Social Value Orientation and Steady-State Configurations in Swarms with Coordinate-Coupling Matrices

Abstract

In this paper, we propose a continuous-time kinematic swarm model inspired by the framework presented in A Generalized Gazi-Passino Model with Coordinate-Coupling Matrices for Swarm Formation with Rotation Behavior. Specifically, we introduce a static parameter, referred to as the Social Value Orientation Parameter (SVOP), which acts as a weight on two coordinate-coupling matrices governing both attractive and repulsive interactions among agents. Our focus is on simulation-based analysis of the swarm dynamics under this new parameterization. When a large group of agents is divided based on the SVOP, a grid-like steady-state spatial configuration emerges. The simulations reveal previously unobserved spatial patterns, highlighting the role of SVOP in shaping group behavior. Numerical simulations are provided to illustrate these results.