On Feedback Speed Control for a Planar Tracking

2026-04-10

AI Summary

This study addresses the problem of side-by-side formation tracking for multi-agent systems in planar space by proposing a novel control law that integrates feedback-based velocity regulation with a constant-bearing guidance strategy. For the first time, this approach unifies these two mechanisms to guarantee asymptotic stability and input-to-state stability (ISS) regardless of whether the leader’s turning trajectory is known or unknown. Moreover, it reveals that under periodic leader maneuvers, followers converge to periodic orbits. The theoretical analysis leverages nonlinear control theory within an ISS framework and is substantiated through numerical simulations and experiments with mobile robots. The method is further extended to an N-agent chain topology, demonstrating its potential for efficiently propagating directional information in both biological and engineered swarms.

Technology Category

• Intelligent Robots: Multi-Robot Systems
• Multiagent Systems: Applications
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systems
• Security and Privacy: Tracking, profiling, and countermeasures against them
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems

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.

Problem

• planar tracking
• leader-follower
• abreast formation
• feedback speed control
• multi-agent systems

Innovation

• feedback speed control
• constant bearing strategy
• input-to-state stability
• asymptotic convergence
• multi-agent scalability