial and temporal information based on the Pontryagin’s maximum principle, timed and positioned surrounding formation is guaranteed to be achieved at any pre-specified time.