Options
Geometric Second-Order Laplacian Flow for Consensus on Lie Groups
Journal
2022 European Control Conference, ECC 2022
Date Issued
2022-01-01
Author(s)
Seshan, Rama
Banavar, Ravi N.
Mahindrakar, Arun D.
Abstract
In this work, the second-order Laplacian flow in Euclidean space which is a standard algorithm for consensus of double integrator systems is generalized to the abstract setting of Lie groups. For double integrator systems on a Lie group, by using gradients of Polar Morse functions whose critical points form a discrete subgroup, it is proved that consensus is achieved for almost all initial conditions of the agents whose connectivity is described by a nearest neighbor network. In this general framework, it turns out that the standard Euclidean second-order Laplacian flow and the Kuramoto oscillator are special cases in Euclidean space and the unit circle respectively.