Fully Distributed Flocking with a Moving Leader for Lagrange Networks with Parametric Uncertainties

TL;DR

This paper develops fully distributed control algorithms for flocking in Lagrange systems with a moving leader, handling parametric uncertainties and ensuring connectivity, collision avoidance, and velocity matching.

Contribution

It introduces novel distributed adaptive control algorithms for flocking with a moving leader under parametric uncertainties, extending to fully distributed gain adaptation laws.

Findings

Achieved flocking with a moving leader under parametric uncertainties.

Ensured connectivity and collision avoidance with local information.

Validated algorithms through numerical simulations.

Abstract

This paper addresses the leader-follower flocking problem with a moving leader for networked Lagrange systems with parametric uncertainties under a proximity graph. Here a group of followers move cohesively with the moving leader to maintain connectivity and avoid collisions for all time and also eventually achieve velocity matching. In the proximity graph, the neighbor relationship is defined according to the relative distance between each pair of agents. Each follower is able to obtain information from only the neighbors in its proximity, involving only local interaction. We consider two cases: i) the leader moves with a constant velocity, and ii) the leader moves with a varying velocity. In the first case, a distributed continuous adaptive control algorithm accounting for unknown parameters is proposed in combination with a distributed continuous estimator for each follower. In the second case, a distributed discontinuous adaptive control algorithm and estimator are proposed. Then the algorithm is extended to be fully distributed with the introduction of gain adaptation laws. In all proposed algorithms, only one-hop neighbors' information (e.g., the relative position and velocity measurements between the neighbors and the absolute position and velocity measurements) is required, and flocking is achieved as long as the connectivity and collision avoidance are ensured at the initial time and the control gains are designed properly. Numerical simulations are presented to illustrate the theoretical results.