Node-wise monotone barrier coupling law for formation control

TL;DR

This paper introduces a node-wise monotone barrier coupling law inspired by neural central pattern generators, enabling flexible pattern assignment, rapid switching, and full control of formation behaviors through state space partitioning.

Contribution

It presents a novel coupling law that mimics neural properties, allowing multiple pattern control and quick transitions in formation systems.

Findings

Allows multiple central patterns on the circle.

Enables rapid switching between patterns.

Achieves full control via state space partitioning.

Abstract

We study a node-wise monotone barrier coupling law, motivated by the synaptic coupling of neural central pattern generators. It is illustrated that this coupling imitates the desirable properties of neural central pattern generators. In particular, the coupling law 1) allows us to assign multiple central patterns on the circle and 2) allows for rapid switching between different patterns via simple `kicks'. In the end, we achieve full control by partitioning the state space by utilizing a barrier effect and assigning a unique steady-state behavior to each element of the resulting partition. We analyze the global behavior and study the viability of the design.