Generalized cyclic algorithms for formation acquisition and control

TL;DR

This paper introduces a novel distributed nonlinear control method for formation acquisition and maintenance, leveraging contraction theory and cyclic topologies to ensure global exponential convergence using only local information.

Contribution

It proposes new control laws based on contraction theory and convergence primitives for formation control, applicable to complex structures with local communication.

Findings

Achieves global exponential convergence to symmetric formations.

Extends to complex formations using linear combinations of control primitives.

Uses only local information and communication for control laws.

Abstract

This paper presents a new approach to distributed nonlinear control for formation acquisition and maintenance, inspired by recent results on cyclic topologies and based on tools from contraction theory. First, simple nonlinear control laws are derived to achieve global exponential convergence to basic symmetric formations. Next, convergence to more complex structures is obtained using control laws based on the idea of convergence primitives, linear combinations of basic control elements. All control laws use only local information and communication to achieve a desired global behavior.