Leader-follower Consensus of Unicycle-type Vehicles via Smooth Time-invariant Feedback

Abstract

For a system of multiple vehicles with nonholonomic constraints and communicating under a directed spanning-tree graph, we solve the problem of full consensus, that is, convergence to a common unspecified value both in position and orientation. Remarkably, our controller is smooth time-invariant thanks to a polar-coordinates based model. Furthermore, the proposed control is quite simple, as it uses only relative information and achieves a more natural behaviour of the vehicles, making it well suited for practical applications. We establish (almost) global asymptotic convergence to the consensus manifold using the Lyapunov framework and cascaded systems theory.

A δ-Persistently-Exciting Formation Controller for Non-Holonomic Systems Over Directed Graphs

“…We stress that such condition is necessary for consensus and, therefore, cannot be relaxed. In particular it is satisfied in leader-follower configurations [5], [12], [22] in which the graph consists in a spanning tree and cycles are excluded. For these systems, we address the following problem.…”

“…However, in both cases knowledge of the Laplacian is needed. Leader-follower-based schemes are often restricted to graphs that consist in (do not simply contain) a spanning tree [5], [12], [22], [23].…”

Robust leader-follower formation control of autonomous vehicles with unknown leader velocities

“…In this paper we propose a polar-coordinates-based, timeinvariant, formation-tracking controller and a linear and angular velocity observer which relies only on relative measurements. Compared to the literature, we consider the polarcoordinates model used in [16], but we emphasize that [16] is devoted to the formation-consensus problem. We assume the robots advance in a leader-follower configuration, forming a multi-agent system with an underlying directed spanningtree topology.…”

Leader-Follower Consensus of Unicycles With Communication Range Constraints via Smooth Time-Invariant Feedback

“…In this paper we present a distributed controller for full consensus (in position and orientation) of nonholonomic vehicles in a leader-follower configuration, under relative distance constraints. More precisely, the full-consensus algorithm proposed in [14] is extended herein to address, also, the problem of connectivity maintenance. Remarkably, the proposed control law is smooth (in the domain of definition) time-invariant.…”

“…: : Now, while the existence of a directed spanning tree is necessary for consensus, taking this for granted may be conservative in certain applications. In this paper, we develop upon the preliminary results obtained in [14] to design controllers that ensure the following property.…”