3D Robots Formation cooperative Control Using EFDs

We study in this work the formation cooperative control of 3D holonomic robots group utilizing parametric and implicit properties of the desired 3D planar curve (pattern shape). This latter is considered as a closed contour and generated based on Elliptical Fourier Descriptors (EFDs). The robots control consists of two stages. Firstly, robots move towards the desired closed contour using its Implicit Polynomial function (IP). The IP is deduced from the EFDs and considered as a potential function. The realized formation shape is considered as a virtual Structure modeled by EFDs, where a desired relative position is assigned to each robot with respect to the desired contour frame. The contour center is considered as the virtual leader that has a reference path along to a predefined target. Secondly, a controller is designed to allow robots tracking their reference path and eventually the time-varying desired configuration. The robots coordinate each to other by introducing virtual forces (linear springs) exercised from each robot to its nearest neighbors. The proposed approach is validated in simulation using different robots group sizes showing its feasibility and effectiveness.