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.