Formation flocking control and curl/divergence interpretation in second-order multi-agent networks

This paper studies a class of modified Olfati-Saber flocking control algorithms in the 2nd-order particle multi-agents with single virtual leaders driven autonomously for translational performances and rotational manoeuvrability; curl/divergence aspects of the individual/average trajectories are scrutinised and related to time response features. More specifically, the modified algorithms are embedded with time-varying weighting matrices for achieving multi-agent formation flocking with translational performances (in terms of formation scaling, sub-dimensional confinement and trajectory expansive/conservative/dissipative-ness) and rotational maneuverabilities (in terms of trajectory rotation and curving swiftness). Flocking existence is validated analytically and individual/average trajectory formulas are derived. Simulations in 2D and 3D cases are sketched to show efficacy and significance of the study.