Robot formation control in nonlinear manifold using Koopman operator theory

TL;DR

This paper develops a Koopman operator-based prediction algorithm for multi-agent formation control on unknown nonlinear manifolds, addressing sensing limitations and validating on robotic experiments.

Contribution

It introduces a novel application of Koopman operator theory to formation control on unknown nonlinear manifolds with limited sensing.

Findings

Effective prediction of leader position on elliptical paraboloid manifold

Successful implementation with two omni-directional robots

Addresses sensing range limitations in formation control

Abstract

Formation control of multi-agent systems has been a prominent research topic, spanning both theoretical and practical domains over the past two decades. Our study delves into the leader-follower framework, addressing two critical, previously overlooked aspects. Firstly, we investigate the impact of an unknown nonlinear manifold, introducing added complexity to the formation control challenge. Secondly, we address the practical constraint of limited follower sensing range, posing difficulties in accurately localizing the leader for followers. Our core objective revolves around employing Koopman operator theory and Extended Dynamic Mode Decomposition to craft a reliable prediction algorithm for the follower robot to anticipate the leader's position effectively. Our experimentation on an elliptical paraboloid manifold, utilizing two omni-directional wheeled robots, validates the prediction algorithm's effectiveness.