Formation control of nonholonomic mobile robots using implicit polynomials and elliptic Fourier descriptors

Abstract

This paper presents a novel method for the formation control of a group of nonholonomic mobile robots using implicit and parametric descriptions of the desired formation shape. The formation control strategy employs implicit polynomial (IP) representations to generate potential fields for achieving the desired formation and the elliptical Fourier descriptors (EFD) to maintain the formation once achieved. Coordination of the robots is modeled by linear springs between each robot and its two nearest neighbors. Advantages of this new method are increased flexibility in the formation shape, scalability to different swarm sizes and easy implementation. The shape formation control is first developed for point particle robots and then extended to nonholonomic mobile robots. Several simulations with robot groups of different sizes are presented to validate our proposed approach.