On Feedback Speed Control for a Planar Tracking

TL;DR

This paper introduces a feedback speed control law for planar agent tracking, ensuring stability and convergence, validated through simulations, experiments, and extended to multi-agent networks.

Contribution

A novel feedback speed control law combined with a constant bearing strategy, with proven stability and scalability for multi-agent formations.

Findings

Control law guarantees asymptotic stability when leader's steering is known.

Follower converges to a periodic orbit if leader's steering is periodic.

Validated through numerical simulations and experiments on mobile robots.

Abstract

This paper investigates a planar tracking problem between a leader and follower agent. We propose a novel feedback speed control law, paired with a constant bearing steering strategy, to maintain an abreast formation between the two agents. We prove that the proposed control yields asymptotic stability of the closed-loop system when the steering of the leader is known. For the case when the leader's steering is unavailable to the follower, we show that the system is still input-to-state stable with respect to the leader's steering viewed as an input. Furthermore, we demonstrate that if the leader's steering is periodic, the follower will asymptotically converge to a periodic orbit with the same period. We validate these results through numerical simulations and experimental implementations on mobile robots. Finally, we demonstrate the scalability of the proposed approach by extending the two-agent control law to an N-agent chain network, illustrating its implications for directional information propagation in biological and engineered flocks.