Port-Hamiltonian-Based Geometric Control for Rigid Body Platoons With Mesh Stability Guarantee

Abstract

Rigid body platoons are widely applied in many scenarios, such as planar vehicular platoons, satellite networks, and aerial/underwater navigation formations. Like string stability, mesh stability is adopted in these higher dimensional platoons to capture the non-increasing tracking errors over the networks. In this letter, we extend the traditional vehicular platooning control to higher dimensional rigid body scenarios with mesh stability concerns. The main challenges stem from the inherent underactuation of rigid body dynamics, the nonlinearity introduced by the $SO\textit {(}3\textit {)}$ -based rotations, and the maintenance of mesh stability for all formations. To this end, we first apply the notion of $l_{2}$ weak mesh stability to capture the effect of propagation of errors over the network. Then, by assuming all the followers have access to the leader’s information, we propose a novel and constructive rigid body platooning control method based on the port-Hamiltonian framework, which also guarantees the $l_{2}$ weak mesh stability. This designed controller is further refined for the case when each follower only knows the neighboring information. Finally, the effectiveness of the proposed methods is verified via numerical simulations.