Scalable Distributed Nonlinear Control Under Flatness-Preserving Coupling

TL;DR

This paper presents a scalable distributed control framework for nonlinear, differentially flat subsystems with a specific class of dynamic couplings that preserve flatness, enabling local control actions and validated on coupled quadrotors.

Contribution

It introduces a class of flatness-preserving couplings for nonlinear systems and constructs a distributed control scheme leveraging the sparsity of the flatness diffeomorphism.

Findings

Distributed controller achieves accurate trajectory tracking.

Flatness is preserved under certain dynamic couplings.

Framework validated on simulated coupled quadrotors.

Abstract

We study distributed control for a network of nonlinear, differentially flat subsystems subject to dynamic coupling. Although differential flatness simplifies planning and control for isolated subsystems, the presence of coupling can destroy this property for the overall joint system. Focusing on subsystems in pure-feedback form, we identify a class of compatible lower-triangular dynamic couplings that preserve flatness and guarantee that the flat outputs of the subsystems remain the flat outputs of the coupled system. Further, we show that the joint flatness diffeomorphism can be constructed from those of the individual subsystems and, crucially, its sparsity structure reflects that of the coupling. Exploiting this structure, we synthesize a distributed tracking controller that computes control actions from local information only, thereby ensuring scalability. We validate our proposed framework on a simulated example of planar quadrotors dynamically coupled via aerodynamic downwash, and show that the distributed controller achieves accurate trajectory tracking.