On Consensus Algorithms for Double-Integrator Dynamics

TLDR

This note considers consensus algorithms for double‑integrator dynamics. We propose and analyze consensus algorithms for double‑integrator dynamics in four scenarios: bounded control input, absence of relative velocity measurements, availability of a group reference velocity to all agents, and bounded control input with group reference state available to only a subset of the team. We show that asymptotic consensus is achieved in the first two scenarios when the undirected interaction graph is connected; in the third scenario when the directed graph has a spanning tree and the velocity‑matching gain exceeds a threshold; and in the fourth scenario if and only if the group reference state propagates directly or indirectly to all vehicles.

Abstract

This note considers consensus algorithms for double-integrator dynamics. We propose and analyze consensus algorithms for double-integrator dynamics in four cases: 1) with a bounded control input, 2) without relative velocity measurements, 3) with a group reference velocity available to each team member, and 4) with a bounded control input when a group reference state is available to only a subset of the team. We show that consensus is reached asymptotically for the first two cases if the undirected interaction graph is connected. We further show that consensus is reached asymptotically for the third case if the directed interaction graph has a directed spanning tree and the gain for velocity matching with the group reference velocity is above a certain bound. We also show that consensus is reached asymptotically for the fourth case if and only if the group reference state flows directly or indirectly to all of the vehicles in the team.