Optic Flow Embodiments of Cucker-Smale Flocking Model

This paper addresses the need for theoretic constructions enabling fast, lightweight al- gorithms that provide vision-guided swarming on maneuverable air vehicles having limited computational tools and no explicit communication network or position measurement. This paperdemonstrates that flockingalgorithmsdependentonpositionandvelocitycan be imple- mented by agents that cannot measure positions and (relative) velocities of their neighbors, but they use optic flow sensors as observed in many flying insects. The study begins by developing a frameworkfor sensing optic flowin a multi-agent environment. It then integrates anidealized inter-agent velocity and distance structure describing distributed feedback under perfect informationwithopticflowperceptiontocreateananalogousvisually-guidedfeedbackpath. We use the seminal Cucker-Smale flocking model as an example to develop a vision-guided update law with rigorous asymptotic convergence guarantees, including under ignorance of agent size. No explicit position reference or communication network is required. Numerical simulations are presented to illustrate the resulting outcomes and performance properties such as nonlinearity and performance under noise. An Appendix illustrates the generality of the optical implementationpathon Vicsek, anotherclassical method.