Formation Control for Fully Actuated Systems: a Quaternion-based Bearing Rigidity Approach

Abstract

This work deals with formations of mobile agents with six independently controllable degrees of freedom able to retrieve relative bearing measurements w.r.t. some neighbors in the group. Exploiting the bearing rigidity framework, two control objectives are here addressed: ( $i$ ) the stabilization of these fully actuated multi-agent systems towards desired configurations, and (i i) their coordinated motion along directions guaranteeing the system shape maintenance. The proposed approach relies on a new formulation of the bearing rigidity theory based on the adoption of the unit quaternion formalism to describe the agents attitude. Through this representation choice, the formation dynamics is linear w.r.t. the input control velocities and the rigidity theory suggests the design of a distributed control scheme for both control goals whose efficacy is confirmed by numerical simulations.