Swarm Formation Control with Potential Fields Formed by Bivariate Normal Functions

A novel method is presented for swarm formation control with potential fields generated from bivariate normal probability density functions (pdfs) that construct the surface the swarm members move upon controlling the swarm geometry and member spacing as well as manage obstacle avoidance. Limiting functions 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. The presented approach, compared to others, is simple, computationally efficient, and scales well to different swarm sizes and swarm models. The method is applied to a simple vehicle model, and simulation results are presented on a homogeneous swarm of ten robot vehicles for different formations