This paper presents a trajectory generation logic for a swarm of unmanned aerial vehicles which uses topological distances instead of metric values. Biologically inspired, this method evades exploiting distance measurements in the absence of such capabilities, as it happens in swarming birds. This newly developed trajectory generation logic provides a stable swarming logic which resembles a large aggregation of birds. The hypothesis of this work is that without depth perception, swarming birds rely primarily on their perception of other birds to estimate proximity and adjust repulsive and attractive forces in real-time. From previous biological behavior studies, it is known that a homogeneous and orderly aggregation is exhibited by swarming birds locating themselves side by side rather than in front or behind each other. This behavior, which is based on the relative spatial proximity perception to their nearest neighbors in the flock, allows birds to converge into a highly cohesive and coordinated formation without explicit control of inter-agent distances. Inspired by this biological pattern, a trajectory generation logic is designed and tested in controlling a multi-agent unmanned aerial systems without the use of inter-distances. A six degrees of freedom nonlinear dynamic model for an unmanned aircraft is used for simulation purposes. Each vehicle is provided with a decentralized agent-based robust nonlinear model predictive controller and a set of nonlinear guidance laws for trajectory tracking. The formulation of the proposed trajectory generation, as well as the selected aircraft control, constitute a truly decentralized technique, that allows for an unlimited number of agents within the swarm, as no centralized computations are made.