Heterogeneous Swarm Formation Control Using Bivariate Normal Functions to Generate Potential Fields

A novel method is presented for dynamic heterogeneous swarm formation control with potential fields generated from bivariate normal probability density functions (pdfs) used to construct the surface which swarm members move on, controlling swarm geometry, individual member spacing, and managing obstacle avoidance. Limiting functions are defined to provide tighter swarm control by modifying and adjusting a set of control variables forcing the swarm to behave according to set constraints. Bivariate normal functions and limiting functions are combined to guarantee obstacle avoidance and control swarm member orientation and swarm movement as a whole. This approach compared to others, is simple, computationally efficient, scales well to different swarm sizes, to heterogeneous systems, and to both centralized and decentralized swarm models. The method is applied to a simple vehicle model and simulation results are presented for a heterogeneous swarm of ten robot vehicles following line and ellipse formations