Taming mismatches in inter-agent distances for the formation-motion control of second-order agents

TL;DR

This paper investigates how distance mismatches affect formation control of second-order agents, revealing undesired behaviors and proposing estimators to eliminate them, while also using mismatches for motion control.

Contribution

It introduces a method combining standard control with distributed estimators to mitigate mismatches and employs mismatches as design parameters for formation motion control.

Findings

Mismatches cause shape distortion and steady-state motion.

Distributed estimators can eliminate undesired behaviors.

Mismatches can be used to control formation translation and rotation.

Abstract

This paper presents the analysis on the influence of distance mismatches on the standard gradient-based rigid formation control for second-order agents. It is shown that, similar to the first-order case as recently discussed in the literature, these mismatches introduce two undesired group behaviors: a distorted final shape and a steady-state motion of the group formation. We show that such undesired behaviors can be eliminated by combining the standard formation control law with distributed estimators. Finally, we show how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation.