Distributed rotational and translational maneuvering of rigid formations and their applications

TL;DR

This paper introduces a novel distributed control method for rigid formations that leverages measurement mismatches as design parameters to enable collective translation and rotation without shape distortion, supported by theoretical proofs and robot experiments.

Contribution

It proposes a new formation control approach that uses mismatches as parameters to achieve simultaneous shape preservation and collective motion.

Findings

Achieves constant translation and rotation of formations

Guarantees asymptotic shape preservation during motion

Validated through mobile robot experiments

Abstract

Recently it has been reported that range-measurement inconsistency, or equivalently mismatches in prescribed inter-agent distances, may prevent the popular gradient controllers from guiding rigid formations of mobile agents to converge to their desired shape, and even worse from standing still at any location. In this paper, instead of treating mismatches as the source of ill performance, we take them as design parameters and show that by introducing such a pair of parameters per distance constraint, distributed controller achieving simultaneously both formation and motion control can be designed that not only encompasses the popular gradient control, but more importantly allows us to achieve constant collective translation, rotation or their combination while guaranteeing asymptotically no distortion in the formation shape occurs. Such motion control results are then applied to (a) the alignment of formations orientations and (b) enclosing and tracking a moving target. Besides rigorous mathematical proof, experiments using mobile robots are demonstrated to show the satisfying performances of the proposed formation-motion distributed controller.