Spherical formation control of mobile target by multi-agent systems with collision avoidance: A limit-cycle-based design approach

Abstract

This paper focuses on the control of spherical formation for multi-agent systems with double-integrator dynamics in three-dimensional space. To achieve the desired formation pattern on a spherical surface, N agents must be distributed evenly around a target. Based on the information gathered about the target and its immediate neighbors, all agents can either remain stationary or rotate around the target at the same velocity on a spherical surface while the target moves in three-dimensional space. A decoupled control method with limit cycle oscillator characteristics is explored to achieve the desired formation geometric pattern. Accordingly, three subproblems are proposed to achieve the spherical formation more effectively. The first subproblem, target-spherical-surface, requires the agents to converge on a specified spherical surface with the target as its center. The second subproblem, target-circling, requires the agents to follow three prescribed orthometric circular orbits on the spherical surface to avoid collisions while moving. The final subproblem is distributed-adjustment, which involves agents to maintaining a prescribed angular distance from their immediate neighbors while remaining relatively stationary or rotating around the target. By addressing the first two sub-problems simultaneously, the agents can be guided to the desired position. The properties of the limit-cycle-based spherical formation controller are analyzed theoretically, and its effectiveness is demonstrated through numerical simulations.