Distributed scaling control of rigid formations

TL;DR

This paper introduces a method to control the steady-state motion and scaling of rigid formations in multi-agent systems by leveraging biased range measurements and distributed parameters, combining graph and bearing rigidity theories.

Contribution

It presents a novel approach to manipulate formation motion and scaling using distributed parameters based on rigidity theories, extending existing formation control methods.

Findings

The method enables controlled translation, rotation, and scaling of formations.

Stability of the modified system is analytically validated.

Simulations confirm the effectiveness of the proposed control strategy.

Abstract

Recently it has been reported that biased range-measurements among neighboring agents in the gradient distance-based formation control can lead to predictable collective motion. In this paper we take advantage of this effect and by introducing distributed parameters to the prescribed inter-distances we are able to manipulate the steady-state motion of the formation. This manipulation is in the form of inducing simultaneously the combination of constant translational and angular velocities and a controlled scaling of the rigid formation. While the computation of the distributed parameters for the translational and angular velocities is based on the well-known graph rigidity theory, the parameters responsible for the scaling are based on some recent findings in bearing rigidity theory. We carry out the stability analysis of the modified gradient system and simulations in order to validate the main result.