On Feedback Speed Control for a Planar Tracking

A team of researchers has developed a new control algorithm that solves a fundamental problem in multi-agent robotics: how to make a follower agent precisely track a leader. In their arXiv paper 'On Feedback Speed Control for a Planar Tracking,' Xincheng Li, Tengyue Liu, and Udit Halder present a novel feedback speed control law. This law is designed to work alongside a constant bearing steering strategy, allowing two agents to maintain a stable, abreast formation. The team provides rigorous mathematical proofs, showing the closed-loop system achieves asymptotic stability when the leader's steering is known. More impressively, they prove the system remains input-to-state stable even when the follower cannot access the leader's steering commands, treating the unknown steering as a bounded disturbance.

The research was validated through both numerical simulations and physical experiments on mobile robots, confirming the theoretical results. A significant extension of the work demonstrates the control law's scalability. The authors successfully applied the two-agent formulation to an N-agent chain network, creating a cascading control structure. This scalability is crucial for applications in engineered systems, such as coordinating drone swarms or autonomous vehicle platoons, and for modeling directional information propagation observed in biological flocks like birds or fish. The work bridges control theory and practical robotics, offering a provably stable solution for formation control that is robust to real-world information constraints.