This paper presents an analytical study of swarm motion in static environments, in which, motion of the swarm is modeled as a quasi static model. Motion of each member is being affected by interactive forces and environmental effects. Interactive effects on each member could be attractive or repulsive due to being far from or close to other members respectively. Environmental effects also could be attractive or repulsive or a combination of both. The method is based on Lyapunov analysis. Two objectives are investigated through the analysis; one is to preserve the unity of swarm i.e. not losing any member through motion, and the other is to move toward attractant areas and away from repellant environmental zones. It is also considered that the visibility of members to each other and to environmental objects will fade due to the increasing distance; which is the most important characteristic of this work. Simulations of swarm motion show behaviors similar to natural swarms which verifies the vision model considered in this paper.
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