Hierarchic distributed stabilization of a class of three‐dimensional formations for underactuated agents

Abstract

The paper presents a distributed hierarchic control design solving a formations problem in three dimension. The agents are modelled as thrust-underactuated rigid bodies. The class of formations addressed encompasses path following of closed convex paths with shape, size, orientation, relative displacements and relative agents' on-path angular positions all seen as formation parameters. This problem can be seen as a generalization of circular formation problems which acquired particular attention in the field of multi-agents, and the agents model used is one that usually models certain unmanned aerial vehicles and other autonomous vehicles. The solution relies on reduction-based set stabilization where the problem is broken down into simpler nested sub-problems. The results illustrate how addressing complex control problems using hierarchical set stabilization is natural, simplifies the solution, and provides useful properties. The results are illustrated via simulations.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.