On the observability of relative positions in left-invariant multi-agent control systems and its application to formation control

TL;DR

This paper investigates the observability of relative positions in multi-agent systems modeled as left-invariant control systems, focusing on formation control scenarios where agents only have access to inter-agent distances.

Contribution

It introduces a framework using left-invariant control systems to analyze the observability of relative positions when only distance measurements are available.

Findings

Established conditions for observability in left-invariant multi-agent systems.

Applied the framework to distance-based formation control scenarios.

Provided insights into reconstructing relative positions without direct access.

Abstract

We consider the localization problem between agents while they run a formation control algorithm. These algorithms typically demand from the agents the information about their relative positions with respect to their neighbors. We assume that this information is not available. Therefore, the agents need to solve the observability problem of reconstructing their relative positions based on other measurements between them. We first model the relative kinematics between the agents as a left-invariant control system so that we can exploit its appealing properties to solve the observability problem. Then, as a particular application, we will focus on agents running a distance-based control algorithm where their relative positions are not accessible but the distances between them are.