On the Stability of Consensus Control under Rotational Ambiguities

TL;DR

This paper analyzes how rotational ambiguities in local coordinate frames affect the stability of consensus control in multiagent systems, providing stability criteria and margins verified through numerical examples.

Contribution

It offers a comprehensive stability analysis under rotational ambiguities, including criteria and margins, which was not thoroughly addressed before.

Findings

Stability criteria depend on the type of rotation ambiguity.

Explicit stability margins are derived for different rotational scenarios.

Numerical verification confirms the theoretical stability conditions.

Abstract

Consensus control of multiagent systems arises in various robotic applications such as rendezvous and formation control. For example, to compute the control inputs of individual agents, the difference in the positions in aligned coordinate frames i.e., the pairwise displacements are typically measured. However, the local coordinate frames might be subject to rotational ambiguities, such as a rotation or a reflection, particularly if the positions of the agent are not directly observed but reconstructed from e.g. pairwise Euclidean distances. This rotational ambiguity causes stability issues in practice, as agents have rotated perceptions of the environment. In this work, we conduct a thorough analysis of the stability in the presence of rotational ambiguities in several scenarios including e.g., proper and improper rotation, and the homogeneity of rotations. We give stability criteria and stability margin on the rotations, which are numerically verified with two traditional examples of consensus control.