Flocking for Multiple Elliptical Agents with Limited Communication Ranges

In existing flocking and coordination control systems of multiple agents, an agent is considered as a single point or a circular disk. For agents with a long and narrow shape, fitting them to circular disks results in a problem with the large conservative area. This paper presents a design of distributed controllers for flocking of N mobile agents with an elliptical shape and with limited communication ranges. A separation condition for elliptical agents is first derived. Smooth or p-times differentiable step functions are then introduced. These functions and the separation condition between the elliptical agents are embedded in novel potential functions to design control algorithms for flocking. The controllers guarantee 1) no switchings in the controllers despite the agents’ limited communication ranges; 2) no collisions between any agents; 3) asymptotic convergence of each agent’s generalized velocity to a desired velocity; and 4) boundedness of the flock size, which is defined as the sum of all generalized distances between the agents, by a constant.