2-D Directed Formation Control Based on Bipolar Coordinates

TL;DR

This paper introduces a decentralized 2-D formation control method using bipolar coordinates for directed graphs, achieving robust, almost globally convergent shape formation with practical implementation considerations.

Contribution

It presents a novel bipolar coordinate-based control scheme for directed graphs, enabling robust, scalable, and practically implementable formation control with maneuvering and scaling capabilities.

Findings

Achieves almost global convergence to desired formation

Handles formation maneuvering, scaling, and orientation simultaneously

Demonstrates effectiveness through simulation studies

Abstract

This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, a formation maneuvering simulation study verifies the proposed approach.